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stat332 | /home/yz979/scratch/chengye/math/data/original_set/statset/images/images/332.png | As shown in the figure, there are two concentric circles. The radius of the larger circle is 3. We randomly scatter 300 sesame seeds in the circular area and record the number of seeds that fall within the smaller circle area (including the boundary). After several trials, it is found that about 100 seeds consistently fall within the smaller circle. Estimate the area of the smaller circle (express the result as an algebraic expression involving π). | 3π | NULL | free_form |
stat333 | /home/yz979/scratch/chengye/math/data/original_set/statset/images/images/333.png | A middle school held a 'Chinese Poetry Contest.' The proportion of students from three grades entering the finals is shown in the figure. What is the central angle of the sector representing the proportion of seventh-grade students? ______°. | 36 | NULL | free_form |
stat334 | /home/yz979/scratch/chengye/math/data/original_set/statset/images/images/334.png | The head of the production department in a company, in order to set a reasonable daily production quota for a product, collected data from 20 workers on the number of parts they produced in one day and created a line chart to visualize it. To ensure that more than half of the workers can achieve the quota while maximizing the amount, what should be the daily production quota per person? | 54 | NULL | free_form |
stat335 | /home/yz979/scratch/chengye/math/data/original_set/statset/images/images/335.png | If the floor shown consists of 15 square tiles, each identical except for color, what is the probability that a freely rolling ball stops on a black tile? | 1/3 | NULL | free_form |
stat336 | /home/yz979/scratch/chengye/math/data/original_set/statset/images/images/336.png | A school conducted a survey as part of the 'Sunshine Sports' activity to find out the favorite sport of 50 students, and created a pie chart as shown. The school has a total of 3200 students. Estimate the number of students in the school who selected badminton as their favorite sport. | 1280 | NULL | free_form |
stat337 | /home/yz979/scratch/chengye/math/data/original_set/statset/images/images/337.png | A school conducted a study to understand the participation of 1200 students in household chores. 40 students were randomly selected, and their weekly household chore hours were surveyed, forming a frequency distribution histogram. Estimate the number of students in the school whose weekly household chore hours are at least 2 hours. | 780 | NULL | free_form |
stat338 | /home/yz979/scratch/chengye/math/data/original_set/statset/images/images/338.png | A landscaping company cultivates 3000 ginkgo trees for sale. It is known that trees with a trunk circumference of no less than 50 cm can be sold. The chart shows the data obtained by randomly selecting 50 ginkgo trees and measuring them. Please estimate the number of ginkgo trees in this batch that meet the sales standard as ______ trees. | 2520 | NULL | free_form |
stat339 | /home/yz979/scratch/chengye/math/data/original_set/statset/images/images/339.png | Refuse sorting refers to the process of classifying waste into several different categories based on its various components, properties, utilization value, and environmental impact, as well as the requirements of different disposal methods. The pie chart shows the waste collection situation in a pilot area of a certain city. It is known that a total of 60 tons of recyclable waste were collected, and the total population of the city is about 10 times that of the pilot area. Estimate the total amount of wet waste that can be collected in the entire city ______ tons. | 870 | NULL | free_form |
stat34 | /home/yz979/scratch/chengye/math/data/original_set/statset/images/images/34.png | As shown in the figure, inside a square with a side length of 2, there is a smaller square with a side length of 1. A frog jumps randomly within this figure. What is the probability that the frog lands in the shaded area? | 3/4 | NULL | free_form |
stat340 | /home/yz979/scratch/chengye/math/data/original_set/statset/images/images/340.png | A school has 2000 students participating in a 'Safety with Me' publicity and education activity. To evaluate the effectiveness of the activity, m students were randomly selected for a test. The full score is 100 points, and the scores are divided into four levels: A, B, C, and D. Based on the collected data, an incomplete statistical chart was drawn. According to the information above, estimate the number of students in the school who achieved an A-level score. | 430 | NULL | free_form |
stat341 | /home/yz979/scratch/chengye/math/data/original_set/statset/images/images/341.png | A certain school wanted to understand parents' attitudes towards their children using mobile phones. They randomly selected 100 parents for a survey. Each parent completed one questionnaire, and each questionnaire indicated only one attitude (these 100 questionnaires were valid). After collecting and organizing these 100 questionnaires, two incomplete statistical charts, Figure 1 and Figure 2, were drawn. If the school has a total of 2000 students, how many parents can be estimated to hold a 'strict management' attitude towards mobile phones? | 400 | NULL | free_form |
stat342 | /home/yz979/scratch/chengye/math/data/original_set/statset/images/images/342.png | As shown in the figure, to measure the area of an irregular region (shaded area) on a flat ground, a square with an area of 4m² is drawn outside the irregular region. Randomly throwing small balls into the square (assuming that each point inside the square is equally likely for the balls to land), after a large number of repeated experiments, it is found that the frequency of the balls landing in the irregular region stabilizes at 0.4. Based on this, the estimated area of the irregular region is ________ m². | 1.6 | NULL | free_form |
stat343 | /home/yz979/scratch/chengye/math/data/original_set/statset/images/images/343.png | If a small ball rolls freely on the floor as shown in the figure and randomly stops on a tile, what is the probability that it will finally stop in the shaded area? ______ | 1/3 | NULL | free_form |
stat344 | /home/yz979/scratch/chengye/math/data/original_set/statset/images/images/344.png | A study group conducted a random sample survey of the transportation methods used by students at their school and produced two incomplete statistical charts, as shown in Figures 1 and 2. Given that the school has 1200 students, estimate the number of students who walk to school as approximately ___. | 240 | NULL | free_form |
stat345 | /home/yz979/scratch/chengye/math/data/original_set/statset/images/images/345.png | Internationally, 5.0 and above is considered normal vision. Below is a statistical chart of the vision conditions of students from a certain school. Given that 500 students have normal vision, the number of students who have not reached normal vision is ________. | 1500 | NULL | free_form |
stat346 | /home/yz979/scratch/chengye/math/data/original_set/statset/images/images/346.png | As shown in the figure, in △ABC, points D, E, and F are the midpoints of AB, AC, and BC, respectively. If a grain of rice is randomly thrown into △ABC, the probability of the grain landing in the shaded area is _________ | 1/4 | NULL | free_form |
stat35 | /home/yz979/scratch/chengye/math/data/original_set/statset/images/images/35.png | "Care for others, dedicate love." A middle school in a certain city held a charity "One-Day Donation" event. During the event, Class 1, Grade 7, with 50 students, voluntarily organized a loving donation activity. The class monitor collected the donation data and created a bar chart for the statistics. Based on the information provided in the chart, what is the total donation amount from all students in the class in yuan? | 1620 | NULL | free_form |
stat350 | /home/yz979/scratch/chengye/math/data/original_set/statset/images/images/350.png | Students in a certain class participated in a school-organized 'waste classification' knowledge competition. The students' scores were compiled into a frequency distribution histogram as shown (each group includes the left endpoint but excludes the right endpoint). The percentage of students with scores classified as 'excellent' (80 points and above) is ________. | 50% | NULL | free_form |
stat351 | /home/yz979/scratch/chengye/math/data/original_set/statset/images/images/351.png | The 'fuel efficiency' of a car refers to the number of kilometers the car can travel per liter of gasoline. The graph below shows the fuel efficiency of cars A and B at different speeds. Based on the information in the graph, which of the following four deductions are reasonable? | ②④ | NULL | free_form |
stat352 | /home/yz979/scratch/chengye/math/data/original_set/statset/images/images/352.png | In a certain experimental base, in order to fully grasp the growth pattern of 'seedless poplar' saplings, regular monitoring of 2000 such saplings is conducted. Recently, 100 saplings were randomly selected from the 2000 for measurement, and their heights (in cm) were recorded. After organizing the data, a frequency distribution histogram (as shown in the figure) was created. If a sapling with a height of no less than 300 cm is considered to have good growth, estimate how many of the 2000 saplings currently being cultivated at the base are growing well. | 940 | NULL | free_form |
stat354 | /home/yz979/scratch/chengye/math/data/original_set/statset/images/images/354.png | The figure below shows the temperature forecast for a certain city at 8 whole hour moments during a specific time period. What is the median temperature among these 8 moments? ______℃. | 16 | NULL | free_form |
stat356 | /home/yz979/scratch/chengye/math/data/original_set/statset/images/images/356.png | In order to understand the monthly time spent by middle school students in a certain district on club activities, 100 students were randomly selected, and their participation time was statistically analyzed. A frequency distribution histogram was drawn (each group includes the minimum value but excludes the maximum value). It is known that there are 8,000 middle school students in the district. Estimate the approximate number of students in the district who spend no less than 8 hours per month on club activities: ________. | 2800 | NULL | free_form |
stat357 | /home/yz979/scratch/chengye/math/data/original_set/statset/images/images/357.png | As shown in the figure, it is the investigation of the unit price of two types of fruits, A and B, in a certain supermarket over five consecutive days. Comparing the unit prices of A and B, the type of fruit with a higher average unit price over these five days is __________, and the type of fruit with a more stable unit price is __________. | B A | NULL | free_form |
stat358 | /home/yz979/scratch/chengye/math/data/original_set/statset/images/images/358.png | To reasonably arrange the school entry and exit times, the school's research team investigated the time spent by ninth-grade students on their way to and from school on a certain day. A total of 20 students were randomly selected from the ninth grade for this survey. A Cartesian coordinate system was established with the time spent on the way to school as the horizontal axis and the time spent on the way home as the vertical axis. Based on the survey results, corresponding points were plotted as shown in the figure. Given that there are 400 ninth-grade students in the school, estimate the number of students whose commute to school takes no more than 15 minutes. | 280 | NULL | free_form |
stat36 | /home/yz979/scratch/chengye/math/data/original_set/statset/images/images/36.png | 8. In an opaque bag, there are 3 red balls and n white balls, all of the same size and texture. A study group conducted an experiment called 'Using Frequency to Estimate Probability' and recorded the frequency of drawing red balls, resulting in a line plot. How many white balls could there possibly be? | 6 | NULL | free_form |
stat361 | /home/yz979/scratch/chengye/math/data/original_set/statset/images/images/361.png | In the ninth-grade exam, there is a multiple-choice question, as shown in the statistical chart. From the chart, the number of people who chose option C is ________. | 28 | NULL | free_form |
stat362 | /home/yz979/scratch/chengye/math/data/original_set/statset/images/images/362.png | As shown in the diagram, Groups One and Two have plotted line graphs based on the average mathematics scores of their respective groups over the last 5 attempts. According to the chart:
(1) For Group Two, the highest average score occurred during attempt number ___;
(2) Between the two groups, Group ___ showed greater improvement over these five attempts. (Choose 'One' or 'Two') | 5 Two | NULL | free_form |
stat363 | /home/yz979/scratch/chengye/math/data/original_set/statset/images/images/363.png | May 30, 2023, is the 7th National Science and Technology Workers' Day. A school held a popular science knowledge lecture competition where 100 works won first, second, third, and merit awards. Based on the award results, a line graph was drawn as shown in the figure. If the award-winning works are represented in a pie chart by the proportions of the four levels, the central angle corresponding to the 'Second Prize' in the pie chart would be ____________. | 108° | NULL | free_form |
stat365 | /home/yz979/scratch/chengye/math/data/original_set/statset/images/images/365.png | As shown in the diagram, a school conducted a survey on students' commuting methods and created a pie chart representing the proportions. If the number of students who ride bicycles is 350, then the number of students who walk is ______. | 400 | NULL | free_form |
stat366 | /home/yz979/scratch/chengye/math/data/original_set/statset/images/images/366.png | As shown in the figure, the statistical chart of Group A and Group B data is displayed. Which group's data is more stable, ________ ("Group A" or "Group B")? | Group B | NULL | free_form |
stat368 | /home/yz979/scratch/chengye/math/data/original_set/statset/images/images/368.png | A certain store sells two types of new energy vehicles, Model A and Model B. Selling one Model A car yields a profit of 2.4 million yuan, and selling one Model B car yields a profit of 2 million yuan. If the quantities of Model A and Model B cars sold by the store are as shown in the diagram, what is the average profit per car sold? ________ million yuan. | 2.16 | NULL | free_form |
stat369 | /home/yz979/scratch/chengye/math/data/original_set/statset/images/images/369.png | In a physics experiment class, the students use three switches, two light bulbs, a power source, and some wires to connect a circuit diagram as shown in the figure. The probability of one light bulb illuminating when randomly closing two switches in the diagram is ___________. | 2/3 | NULL | free_form |
stat37 | /home/yz979/scratch/chengye/math/data/original_set/statset/images/images/37.png | To prepare for the ninth-grade physical fitness test in May, Xiao Qiang practiced pull-ups every day. He recorded the number of pull-ups he did each day for a week, as shown in the table below. Three of the numbers are missing, but Xiao Qiang has calculated that the average of this dataset is 13, and the mean is 12. What is the variance of this dataset? ________. | 8/7 | NULL | free_form |
stat370 | /home/yz979/scratch/chengye/math/data/original_set/statset/images/images/370.png | In a certain school, in order to understand the weekly pocket money expenditure of eighth-grade students, 50 eighth-grade students were randomly sampled for a survey. The results of the survey are presented in the form of a pie chart. Based on the information in the chart, estimate the number of eighth-grade students out of 500 in the school whose weekly pocket money expenditure exceeds 50 yuan. The estimated number is ________. | 110 | NULL | free_form |
stat371 | /home/yz979/scratch/chengye/math/data/original_set/statset/images/images/371.png | In 2011, the International Mathematical Union officially announced that March 14 of each year would be designated as 'International Mathematics Day.' A school held a campus mathematics festival on March 14, where students could earn points (out of 100) by participating in various mathematical activities and exchange them for prizes the next day. To better prepare the prizes, the student council randomly selected the scores of 60 students from a total of 300 students in the school. The data is displayed in a frequency histogram (the data grouping intervals are: 40 ≤ x < 50, 50 ≤ x < 60, 60 ≤ x < 70, 70 ≤ x < 80, 80 ≤ x < 90, 90 ≤ x ≤ 100). Based on the data, estimate the number of students among the 300 in the school whose scores are 70 or higher. The approximate number is ______. | 200 | NULL | free_form |
stat372 | /home/yz979/scratch/chengye/math/data/original_set/statset/images/images/372.png | To encourage more middle school students to participate in fire safety education activities, students who participate in a one-week learning session on a certain platform can get two chances to draw lots. As shown in the diagram, the wheel is divided into six equal sectors. The pointer is fixed in position, and by clicking the lottery button, the wheel rotates freely. Once it stops, the pointer points to the middle section of a specific area. The probability of obtaining points in both lottery draws is ______. | 1/4 | NULL | free_form |
stat373 | /home/yz979/scratch/chengye/math/data/original_set/statset/images/images/373.png | Based on the information provided by the statistical chart, there are the following three conclusions: ① April 4th ranks 30th in terms of daily maximum temperature from high to low; ② The largest temperature rise occurred from April 7th to April 8th; ③ Let the variance of the maximum temperatures in the first ten days of April (April 1st to 10th) be S₁², in the middle ten days (April 11th to 20th) be S₂², and in the last ten days (April 21st to 30th) be S₃². Then, S₂² ≤ S₁² ≤ S₃². The correct conclusion(s) is/are ______. | ③ | NULL | free_form |
stat374 | /home/yz979/scratch/chengye/math/data/original_set/statset/images/images/374.png | To implement the 'Environmental Protection Declaration,' a school held a themed speech contest for primary and middle school students. The graph shows the scores given by 7 judges to two contestants, A and B. From the line graph, it can be observed that the 7 judges gave more consistent evaluations to contestant ________ in the speech contest. (Answer 'A' or 'B') | B | NULL | free_form |
stat375 | /home/yz979/scratch/chengye/math/data/original_set/statset/images/images/375.png | A school conducted a survey to understand the modes of transportation students use to reach school. They randomly selected some students for the survey and presented the results in the form of the incomplete bar graph and pie chart shown in the figure. What is the central angle in the pie chart corresponding to 'walking'? | 72 | NULL | free_form |
stat376 | /home/yz979/scratch/chengye/math/data/original_set/statset/images/images/376.png | As shown in the figure, in the parallelogram ABCD, E is the midpoint of BC, and BD and AE intersect at point O. If a grain of rice is randomly thrown inside the parallelogram ABCD, the probability of the rice landing in the shaded area is ___. | 1/12 | NULL | free_form |
stat378 | /home/yz979/scratch/chengye/math/data/original_set/statset/images/images/378.png | As shown in the figure, a dart game board is composed of 9 equally sized small square grids. If a dart is randomly thrown at the game board, the probability of hitting the white area is ________. | 2/3 | NULL | free_form |
stat379 | /home/yz979/scratch/chengye/math/data/original_set/statset/images/images/379.png | April 23rd is World Book Day. To understand the weekly extracurricular reading time of sixth-grade students at a certain school, 30 sixth-grade students were randomly selected, and their weekly extracurricular reading time was surveyed. The data was presented in the form of the frequency distribution histogram shown. Based on this information, estimate the number of sixth-grade students at the school who read extracurricular books for at least 5 hours a week. | 98 | NULL | free_form |
stat38 | /home/yz979/scratch/chengye/math/data/original_set/statset/images/images/38.png | The statistical chart shows the participation of students from a certain school in sports interest groups. If the group with the least number of participants has 30 people, how many people does the group with the most participants have? | 48 | NULL | free_form |
stat380 | /home/yz979/scratch/chengye/math/data/original_set/statset/images/images/380.png | Draw line charts for two groups of data, Group A and Group B, each containing 10 data points (as shown in the figure). The mean of both groups is 7. Let the variances of Group A and Group B be denoted as S_A² and S_B², respectively. Then S_A² <> S_B² ('>' or '<'). | < | NULL | free_form |
stat381 | /home/yz979/scratch/chengye/math/data/original_set/statset/images/images/381.png | In the women's basketball final of the Hangzhou Asian Games on October 6, 2023, the Chinese women's basketball team successfully defended their title. The heights of the 5 starting players of the Chinese team are shown in the figure: During the game, Player No. 14 with a height of 201 cm and Player No. 10 with a height of 185 cm went onto the court, replacing Players No. 15 and No. 9. At this point, the variance of the heights of the 5 players on the court is denoted as S². Compared to the variance S²₀ of the heights of the initial 5 starting players, S² is _________ (“increase,” “decrease,” or “=”). | < | NULL | free_form |
stat382 | /home/yz979/scratch/chengye/math/data/original_set/statset/images/images/382.png | In a middle school, there are three classes in the eighth grade: Class A, Class B, and Class C, each with 40 students. The math exam scores were statistically analyzed as follows: Based on the information provided in the charts (each score group includes the minimum score but excludes the maximum score), answer the following questions: (1) The percentage of students in Class A whose math scores are in the 80-90 range is ________; (2) Among the three eighth-grade classes, the class with the highest number of students scoring in the 80-90 range is ________ (fill in either 'Class A' or 'Class B'). | 32.5%, Class A | NULL | free_form |
stat383 | /home/yz979/scratch/chengye/math/data/original_set/statset/images/images/383.png | As shown in the diagram, a rectangular dartboard ABCD has diagonals AC and BD intersecting at point O. Line EF is drawn through point O, intersecting sides AD and BC at points E and F, respectively. Assume that every point on the dartboard is equally likely to be hit by a dart (if the dart hits the boundaries of the triangles or misses the dartboard, it is regarded as a re-throw). If one dart is randomly thrown at the dartboard, what is the probability of hitting the shaded region? | 1/2 | NULL | free_form |
stat384 | /home/yz979/scratch/chengye/math/data/original_set/statset/images/images/384.png | A certain middle school aimed to understand students' favorite extracurricular activities to better organize after-school services. They randomly surveyed a number of students with the following questionnaire: (Single choice) Among the following extracurricular activities, which one do you like the most? A. Literature B. Science and Technology C. Arts D. Sports Please complete the task and determine the final parameters. Based on the statistical results, the two incomplete statistical charts below were drawn: It is known that among the students who chose 'Arts' as their favorite extracurricular activity, there are 16 boys and a certain number of girls. If one girl is randomly selected for a discussion from the students in the 'Arts' category, with each student having an equal chance of being selected, the probability of selecting a girl is ________. | 5/9 | NULL | free_form |
stat386 | /home/yz979/scratch/chengye/math/data/original_set/statset/images/images/386.png | As shown in the figure, the histogram represents the age frequency distribution of all teachers at a school (using the principle of 'upper limit not included,' meaning that an age of 36 is categorized under the group 36 ≤ x < 38, not 34 ≤ x < 36). Based on the information provided in the figure, the following statements are made:
① The total number of teachers at the school is 50.
② The number of teachers in the age group 40 ≤ x < 42 accounts for 20% of the total number of teachers at the school.
③ The median age of the teachers must fall within the group 40 ≤ x < 42.
④ The mode of the teachers' ages must fall within the group 38 ≤ x < 40.
Which of the above statements is correct? ________. | ①②③ | NULL | free_form |
stat387 | /home/yz979/scratch/chengye/math/data/original_set/statset/images/images/387.png | In 2024, the National Two Sessions proposed: promoting industrial innovation through technological innovation, fostering new industries, models, and momentum with cutting-edge technologies, developing new productive forces, and promoting high-quality development. A school mathematics club conducted a survey titled 'How much do you know about Artificial Intelligence (AI)?' using the Wenjuanxing app. The level of knowledge was rated from low to high with scores of 1, 2, 3, 4, and 5 points. A pie chart based on the result is drawn, as shown in the figure. What is the mode of the scores? ________. | 1 | NULL | free_form |
stat388 | /home/yz979/scratch/chengye/math/data/original_set/statset/images/images/388.png | As shown in the figure, every small square on the dartboard is the same except for the shaded areas. When throwing a dart once (assuming the dart always lands on the board), what is the probability of hitting the shaded area? | 9/25 | NULL | free_form |
stat39 | /home/yz979/scratch/chengye/math/data/original_set/statset/images/images/39.png | A middle school held a 'Sunshine Sports Activity,' and all ninth-grade students from Class One participated in activities involving square dancing, table tennis, and basketball at 6 PM on April 18, 2019. At this time, Teacher Wang collected statistics on the number of students engaged in these three activities and created a pie chart and a bar chart based on this data. Based on the two charts, how many students were participating in the table tennis activity at this time? | 15 | NULL | free_form |
stat390 | /home/yz979/scratch/chengye/math/data/original_set/statset/images/images/390.png | Reviewing test papers is a very important part of the ninth-grade review phase. A mathematics teacher conducted a survey on student participation in test review lessons. The evaluation items are: A. Independent Thinking, B. Voluntary Error Correction, C. Focused Listening, D. Explanation and Reminder. Students could select one item at random. Several ninth-grade students were randomly selected for the survey, and the results of the survey are represented in the form of an incomplete bar chart and pie chart. If there are 80,000 ninth-grade students in the entire city, approximately how many ninth-grade students 'focus on listening' during test review lessons? | 32000 | NULL | free_form |
stat391 | /home/yz979/scratch/chengye/math/data/original_set/statset/images/images/391.png | In March 2024, a school organized a reading activity titled 'The Dragon Year Echoes with Books, Spring Brings the Fragrance of Ink.' The graph shows the number of books read by students of different grades during the winter break. Based on the information provided in the graph, how many books were read by eighth-grade students at this school? | 450 | NULL | free_form |
stat393 | /home/yz979/scratch/chengye/math/data/original_set/statset/images/images/393.png | As shown in the figure, a 6×6 square grid simulates a dartboard game area. Each vertex and diagonal point of the small squares forms a droplet-shaped pattern in the shaded area. Points A, B, C, and D are grid points. The pattern is formed by the circular arc passing through points B, C, and D and the two chords created by straight lines. Assuming that hitting each small square is equally probable (if hitting the boundary or missing the game area, the dart is thrown again), the probability of hitting the shaded area in a single dart throw is ___ . | 2x + 3√3 / 27 | NULL | free_form |
stat394 | /home/yz979/scratch/chengye/math/data/original_set/statset/images/images/394.png | As shown in the figure, in a 5×6 rectangular dartboard grid, all small square tiles have the same color. The vertices of the small squares are called grid points. The sector OAB has its center and endpoints of the arc located at grid points. Assume that hitting any small square tile with a dart is equally likely (if the dart hits the boundary of the sector or misses the board, it is retaken). When a dart is thrown once, the probability of hitting the sector OAB (the shaded area) is π/12. Then the area of the sector in the figure is ________. | 5/2π | NULL | free_form |
stat395 | /home/yz979/scratch/chengye/math/data/original_set/statset/images/images/395.png | A comprehensive and practical study group at a certain school conducted a survey to understand the reading habits of 2,400 students in the school. They randomly selected a portion of students to fill out a questionnaire and created the following statistical chart: The survey question was: The average amount of time you spend reading extracurricular books each week is approximately (including endpoints for all four options, with each option containing the minimum value but excluding the maximum value) ________. A. 8 hours or more B. 6~8 hours C. 4~6 hours D. 0~4 hours. Estimate the number of students among the 2,400 who spend 6 hours or more weekly reading extracurricular books. __________ students. | 1152 | NULL | free_form |
stat396 | /home/yz979/scratch/chengye/math/data/original_set/statset/images/images/396.png | As shown in the figure, it is the entrance of a cinema, which has 3 ticket-checking gates. If Wang Lin and Li Hua randomly choose one gate to enter the cinema, what is the probability that both enter through the same gate? | 1/3 | NULL | free_form |
stat397 | /home/yz979/scratch/chengye/math/data/original_set/statset/images/images/397.png | On a flat ground, there is an irregular pattern (shaded area in the figure). Xiaoming wants to find out the area of this pattern. He used the following method: he covered the irregular pattern with a rectangle that is 5 meters long and 4 meters wide, and then randomly threw small balls evenly onto this area and recorded the number of balls falling inside the irregular pattern. The results of several valid trials were plotted into the line chart shown in Figure ②. Assuming that every point inside the rectangle has an equal probability of being hit by the balls, Xiaoming can estimate the area of the irregular pattern to be ______m². | 7 | NULL | free_form |
stat398 | /home/yz979/scratch/chengye/math/data/original_set/statset/images/images/398.png | As shown in the figure, there is a cable break point among points A, B, and C (AB > BC). The probability that the break point occurs between A and B is P1, and the probability that the break point occurs between B and C is P2. Then P1 ____ P2 (fill in '>', '<', or '='). | > | NULL | free_form |
stat399 | /home/yz979/scratch/chengye/math/data/original_set/statset/images/images/399.png | "Protect your eyes, embrace the light." A mathematics interest group at a school conducted a survey on vision problems among some students and compiled statistics according to national classification standards. The data is presented in two incomplete charts below: Surveyed Student Vision Statistics Table
Category Result Number of Students
A Normal 80
B Mild Myopia
C Moderate Myopia 70
D Severe Myopia
Surveyed Student Vision Statistics Chart
If there are 1,600 students in the school, estimate the total number of students with moderate and severe myopia as __________ students. | 720 | NULL | free_form |
stat4 | /home/yz979/scratch/chengye/math/data/original_set/statset/images/images/4.png | 3. In the computer system, there is a 'Minesweeper' game that requires the player to mark all the mines. Game rules: A square can have at most one mine beneath it. If there are no mines, opening the square will reveal a number, indicating how many mines are in the surrounding squares (up to 8 squares). For clarity, I have marked the '6 buckets' in figure B, using them to distinguish from unmarked squares. For example, '3' in the grid means that there are 3 mines in the surrounding squares, including diagonals. Figure B shows a part of the game played by Zhang San, where 4 squares have been confirmed to be mines (as they are marked with pieces on the squares). From the second row of 6 squares in Figure B (the squares labeled with alphabet letters), those that can be confirmed as mines are _____. (Please list the corresponding letters on the squares.) | B, D, F, G. | NULL | free_form |
stat40 | /home/yz979/scratch/chengye/math/data/original_set/statset/images/images/40.png | 8. As shown in the figure, there is a square and its inscribed circle. The side length of the square is 4. If a grain of rice is randomly thrown into the square, what is the probability that it lands inside the circle? | π/4 | NULL | free_form |
stat401 | /home/yz979/scratch/chengye/math/data/original_set/statset/images/images/401.png | As shown in the figure, a spinning wheel is created during a math activity class. The wheel is divided into four equal sectors, marked with the numbers -3, -2, -1, and 1. If the wheel is spun twice, and the numbers corresponding to the sectors pointed to by the pointer after each spin are recorded as m and n respectively (if the pointer ends up on a boundary line, the wheel must be spun again), what is the probability that the line y = mx + n does not pass through the fourth quadrant? | 1/16 | NULL | free_form |
stat404 | /home/yz979/scratch/chengye/math/data/original_set/statset/images/images/404.png | A simple random sampling method was used to select the grades of 60 students from the entire school for analysis, and a frequency histogram (where each interval includes the lower bound but excludes the upper bound) was drawn as shown in the figure. The bar for the 70~80 score range has not yet been drawn. If a score of 60 or above (inclusive) is considered passing, estimate the pass percentage for the entire school. | 75% | NULL | free_form |
stat405 | /home/yz979/scratch/chengye/math/data/original_set/statset/images/images/405.png | The tangram is an ancient invention from China, known as the 'Oriental Magic Puzzle'. It is composed of five isosceles right triangle pieces, one square piece, and one parallelogram piece. As shown in the figure, a small ball rolls freely on the square floor formed by the tangram. What is the probability that the ball stays in the shaded region? | 1/4 | NULL | free_form |
stat407 | /home/yz979/scratch/chengye/math/data/original_set/statset/images/images/407.png | In a "My Chinese Dream" speech competition held at a certain school, the results of 10 participating students are shown in the figure. Regarding the competition results of these 10 students, which of the following statements is incorrect?
A. The median is 80
B. The mode is 80
C. The mean is 82
D. The range is 40 | C | ['The median score is 80', 'The mode is 80', 'The average score is 82', 'The range is 40'] | multi_choice |
stat408 | /home/yz979/scratch/chengye/math/data/original_set/statset/images/images/408.png | To implement the 'Double Reduction' policy, the school randomly surveyed some students about their average daily sleep duration over a week. The statistical results are shown in the graph. What are the mode and median of the sleep durations among these surveyed students? ( ) | A. 8, 9 | ['8, 9', '8, 8.5', '16, 8.5', '16, 14'] | multi_choice |
stat409 | /home/yz979/scratch/chengye/math/data/original_set/statset/images/images/409.png | As shown in the diagram, Group One and Group Two students have plotted the average mathematics scores of their most recent 5 tests on bar charts, respectively. From the charts, we can conclude that the group with the greater improvement in scores is ( ). | A. Group One | ['Group 1', 'Group 2', 'Both groups have the same improvement', 'Cannot be determined'] | multi_choice |
stat41 | /home/yz979/scratch/chengye/math/data/original_set/statset/images/images/41.png | As shown in the line chart, which displays the sales revenue growth of Company A and Company B over the past few years, the company with the faster growth in sales revenue is ________. | Company A | NULL | free_form |
stat410 | /home/yz979/scratch/chengye/math/data/original_set/statset/images/images/410.png | As shown in the figure, the circuit diagram has three switches S1, S2, S3 and two bulbs L1, L2. When randomly closing two of the switches S1, S2, S3, what is the probability of bulb L2 lighting up? | D | ['1/2', '1/4', '2/3', '1/3'] | multi_choice |
stat411 | /home/yz979/scratch/chengye/math/data/original_set/statset/images/images/411.png | Xiao Ming hangs a 3×3 square grid board on the wall to play darts (each dart equally likely lands on any point of the board), as shown in the figure. What is the probability that the dart lands in the shaded area ( )? | B | ['5/9', '4/9', '1/2', '3/5'] | multi_choice |
stat412 | /home/yz979/scratch/chengye/math/data/original_set/statset/images/images/412.png | In a shooting competition, the scores of a certain player in 10 shots are as shown in the figure. Which of the following conclusions is incorrect? ( ) A. The mean is 9 rings B. The median is 9 rings C. The mode is 9 rings D. The variance is 0.8 | D | ['The average score is 9 rings', 'The median score is 9 rings', 'The mode is 9 rings', 'The variance is 0.8'] | multi_choice |
stat413 | /home/yz979/scratch/chengye/math/data/original_set/statset/images/images/413.png | A certain school has launched a 'Love Reading' activity. Class 7(1) has collected data on extracurricular reading quantities (in books) for all students in January through June and created a line chart (as shown in the figure). Which of the following statements is correct? | C | ['The number of books read in June is the highest.', 'There are 5 months where the number of books read exceeds 40.', 'Among the two adjacent months, the growth rate of the number of books read from January to February is the fastest.', 'The number of books read in April is 38.'] | multi_choice |
stat414 | /home/yz979/scratch/chengye/math/data/original_set/statset/images/images/414.png | As shown in the figure, the probability of making the shape formed by all the black squares an axisymmetric figure by randomly painting any of the white squares black is (). | A | ['2/3', '1/2', '1/3', '1/6'] | multi_choice |
stat415 | /home/yz979/scratch/chengye/math/data/original_set/statset/images/images/415.png | Reading lights up dreams. A certain school held a 'Fragrant Youth' activity on World Book Day. The following graph represents the extracurricular book reading volume (unit: books) for all 50 students of a Grade 8 class this semester, as counted by the class monitor. What is the median number of books read by these 50 students? ( ) | B | ['12', '15', '18', '21'] | multi_choice |
stat416 | /home/yz979/scratch/chengye/math/data/original_set/statset/images/images/416.png | As shown in the graph, a nurse is recording the temperature changes of a patient. The patient's temperature at 16:00 is approximately ( ). | C. 38.7°C | ['37.8°C', '38.5°C', '38.7°C', '39.4°C'] | multi_choice |
stat417 | /home/yz979/scratch/chengye/math/data/original_set/statset/images/images/417.png | As shown in the diagram, it represents the modes of transportation (by bus, walking, cycling) for students in Class 9 (3) of a certain school in a bar chart (partial) and a pie chart. Which of the following statements is correct?
A. There are a total of 42 students going out from Class 9 (3).
B. There are 8 students walking from Class 9 (3).
C. In the pie chart, the central angle representing the proportion of walking students is 82°.
D. If there are 500 students going out in the entire grade, then it is estimated that about 140 students from the whole grade go out cycling. | B | ['There are 42 students in Class 9 (3) who go out.', 'There are 8 students in Class 9 (3) who go out by walking.', 'In the pie chart, the central angle of the sector representing the number of students who walk is 82°.', 'If there are 500 students in the whole grade who go out, then the number of students who go out by cycling is about 140.'] | multi_choice |
stat418 | /home/yz979/scratch/chengye/math/data/original_set/statset/images/images/418.png | As shown in the figure, a histogram represents the frequency distribution of scores in a math test for a certain class (each interval includes the upper bound but excludes the lower bound). Which of the following statements is incorrect? A. The number of people scoring between 70 and 80 is the highest. B. The class width is 10. C. The frequency of the score interval with the least number of people is 5%. D. The number of people who passed (scores > 60) is 12. | D | ['The number of people scoring between 70 and 80 is the highest.', 'The group interval is 10.', 'The frequency of the least populated score range is 5%.', 'There are 12 people who scored above 60.'] | multi_choice |
stat419 | /home/yz979/scratch/chengye/math/data/original_set/statset/images/images/419.png | Given the natural population growth rate, birth rate, and death rate, which of the following judgments is incorrect?
A. Compared to 2012, the birth rate in 2021 has dropped by nearly half
B. The death rate has remained basically stable over the past ten years
C. The total population has been continuously declining over the past five years
D. The natural population growth rate has been continuously declining over the past five years | C | ['Compared to 2012, the birth rate in 2021 has dropped by nearly half.', 'The death rate of the population has remained basically stable in the past decade.', 'The total population growth rate has declined in the past decade.', 'The natural population growth rate has continued to decline in the past decade.'] | multi_choice |
stat420 | /home/yz979/scratch/chengye/math/data/original_set/statset/images/images/420.png | A dart is randomly thrown onto the regular hexagonal dartboard shown in the figure. If each point on the dartboard is equally likely to be hit, what is the probability of the dart landing in the shaded region? | B | ['1/4', '1/3', '1/2', '√3/3'] | multi_choice |
stat421 | /home/yz979/scratch/chengye/math/data/original_set/statset/images/images/421.png | 2. In an opaque bag, there are 6 yellow balls, 1 red ball, and n blue balls. These balls are identical except for their color. A school extracurricular group draws one ball at a time, records its color, and then puts it back. They have tallied the frequency of yellow balls appearing, as shown in the figure. What is the value of n? ( )
A. 2 B. 3 C. 5 D. 8 | B | ['2', '3', '5', '8'] | multi_choice |
stat422 | /home/yz979/scratch/chengye/math/data/original_set/statset/images/images/422.png | As shown in the figure, the circuit is well connected, and all components work normally. Two of the switches S1, S2, and S3 are randomly closed. What is the probability that the two small bulbs light up simultaneously?
A. 0
B. 1/2
C. 1/3
D. 1/4 | C | ['0', '1/2', '1/3', '1/4'] | multi_choice |
stat423 | /home/yz979/scratch/chengye/math/data/original_set/statset/images/images/423.png | As shown in the figure, to understand the extracurricular sports activities of sixth-grade students, 30 sixth-grade students were randomly surveyed about their extracurricular exercise time. The survey results were divided into four categories: A, B, C, and D, and the following bar chart was created (the D category is obscured by water pollution). If the height ratio of categories A, B, and C is 1:2:4, and the number of people in category B is 6, then the number of people in category D is ( ). | A. 9 | ['9', '8', '7', '6'] | multi_choice |
stat424 | /home/yz979/scratch/chengye/math/data/original_set/statset/images/images/424.png | Starting from 2021, a certain province will pilot a new '3+1+2' general high school entrance examination model. In addition to the three mandatory subjects of Chinese, Mathematics, and Foreign Language, students will choose one subject between Physics and History, and two subjects from Chemistry, Biology, Geography, and Politics as elective subjects. To help politics students reasonably select their elective subjects, a certain high school scaled each student's comprehensive scores for the six subjects to a 5-point scale, creating a chart. The radar chart of Student A's scores is shown. Which of the following statements is definitely incorrect? ( ) A. Student A's Physics score leads the grade average score the most B. Student A has scores in two subjects below the grade average C. Student A's top three subjects ranked from high to low are Physics, Chemistry, and History D. For Student A, a relatively ideal selection of subjects would be Physics, Chemistry, and Geography | C | ["The average score of A's physics performance is the lowest.", "The average score of A's performance in the two subjects is lower than the annual average score.", "The top three subjects in A's performance are physics, chemistry, and history.", 'For A, physics, chemistry, and biology are more ideal subject combinations.'] | multi_choice |
stat425 | /home/yz979/scratch/chengye/math/data/original_set/statset/images/images/425.png | As shown in the diagram, Xiao Ming and Xiao Gang each designed a spinning wheel (the sector areas in each spinning wheel are equal). They play the 'Pair Purple' game by spinning each wheel once. If red and blue respectively appear on the two wheels, it indicates they can pair into purple. What is the probability that Xiao Ming pairs into purple? | C | ['1/3', '1/2', '1/6', '2/9'] | multi_choice |
stat426 | /home/yz979/scratch/chengye/math/data/original_set/statset/images/images/426.png | The 'Welcoming the 20th National Congress · Forge Ahead on a New Journey - Rural Revitalization Achievement Exhibition' held in our city attracted many citizens to visit. The figure shows the schematic diagram of the exhibition hall entrance and exit. Xiaoying and her mother enter through the same entrance to visit separately, and the probability that they happen to exit from the same exit is ( ). | C | ['2/3', '1/2', '1/3', '1/6'] | multi_choice |
stat427 | /home/yz979/scratch/chengye/math/data/original_set/statset/images/images/427.png | In an experiment where two students, A and B, estimate probability through frequency, they recorded the frequency of a certain outcome. The statistical chart they drew is shown. Which experiment could this outcome correspond to? ( ) | A | ['Randomly draw a ball from a bag that contains 2 white balls and 1 red ball, then find the probability of getting a red ball', 'Randomly buy a cinema ticket, the probability that the seat number is even', 'Flip a coin that has evenly distributed quality, the probability that it lands face up', 'Roll a regular hexahedron dice, the probability of getting 1 point'] | multi_choice |
stat428 | /home/yz979/scratch/chengye/math/data/original_set/statset/images/images/428.png | As shown in the figure, four identical small balls are labeled 1, 2, 3, and 4. They are placed in a bag, thoroughly mixed, and randomly divided into two equal parts. What is the probability that the balls labeled with odd numbers will be grouped together? | C | ['1/2', '1/4', '1/3', '1/6'] | multi_choice |
stat429 | /home/yz979/scratch/chengye/math/data/original_set/statset/images/images/429.png | If you spin the pointer of disk A and disk B with force, which disk has a higher probability of the pointer stopping in the white area? | D. The same | ['Disk A', 'Disk B', 'Cannot be determined', 'Same probability'] | multi_choice |
stat430 | /home/yz979/scratch/chengye/math/data/original_set/statset/images/images/430.png | With the junior high school academic level examination approaching, a school conducted subject simulation tests over four consecutive months and organized the test scores into a statistical chart (the number of students participating in the four simulation exams remained unchanged). Which of the following statements is correct? ( ) | D | ['A total of 500 students participated in the mock test', "From January to April, the number of students with 'excellent' test scores increased, and the proportion of the total number of students increased week by week", "The increase in the number of 'excellent' students in April is greater than the increase in the number of 'excellent' students in March", "The number of students with 'excellent' test scores in April reached 100"] | multi_choice |
stat432 | /home/yz979/scratch/chengye/math/data/original_set/statset/images/images/432.png | A team conducting an experiment on 'estimating probabilities using frequency' recorded the frequency of a specific outcome and plotted it as shown in the line chart. Which experiment is most likely consistent with the result?
A. Rolling a fair six-sided die, with the face showing the number 4.
B. Shuffling a standard deck of cards (excluding jokers) and drawing a card with the suit hearts.
C. In a game of rock-paper-scissors, randomly choosing 'scissors'.
D. From a box containing 1 red ball and 2 yellow balls (distinguishable only by color), randomly drawing a yellow ball. | A | ['Roll a regular hexahedron dice, the upward face is 4', 'A pack of regular poker cards is shuffled, an arbitrary card is drawn, the color of which is a red peach', "In the game of stone, scissors, and cloth, Xiao Ming randomly shows 'scissors'", 'In a dark box, there is 1 red ball and 2 yellow balls that only differ in color, an arbitrary ball is felt out, it turns out to be a yellow ball'] | multi_choice |
stat433 | /home/yz979/scratch/chengye/math/data/original_set/statset/images/images/433.png | If the ball freely rolls on the ground as shown in the figure and randomly stops inside the parallelogram, what is the probability that it finally stops in the black region? | C | ['1/2', '1/3', '1/4', '1/6'] | multi_choice |
stat435 | /home/yz979/scratch/chengye/math/data/original_set/statset/images/images/435.png | As shown in Figure 5, there is an irregular pattern (the shaded part in the figure) on a flat ground. Xiao Ming wants to determine the area of this pattern. He adopted the following method: he surrounded the irregular pattern with a rectangle of 10m in length and 8m in width, then randomly threw small balls into the area and recorded the number of balls that landed on the irregular pattern (balls landing on the boundaries or outside the rectangular region were not counted). He plotted the results from several valid experiments into the shown line graph. Based on this, he estimated the approximate area of the irregular pattern as ( ). | D. 28m² | ['25m²', '26m²', '27m²', '28m²'] | multi_choice |
stat436 | /home/yz979/scratch/chengye/math/data/original_set/statset/images/images/436.png | A school organizes 300 students to participate in interest group activities. The enrollment situation for each group is shown in the chart. Which of the following statements is correct? A. The central angle corresponding to the number of people participating in the dance interest group in the statistical chart is 72°. B. The number of people in the art interest group is 90. C. The basketball interest group has the fewest participants. D. The number of people in the art interest group is 6. | D | ['The number of students participating in the dance interest group corresponds to an angle of 72° in the statistical chart.', 'The number of students participating in the art interest group is 90.', 'The number of students participating in the basketball interest group is the smallest.', 'The number of students participating in the elephant interest group is 6.'] | multi_choice |
stat438 | /home/yz979/scratch/chengye/math/data/original_set/statset/images/images/438.png | The gender of a human is determined by a pair of sex chromosomes (X, Y). When the chromosomes are XX, the individual is female; when the chromosomes are XY, the individual is male. The diagram shows the genetic map of the sex chromosomes for a couple. If this woman becomes pregnant, what is the probability that the child will be a girl? | C | ['1/4', '1/3', '1/2', '3/4'] | multi_choice |
stat440 | /home/yz979/scratch/chengye/math/data/original_set/statset/images/images/440.png | As shown in the figure, the areas of all sectors on the spinner are equal. When the spinner is rotated randomly once, the probability that the pointer lands in the shaded area is ( ). | B | ['1/4', '1/5', '4/5', '1/6'] | multi_choice |
stat441 | /home/yz979/scratch/chengye/math/data/original_set/statset/images/images/441.png | Two students, A and B, performed an experiment using frequency to estimate probability. The statistical graph of the frequency of a certain outcome observed during the experiment is shown. Which of the following experiments is consistent with the results of the graph? A. Rolling a six-sided die, the probability of getting a 1 B. Tossing a coin, the probability of getting heads C. Writing a random integer, the probability of it being divisible by 3 D. Drawing a ball from a bag containing 2 white balls and 1 red ball, the probability of drawing a white ball | C | ['Roll a regular hexahedron dice, the probability of getting 1 point', 'Flip a coin, the probability of it landing face up', 'Write an arbitrary whole number, the probability that it can be divided by 3', 'Randomly draw a ball from a bag that contains 2 white balls and 1 red ball, the probability of getting a white ball'] | multi_choice |
stat443 | /home/yz979/scratch/chengye/math/data/original_set/statset/images/images/443.png | The school club activities can enrich students' learning life, balance work and rest, and develop their interests. A certain school conducted statistics on the number of students participating in school club activities and drew a pie chart as shown below. If there are 60 students in the Information Technology club, how many students are there in the Labor Practice club? | B | ['75', '90', '108', '150'] | multi_choice |
stat445 | /home/yz979/scratch/chengye/math/data/original_set/statset/images/images/445.png | In an opaque bag, 2 yellow balls, 1 white ball, 1 red ball, and n blue balls are placed. These balls are identical except for their colors. The extracurricular interest group draws one ball at a time, records the color, and then puts it back. They also tally the frequency of blue balls appearing (as shown in the figure). What is the most likely value of n? | C | ['4', '5', '6', '7'] | multi_choice |
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