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stat1065 | /home/yz979/scratch/chengye/math/data/original_set/statset/images/images/1065.png | According to statistics, the community of mathematicians is a long-lived group. A research team randomly sampled the ages of several mathematicians aged 90 and above from the 'Biographical Dictionary of Mathematicians,' which contains records of approximately 2,200 mathematicians. The data was organized and analyzed, and the statistical frequencies (percentages) are provided below. Which of the following conclusions is incorrect ( )? | D | ['The team has counted the ages of 100 mathematicians.', 'The value in the statistical table is 5.', 'The age group with the most long-lived mathematicians is 92-93 years old.', "The number of mathematicians aged 96-97 in the 'Mathematician Biography' is estimated to be 110."] | multi_choice |
stat1069 | /home/yz979/scratch/chengye/math/data/original_set/statset/images/images/1069.png | The statistics table and pie chart of a certain class's favorite sports are shown below, where a portion of the pie chart has been torn off.
Conclusion 1: The sum of m and n in the pie chart is 52;
Conclusion 2: The number of students in the class who prefer basketball is less than 13.
Regarding conclusions 1 and 2, the correct statement is ( )
A. Both Ⅰ and Ⅱ are correct
B. Both Ⅰ and Ⅱ are incorrect
C. Ⅰ is correct, Ⅱ is incorrect
D. Ⅰ is incorrect, Ⅱ is correct | A | ['Both I and II are correct', 'Both I and II are incorrect', 'I is correct, II is incorrect', 'I is incorrect, II is correct'] | multi_choice |
stat107 | /home/yz979/scratch/chengye/math/data/original_set/statset/images/images/107.png | If the bar chart shows the unit price of apples for the first three purchases, and the unit price of apples for the fourth purchase is 8 yuan/kg, it is found that the median of these four unit prices is exactly the same as the mode, then a = | 8 | NULL | free_form |
stat108 | /home/yz979/scratch/chengye/math/data/original_set/statset/images/images/108.png | In the circuit diagram, there are four switches S1, S2, S3, S4, and a small light bulb. If any two of the switches S1, S2, S3, S4 are closed at the same time, what is the probability that the small light bulb will light up? ______. | 1/3 | NULL | free_form |
stat109 | /home/yz979/scratch/chengye/math/data/original_set/statset/images/images/109.png | If a computer is used to simulate the results of tossing a beer bottle cap, as the number of trials increases, the frequency of 'convex side up' shows a certain stability. The probability of 'convex side up' can be estimated as ___ (accurate to 0.001). | 0.440 | NULL | free_form |
stat11 | /home/yz979/scratch/chengye/math/data/original_set/statset/images/images/11.png | The 'Zhao Shuang's diagram of a chord' is composed of four congruent right triangles and a smaller square in the middle, forming a larger square (as shown in the figure). Xiao Liang randomly throws a dart into the interior region of the larger square. If the lengths of the two legs of the right-angled triangle are 2 and 1, respectively, what is the probability that the dart lands in the smaller square (shaded region)? ______. | 1/5 | NULL | free_form |
stat110 | /home/yz979/scratch/chengye/math/data/original_set/statset/images/images/110.png | The PE time distribution of some Grade 8 students in a week is surveyed, and the corresponding frequency histogram (each interval includes the lower bound and excludes the upper bound) is shown. Estimate the number of Grade 8 students in the school, out of 900, who spend at least 8 hours on physical exercise per week. | 120 | NULL | free_form |
stat111 | /home/yz979/scratch/chengye/math/data/original_set/statset/images/images/111.png | If a ball rolls freely on the floor as shown in the figure and randomly stops on one of the tiles, what is the probability that the ball will finally stop in the black area? | 1/3 | NULL | free_form |
stat112 | /home/yz979/scratch/chengye/math/data/original_set/statset/images/images/112.png | A school conducted a survey to understand the time taken by seventh-grade students to complete their written homework on a particular day. They randomly selected 40 students from the seventh grade and plotted the results into a frequency distribution histogram (each group includes the boundary value but excludes the maximum value). Based on the information provided in the histogram, approximately how many of the 200 seventh-grade students in the school took less than 90 minutes to complete their homework that day? | 170 | NULL | free_form |
stat113 | /home/yz979/scratch/chengye/math/data/original_set/statset/images/images/113.png | An ant climbs onto a wall as shown in the figure. What is the probability that it finally stops in the black area? | 1/3 | NULL | free_form |
stat114 | /home/yz979/scratch/chengye/math/data/original_set/statset/images/images/114.png | The percentage of monthly output value to the total output value of the first quarter for a company is shown in the figure. It is known that the output value in February is 36 million yuan. What is the average monthly output value of this company in the first quarter in million yuan? | 40 | NULL | free_form |
stat115 | /home/yz979/scratch/chengye/math/data/original_set/statset/images/images/115.png | In a certain district, 1200 students participated in a 'waste sorting' knowledge contest. To understand the score distribution of this contest, the organizing committee randomly selected some students' scores (all scores are integers) as a sample and plotted a frequency distribution histogram (as shown in the figure). Based on the information provided, estimate how many students in this district scored between 89.5 and 99.5 points. | 180 | NULL | free_form |
stat116 | /home/yz979/scratch/chengye/math/data/original_set/statset/images/images/116.png | A school plans to choose one of two students, Zhang Ping and Li Bo, who excel in long jump, to represent the school in the district's spring sports meet. The physical education teacher conducted statistical analysis on their 10 most recent test results and found that their average jump lengths were both 5.72 meters. A line chart was created based on the test data. If selecting the student with relatively stable performance, who should be chosen (fill in 'Zhang Ping' or 'Li Bo')? | Li Bo | NULL | free_form |
stat117 | /home/yz979/scratch/chengye/math/data/original_set/statset/images/images/117.png | In order to understand the situation of students doing housework at home, a school conducted a sampling survey of some students and produced a frequency distribution histogram as shown in the figure (each data group includes the minimum value but not the maximum value). If the school has 1500 students, estimate the number of students whose average weekly housework time is less than 2 hours. The approximate number is ______. | 720 | NULL | free_form |
stat118 | /home/yz979/scratch/chengye/math/data/original_set/statset/images/images/118.png | In order to further understand the physical fitness of Grade 9 students in a certain school, 50 students were randomly selected for a 1-minute rope skipping test. The test data was used as a sample and was plotted into an incomplete frequency histogram (as shown in the figure) (each group of data includes the minimum value but excludes the maximum value, unit: skips). If there are a total of 450 Grade 9 students in the school, how many students skipped rope 120 to 140 times in one minute? | 135 | NULL | free_form |
stat12 | /home/yz979/scratch/chengye/math/data/original_set/statset/images/images/12.png | As shown in the figure, switches K1, K2, and K3 are in the open state. If two of the switches K1, K2, and K3 are closed randomly, what is the probability that the two lamps light up simultaneously? | 1/3 | NULL | free_form |
stat120 | /home/yz979/scratch/chengye/math/data/original_set/statset/images/images/120.png | A tourist scenic area offers three ticket packages priced at 100, 150, and 200 (units: yuan) to meet the needs of different visitors. The scenic spot collected and analyzed the sales data of these three ticket packages over a year and represented the data as a pie chart (as shown in the figure). What is the average price of the ticket packages sold that year in yuan? | 175 | NULL | free_form |
stat124 | /home/yz979/scratch/chengye/math/data/original_set/statset/images/images/124.png | As shown in the figure, it is a pie chart of the revenue composition of a certain mall in the four quarters of 2022, where the revenue in the second quarter is 1 million yuan. What is the mall's total annual revenue in ________ million yuan? | 500 | NULL | free_form |
stat125 | /home/yz979/scratch/chengye/math/data/original_set/statset/images/images/125.png | A school sampled some students to participate in a “big reading” learning questionnaire and conducted statistical analysis of their scores, creating the frequency distribution histogram shown in the figure. What is the frequency of scores between 60 (inclusive) and 70 (exclusive)? | 0.2 | NULL | free_form |
stat126 | /home/yz979/scratch/chengye/math/data/original_set/statset/images/images/126.png | In a school, 200 eighth-grade students participated in a life safety knowledge test. The test scores are all greater than or equal to 60 and less than 100. The frequency distribution of the score intervals is shown in the table below (each score interval includes the minimum value but does not include the maximum value). Based on the information in the table, the number of students who scored in the 80-90 interval is ______. | 60 | NULL | free_form |
stat127 | /home/yz979/scratch/chengye/math/data/original_set/statset/images/images/127.png | If it is the frequency distribution line chart of high jump test scores for some eighth-grade students (in the line chart, each group includes the former boundary value but not the latter boundary value), from the chart we can conclude: The group midpoint with the highest frequency is _________m, and the number of people with high jump scores below 1.25m is ________. | 1.3 20 | NULL | free_form |
stat128 | /home/yz979/scratch/chengye/math/data/original_set/statset/images/images/128.png | As shown in the figure, Xiao Ming made a circular target containing an inscribed equilateral triangle. The shaded area in the figure is the incircle of the triangle. Xiao Ming randomly throws a dart at the target area. The probability that the dart lands in the shaded region is ________. | 1/4 | NULL | free_form |
stat129 | /home/yz979/scratch/chengye/math/data/original_set/statset/images/images/129.png | Class A and Class B each have 20 male students who were tested for 'pull-ups.' The performance is shown in the chart:
Let the variances of the number of 'pull-ups' performed by male students in Class A and Class B be S₁² and S₂², respectively. Then S₁² ___ S₂². (Fill in with '>', '<', or '=') | < | NULL | free_form |
stat13 | /home/yz979/scratch/chengye/math/data/original_set/statset/images/images/13.png | Since 1984, China has participated in multiple Summer Olympic Games and achieved remarkable results. The line chart below shows the number of gold medals won by China from the 23rd to the 30th Summer Olympic Games. Observing the chart, the second Summer Olympics with the largest increase compared to the previous one is the ______ Summer Olympics. | 29 | NULL | free_form |
stat130 | /home/yz979/scratch/chengye/math/data/original_set/statset/images/images/130.png | The school conducted a survey to understand the commuting methods of its Grade 9 students. They randomly selected 20 Grade 9 students for the survey, among which 2 students were commuting by private car. If a pie chart is drawn based on the collected data, and assuming there are 200 Grade 9 students in the school, approximately how many students commute to school by bicycle? | 30 | NULL | free_form |
stat131 | /home/yz979/scratch/chengye/math/data/original_set/statset/images/images/131.png | A school's student participation in extracurricular interest groups is shown in the chart. If the Information Technology group has 40 people, how many people are in the Labor Practice group? | 60 | NULL | free_form |
stat132 | /home/yz979/scratch/chengye/math/data/original_set/statset/images/images/132.png | A small ball can randomly roll and stop on the tiles of a grid as shown in the figure. Each tile has the same size and texture. What is the probability that the ball stops in the white area? | 7/9 | NULL | free_form |
stat136 | /home/yz979/scratch/chengye/math/data/original_set/statset/images/images/136.png | Refuse sorting refers to classifying garbage into different categories based on its components, properties, utilization value, and environmental impact, as well as the requirements of various disposal methods. The pie chart illustrates the garbage collection situation in a pilot area of a certain city. It is known that 60 tons of recyclable waste have been collected, and the city's total population is approximately 10 times that of the pilot area's population. Estimate the total amount of dry waste that can be collected in the entire city. | 1500 tons | NULL | free_form |
stat137 | /home/yz979/scratch/chengye/math/data/original_set/statset/images/images/137.png | As shown in the figure, in rectangle ABCD, an arc is drawn with center D and radius AD, and another arc is drawn with center C and radius CD. The two arcs intersect perfectly at point E on side BC. If a point is randomly chosen within the rectangle, and AB = 1, what is the probability that the point lies in the shaded region? | √2/4 | NULL | free_form |
stat138 | /home/yz979/scratch/chengye/math/data/original_set/statset/images/images/138.png | Xiao Hui drew a pie chart based on the output data of high-tech industries in the first quarter of 2023 released by the municipal statistics bureau. What is the central angle of the sector corresponding to 'New Materials'? _____________________ | 72° | NULL | free_form |
stat14 | /home/yz979/scratch/chengye/math/data/original_set/statset/images/images/14.png | To understand the weight situation of 5000 junior high school graduates in the district, the weights of 400 students were randomly sampled, and the frequency distribution is shown in the figure (each group of data includes the minimum value but excludes the maximum value). Among them, the heights of the first four small rectangles from left to right are 0.02, 0.03, 0.04, and 0.05, respectively. Based on this, the number of students whose weight is no less than 60 kg in the district is approximately ______. | 1500 | NULL | free_form |
stat140 | /home/yz979/scratch/chengye/math/data/original_set/statset/images/images/140.png | As shown in the figure, the bar chart describes the number of parts processed daily by workers in a certain workshop. The median number of parts processed daily by these workers is __________. | 6 | NULL | free_form |
stat141 | /home/yz979/scratch/chengye/math/data/original_set/statset/images/images/141.png | A tree breeding trial base for a forest species, known as 'Seedless Poplar,' conducts regular measurements to fully understand the growth patterns of seedlings from this species. A random sample of 1000 seedlings was taken, and the height (x) in cm was measured. As shown in the chart, approximately how many of these 'Seedless Poplar' seedlings have a height of 300 cm or more? | 280 | NULL | free_form |
stat142 | /home/yz979/scratch/chengye/math/data/original_set/statset/images/images/142.png | The following is a bar chart showing the number of new energy vehicles in China from 2018 to 2022. In 2022, the number of new energy vehicles increased by _______ million compared to 2021. From 2019 to 2022, the year with the highest annual growth rate of new energy vehicles was _______. | 526 2022 | NULL | free_form |
stat143 | /home/yz979/scratch/chengye/math/data/original_set/statset/images/images/143.png | As shown in the figure, an impurity flows into a horizontally placed 'sun-shaped' pipe with the same thickness through the inlet. There are filters installed at points A, B, and C. The impurity is most likely to pass through the filter at ________. | B | NULL | free_form |
stat144 | /home/yz979/scratch/chengye/math/data/original_set/statset/images/images/144.png | To understand the physical fitness of seventh-grade boys in a certain school, 50 boys from the seventh grade were selected for a one-minute rope skipping test. After organizing the obtained data, a frequency distribution histogram was created (as shown). It is known that the frequency ratios of the first, second, third, and fourth groups in the chart, from left to right, are 1:3:4:2. Then the number of boys among the 50 selected who skipped rope 100 times or more in one minute is ______. | 30 | NULL | free_form |
stat145 | /home/yz979/scratch/chengye/math/data/original_set/statset/images/images/145.png | A middle school has 1600 students. To understand the students' commuting methods, a bar chart was created after surveying some students. What is the sample size for this survey? | 48 | NULL | free_form |
stat146 | /home/yz979/scratch/chengye/math/data/original_set/statset/images/images/146.png | As shown in the figure, assume that a point can be freely chosen in the pattern composed of two identical squares. What is the probability that this point is located in the shaded area? | 2/7 | NULL | free_form |
stat147 | /home/yz979/scratch/chengye/math/data/original_set/statset/images/images/147.png | As shown in the figure, a dart game board is composed of equally-sized small square grids. A dart is randomly thrown onto the game board, and each time the dart lands on the board. What is the probability of hitting the shaded area? | 1/3 | NULL | free_form |
stat148 | /home/yz979/scratch/chengye/math/data/original_set/statset/images/images/148.png | As shown in the figure, Xiao Liang has drawn two incomplete statistical charts based on the number of students in the class who like four types of ball games (each student in the class chooses one of these four kinds of ball games). The number of students who like 'table tennis' is ____. | 20 | NULL | free_form |
stat15 | /home/yz979/scratch/chengye/math/data/original_set/statset/images/images/15.png | As shown in the figure, two concentric circles are divided into eight equal parts by four diameters. What is the probability of a dart landing in the black region? | 1/2 | NULL | free_form |
stat150 | /home/yz979/scratch/chengye/math/data/original_set/statset/images/images/150.png | As shown in the circuit diagram, the probability that the light bulb does not light up when two of the switches S1, S2, and S3 are randomly closed is _____. | 1/3 | NULL | free_form |
stat151 | /home/yz979/scratch/chengye/math/data/original_set/statset/images/images/151.png | 3. As shown in the figure, when a group conducted the experiment 'using relative frequency to estimate probability,' they provided the above frequency histogram. The experiment that matches this result is ______ (fill in the serial number). ① Tossing a coin with the result of heads up; ② Drawing a card randomly from a deck without jokers, with the card's suit being spades; ③ Rolling a six-sided die, with the result being 6 upward; ④ Drawing one ball randomly from a bag containing 1 red ball and 2 black balls, with the result being a red ball. | ④ | NULL | free_form |
stat152 | /home/yz979/scratch/chengye/math/data/original_set/statset/images/images/152.png | Based on the frequency distribution histogram of the heights of 40 students in a class (each group does not include the starting value but includes the ending value), answer the following questions:
(1) The height range with the greatest number of students is ______;
(2) The percentage of students taller than 175cm in the entire class is ______. | Between 165cm and 170cm (inclusive of 170cm) 15% | NULL | free_form |
stat153 | /home/yz979/scratch/chengye/math/data/original_set/statset/images/images/153.png | In the diagram, in a 2x2 grid marked with numbers 1, 2, 3, and 4, if two small squares are selected at random, what is the probability that the sum of the numbers on the selected squares equals 4? | 1/6 | NULL | free_form |
stat154 | /home/yz979/scratch/chengye/math/data/original_set/statset/images/images/154.png | The frequency distribution histogram of the housework time for Class 7(1) with 40 students last week is shown in the figure. Let the median of this data be mh, then m ________ 2.6 (fill with '>', '=', '<'). | < | NULL | free_form |
stat156 | /home/yz979/scratch/chengye/math/data/original_set/statset/images/images/156.png | As shown in the diagram, it reflects the methods of commuting (by car, walking, cycling) for students in Class 3, Grade 9, of a certain school in the form of a bar chart (partial) and a pie chart. What is the central angle representing the percentage of students walking in the pie chart? | 72° | NULL | free_form |
stat158 | /home/yz979/scratch/chengye/math/data/original_set/statset/images/images/158.png | As shown in the figure, it is a pattern consisting of 12 congruent equilateral triangles. Suppose a point is randomly selected in the figure, what is the probability that this point lies in the shaded area? | 1/2 | NULL | free_form |
stat159 | /home/yz979/scratch/chengye/math/data/original_set/statset/images/images/159.png | In an opaque box, there are ten balls of two colors, black and white, which are identical in all other aspects except for their color. After thoroughly mixing the balls in the box, a ball is randomly drawn, its color is noted, and then it is returned to the box. The process is repeated continuously. After organizing the data, a graph showing the relationship between 'the frequency of drawing a black ball' and 'the total number of draws' is produced, as illustrated in the figure. Based on the analysis, it can be inferred that the balls with the higher count in the box are (fill in 'black balls' or 'white balls'). | White balls | NULL | free_form |
stat16 | /home/yz979/scratch/chengye/math/data/original_set/statset/images/images/16.png | Jia and Yi participated in five standing long jump tests before this year's physical fitness exam. Their scores are shown in the chart. Based on the analysis, who do you think has more stable results? | Jia | NULL | free_form |
stat160 | /home/yz979/scratch/chengye/math/data/original_set/statset/images/images/160.png | Every year on June 5th is 'World Environment Day'. To promote this year's 'World Environment Day', a middle school conducted a survey among all teachers and students with the theme 'Protect the environment, start with me'. The survey results were analyzed and organized into the following two statistical charts. Among them:
A. Can throw trash into designated areas and also consider waste classification.
B. Can throw trash into designated areas but do not consider waste classification.
C. Occasionally throw trash into designated areas.
D. Randomly litter.
Based on the information above, answer the following question: If the school has a total of 1600 teachers and students, approximately how many people randomly litter? | 160 | NULL | free_form |
stat161 | /home/yz979/scratch/chengye/math/data/original_set/statset/images/images/161.png | The librarian of a school was organizing extracurricular books in the reading room and created an incomplete pie chart with data on three categories of books: Category A, Category B, and Category C. It is known that there are 30 books in Category A. How many books are there in Category C? | 80 | NULL | free_form |
stat162 | /home/yz979/scratch/chengye/math/data/original_set/statset/images/images/162.png | A flower shop sells three types of flowers priced at 10 yuan, 18 yuan, and 25 yuan respectively. If a pie chart represents the sales volume of these three types of flowers for a certain month, calculate the average selling price of the flowers in this shop based on the chart. | 17 | NULL | free_form |
stat164 | /home/yz979/scratch/chengye/math/data/original_set/statset/images/images/164.png | A dairy company plans to export a batch of milk powder with a specification of 500 grams per can. There are two suppliers, A and B, offering the goods. Their prices are the same, and the quality is also similar. The quality inspector randomly samples 15 cans from each supplier for testing. The measured average weight of both batches is 500 grams, and the weight data is displayed as a broken line statistics chart. Based on the chart, compare the variances of the weights of milk powder from suppliers A and B, denoted as S²_1 and S²_2 (fill in '>' or '=' or '<'). | < | NULL | free_form |
stat165 | /home/yz979/scratch/chengye/math/data/original_set/statset/images/images/165.png | A math test score of a certain class was analyzed statistically, and the number of students in each score segment is shown in the figure. Please answer the following questions based on the graph: The class has ______ students, the frequency of the 70~79 segment is ______, and the relative frequency is ______. | 60 18 0.3 | NULL | free_form |
stat166 | /home/yz979/scratch/chengye/math/data/original_set/statset/images/images/166.png | 8. Xiaohua is playing a dart game on a 4×4 square grid paperboard as shown in the figure (each dart falls on the board, and the chances of landing on any point on the board are equal). What is the probability of the dart landing in the shaded region? | 5/16 | NULL | free_form |
stat167 | /home/yz979/scratch/chengye/math/data/original_set/statset/images/images/167.png | As shown in the figure, during a physical education class, six students A, B, C, D, E, and F stand at the six vertices of a regular hexagon (facing the interior of the hexagon) to play a passing game. The rule is: the ball cannot be passed to oneself or to the person on the immediate left or right. If the ball is currently with A, what is the probability that after two passes, the ball ends up back with A? | 1/3 | NULL | free_form |
stat168 | /home/yz979/scratch/chengye/math/data/original_set/statset/images/images/168.png | Two groups of 10 data points, Group A and Group B, are plotted as a line chart (as shown in the figure). The mean of both groups is 7. Let the variances of Group A and Group B be S_A² and S_B², respectively. Then S_A² ______ S_B². (Fill in '>', '=', or '<') | < | NULL | free_form |
stat169 | /home/yz979/scratch/chengye/math/data/original_set/statset/images/images/169.png | Dongdong Community, in the activity of creating a National Sanitary City, randomly selected some households in the community to check the implementation of 'garbage classification' during a certain week in May, and created an incomplete statistical chart as shown (A. Less than 5 days; B. 5 days; C. 6 days; D. 7 days). The sample size of this survey is ________, and the central angle of the sector corresponding to part A of the pie chart is ________. | 60 108° | NULL | free_form |
stat17 | /home/yz979/scratch/chengye/math/data/original_set/statset/images/images/17.png | Since the course reform, math teachers have actively organized students to participate in 'comprehensive and practical' activities. The school randomly surveyed some seventh-grade students about the time they spent participating in the 'comprehensive and practical' activities during a certain month and used the obtained data to create an incomplete statistical chart (as shown in the figure). According to the information in the figure, the central angle of the '1.5-hour' section in the pie chart is ____________. | 144° | NULL | free_form |
stat170 | /home/yz979/scratch/chengye/math/data/original_set/statset/images/images/170.png | As shown in the figure, the chart represents the scores of basketball shooting tests (10 attempts per round) for two players, A and B, each taking six rounds. We can determine which player's performance is more consistent (fill in A or B). | A | NULL | free_form |
stat171 | /home/yz979/scratch/chengye/math/data/original_set/statset/images/images/171.png | As shown in the diagram, in the square ABCD, arcs are drawn with the four vertices as centers and half the side length as their radii. If a grain of rice (the size of the grain can be ignored) is randomly thrown into square ABCD, what is the probability that the grain will land in the shaded region in the diagram? ________. | π/4 | NULL | free_form |
stat172 | /home/yz979/scratch/chengye/math/data/original_set/statset/images/images/172.png | As shown in the diagram, in the dart game board, each small square is identical except for the colored area shown in the figure. If a dart is thrown once (assuming each dart always lands on the game board), what is the probability of hitting the colored small square (shaded area)? | 5/9 | NULL | free_form |
stat173 | /home/yz979/scratch/chengye/math/data/original_set/statset/images/images/173.png | As shown in the diagram, if two of the four switches S1, S2, S3, and S4 are randomly closed, what is the probability of making the small bulb L light up? | 2/3 | NULL | free_form |
stat174 | /home/yz979/scratch/chengye/math/data/original_set/statset/images/images/174.png | The "Double Reduction" policy stipulates that the average time for completing written homework in junior high school should not exceed 90 minutes. A certain school surveyed the time taken by 640 ninth-grade students to complete their written homework after the "Double Reduction" policy. From this grade, 40 students were randomly selected for investigation. The statistical results are shown in the graph. Estimate the approximate number of students in this grade who complete their written homework in no more than 90 minutes after the "Double Reduction" policy. | 576 | NULL | free_form |
stat175 | /home/yz979/scratch/chengye/math/data/original_set/statset/images/images/175.png | As shown in the figure, there is a circuit diagram with 4 switches A, B, C, D, and 1 small light bulb. Closing switches A and B simultaneously or closing switches C and D simultaneously can make the light bulb glow. Now, two switches are closed at random. What is the probability that the light bulb will glow? | 1/3 | NULL | free_form |
stat176 | /home/yz979/scratch/chengye/math/data/original_set/statset/images/images/176.png | Lucky draw! There are 3 opaque boxes, each containing several small balls (identical except for their colors). Rule: Each time, only one ball can be drawn. Drawing a red ball rewards a cup of milk tea, while drawing a yellow ball rewards an ice cream. If Xiaoli wants to get a cup of milk tea, she should choose to draw from box number ______ to maximize her chances. | 2 | NULL | free_form |
stat177 | /home/yz979/scratch/chengye/math/data/original_set/statset/images/images/177.png | A pig farm has a total of 5000 pigs. Randomly selecting 200 pigs for quality statistics results in a frequency distribution histogram (each group includes the lower boundary but not the upper boundary) as shown in the diagram. The frequency of pigs weighing less than 80kg is ________. | 30% | NULL | free_form |
stat178 | /home/yz979/scratch/chengye/math/data/original_set/statset/images/images/178.png | As shown in Figure 1, the logo of the 24th International Congress of Mathematicians was designed based on the chord diagram of Zhao Shuang, an ancient Chinese mathematician. Suppose a point is randomly selected in the chord diagram region as shown in Figure 2. If the square ABCD has AB=5 and AF=4, then the probability that the point falls in the shaded area is _____. | 24/25 | NULL | free_form |
stat179 | /home/yz979/scratch/chengye/math/data/original_set/statset/images/images/179.png | As shown in the figure, it is a pie chart being drawn, where the entire circle represents the total number of eighth-grade students participating in extension courses. Which sector represents the number of students participating in the 'Practical Mathematics' extension course, accounting for 35% of the total number? (Fill in 'N', 'M', 'P', or 'Q') | M | NULL | free_form |
stat18 | /home/yz979/scratch/chengye/math/data/original_set/statset/images/images/18.png | As shown in the diagram, it is a statistical chart of the average daily temperature in May's early days for locations A and B. Determine the relationship of the temperature variances: s²_A ______ s²_B (fill in '<' or '>'), and identify which location has more stable temperatures: ______. | > B | NULL | free_form |
stat180 | /home/yz979/scratch/chengye/math/data/original_set/statset/images/images/180.png | As shown in the figure, to measure the area of an irregular region on flat ground (the shaded part in the figure), a square with a side length of 3m is drawn so that the irregular region is within the square. Now, small stones are randomly scattered within the square (assuming that every point within the square is equally likely to have a stone fall on it). After numerous repeated trials, it is found that the frequency of small stones falling in the irregular region stabilizes at a constant 0.25. Based on this, the estimated area of the irregular region is _________ m². | 2.25 | NULL | free_form |
stat181 | /home/yz979/scratch/chengye/math/data/original_set/statset/images/images/181.png | To implement the Ministry of Education's requirement to 'ensure students have one hour of physical activity inside and outside school every day', the school requires students to exercise regularly. Xiao Liang recorded his outdoor exercise time (in minutes) over seven days in a week and created the following statistical chart: What is the median time of Xiao Liang's outdoor exercise over these seven days (in minutes)? | 70 | NULL | free_form |
stat182 | /home/yz979/scratch/chengye/math/data/original_set/statset/images/images/182.png | A company has two workshops producing the same product, with their output increasing from 1,000 units last year to 1,500 units this year. However, the statistical graphs reported by the two workshop heads are different. Which workshop head's graph—'Graph A' or 'Graph B'—more accurately reflects the increase in product output? | Graph A | NULL | free_form |
stat183 | /home/yz979/scratch/chengye/math/data/original_set/statset/images/images/183.png | As shown in the figure, a floor is paved with identical square tiles, and a treasure is hidden under one of the tiles. What is the probability that the treasure is in the black area? | 1/2 | NULL | free_form |
stat185 | /home/yz979/scratch/chengye/math/data/original_set/statset/images/images/185.png | As shown in the figure, on a circular disc with a radius of 30 cm, the length of AB is 20 cm. If the pointer at the center of the disc rotates, what is the probability that the pointer points to position I? | 1/3 | NULL | free_form |
stat186 | /home/yz979/scratch/chengye/math/data/original_set/statset/images/images/186.png | As shown in the figure, point O is located on the diagonal FD of a regular hexagon ABCDEF. If a point P is randomly selected within the hexagon, what is the probability that point P lies in the shaded region? | 1/3 | NULL | free_form |
stat187 | /home/yz979/scratch/chengye/math/data/original_set/statset/images/images/187.png | A company decided to recruit an employee. The scores of an applicant in three quality tests are shown in the table below: Test Item Innovation Ability Professional Knowledge Language Expression Test Score (points) 70 80 92 The comprehensive score is determined according to the proportions shown in the figure. What is the applicant's final score? | 79.5 | NULL | free_form |
stat188 | /home/yz979/scratch/chengye/math/data/original_set/statset/images/images/188.png | 9. An ant crawls onto a tile as shown in the figure and randomly stops at a certain position. What is the probability that it stops in the shaded area? ______ | 1/3 | NULL | free_form |
stat189 | /home/yz979/scratch/chengye/math/data/original_set/statset/images/images/189.png | 4. Two people, A and B, play a game. Each of them randomly picks a card. If the product of the two numbers is even, A wins; otherwise, B wins. Based on this rule, _______ has a higher chance of winning. | A | NULL | free_form |
stat19 | /home/yz979/scratch/chengye/math/data/original_set/statset/images/images/19.png | There are two classes, A and B, each with 45 students taking a test. Each participant can score one of the following values: 0, 1, 2, 3, 4, 5, 6, 7, 8, or 9. The test results of Class A are shown in the table, and the results of Class B are shown in the figure.
(1) Based on observation, the class with the larger variance is _______________.
(2) If a total of 60 students from both classes pass, what is the minimum score a participant must achieve to pass? __________ | A 4 | NULL | free_form |
stat190 | /home/yz979/scratch/chengye/math/data/original_set/statset/images/images/190.png | As shown in the figure, the areas of the six sectors on the spinning wheel are equal. The wheel is spun 3 times (if the pointer stops on a dividing line, it is spun again). It is recorded that the pointer points to the number 2 a total of 2 times. What is the frequency of the number 2 appearing? | 2/3 | NULL | free_form |
stat191 | /home/yz979/scratch/chengye/math/data/original_set/statset/images/images/191.png | As shown in the figure, in a 3×3 square grid, three small squares are painted black, while the others are white. Now, one white square is painted black. What is the probability that the black parts will form a centrally symmetric figure? | 1/2 | NULL | free_form |
stat193 | /home/yz979/scratch/chengye/math/data/original_set/statset/images/images/193.png | As shown in the figure, the probability of randomly closing two of the switches K1, K2, and K3, such that both bulbs L1 and L2 light up simultaneously, is ________. | 1/3 | NULL | free_form |
stat194 | /home/yz979/scratch/chengye/math/data/original_set/statset/images/images/194.png | Use two freely rotating spinners as shown in the figure to play the 'Match Purple' game: The player spins both spinners simultaneously. If one spinner lands on red and the other spinner lands on blue, the player wins. What is the probability of the player winning? ______. | 2/3 | NULL | free_form |
stat195 | /home/yz979/scratch/chengye/math/data/original_set/statset/images/images/195.png | 5. Five students, A, B, C, D, and E, participated in a holiday event. Fortunately, each of them received a delicate gift (as shown in the diagram). They can only take a gift from the bottom of one branch at a time until all gifts are taken. A picks the first gift, followed by B, C, D, and finally E, who take the second to fifth gifts respectively. Naturally, there are various ways to pick the gifts. How many different ways can they pick gifts in total? Afterward, they opened the gifts and compared them carefully, discovering that gift D is the most exquisite. Based on the possibilities, which student is most likely to obtain gift D? | 10 C | NULL | free_form |
stat196 | /home/yz979/scratch/chengye/math/data/original_set/statset/images/images/196.png | Two large squares with a side length of 6 overlap to form a small square with a side length of 3. Xiao Ming and Xiao Gang are playing a game of hiding objects. The probability that Xiao Ming hides the object in the shaded area is __________. | 6/7 | NULL | free_form |
stat198 | /home/yz979/scratch/chengye/math/data/original_set/statset/images/images/198.png | Company A and Company B have compiled the following line charts based on car sales over the past few years. From 2010 to 2014, which of these two companies experienced faster sales growth? | Company A | NULL | free_form |
stat199 | /home/yz979/scratch/chengye/math/data/original_set/statset/images/images/199.png | As shown in the figure, there are 9 blind boxes placed horizontally on the shelf, all with identical outer packaging. Each blind box contains one item. There are 5 blind boxes containing product A and 4 blind boxes containing product B. If one blind box is randomly selected, which product is more likely to be drawn? (Answer with 'A' or 'B') | A | NULL | free_form |
stat20 | /home/yz979/scratch/chengye/math/data/original_set/statset/images/images/20.png | In order to understand the construction of the 'Book Aroma Campus' in a certain school in our city, an inspection team randomly selected 40 students from the school to investigate their extracurricular reading time over a week and plotted the results into a frequency distribution chart (the time value for each group includes the minimum value but excludes the maximum value). Based on the information in the chart, estimate the percentage of students in the school whose weekly extracurricular reading time is no less than 4 hours to the nearest whole number. | 60% | NULL | free_form |
stat200 | /home/yz979/scratch/chengye/math/data/original_set/statset/images/images/200.png | In 2022, the sales of new energy vehicles (NEVs) in China continued to grow, with annual sales reaching approximately 5.267 million units, an increase of 9.7%, marking the eighth consecutive year of being ranked first globally. The chart reflects the monthly NEV sales and year-on-year growth rates for 2021 and 2022. (The 2022 year-on-year growth rate = (2022 monthly sales − 2021 monthly sales) ÷ 2021 monthly sales × 100%). Based on the data provided in the chart, which of the following statements are correct? (Answer with the sequence numbers only). ① Compared to 2021, the highest year-on-year growth rate for NEVs in 2022 occurred in February, reaching 181.1%. ② Compared to 2021, the year-on-year growth rate for NEVs in 2022 remained consistently lower from June onward. ③ In 2021, the month with the highest NEV sales was December, exceeding 400,000 units. ④ In 2022, the months with NEV sales exceeding 500,000 units numbered six. ⑤ December 2022 was the month with the highest NEV sales. | ①②③④⑤ | NULL | free_form |
stat201 | /home/yz979/scratch/chengye/math/data/original_set/statset/images/images/201.png | After school, Zhao Hua first took a bus to the bookstore to buy books and then walked home. His journey is shown in the diagram. How many minutes did the entire trip take in total? | 32 | NULL | free_form |
stat202 | /home/yz979/scratch/chengye/math/data/original_set/statset/images/images/202.png | As shown in the diagram, a Zhaoshang chord diagram is formed by four congruent right triangles and a small square. If a dart is randomly thrown onto the board, what is the probability that the dart lands in the shaded area? | 1/4 | NULL | free_form |
stat203 | /home/yz979/scratch/chengye/math/data/original_set/statset/images/images/203.png | As shown in the figure, the spinner is divided into four equal sectors. If the spinner is spun twice, what is the probability that the pointer lands in the gray region both times? | 1/4 | NULL | free_form |
stat204 | /home/yz979/scratch/chengye/math/data/original_set/statset/images/images/204.png | As shown in the diagram, there are three switches (①, ②, ③) and a small light bulb in the circuit. If any two switches on the circuit are closed, what is the probability that the small light bulb lights up? | 2/3 | NULL | free_form |
stat205 | /home/yz979/scratch/chengye/math/data/original_set/statset/images/images/205.png | In the 'Books into Campus' reading activity, a student created a line graph showing the number of extracurricular books read by their group from August to December. The group's average number of extracurricular books read per month is ___ books. | 25 | NULL | free_form |
stat206 | /home/yz979/scratch/chengye/math/data/original_set/statset/images/images/206.png | As shown in the figure, one of the switches S1 or S2 in the circuit diagram is randomly closed. What is the probability that the light bulb will light up? | 1/2 | NULL | free_form |
stat207 | /home/yz979/scratch/chengye/math/data/original_set/statset/images/images/207.png | The sales department of a computer company conducted a statistics survey on the sales volume of 20 salespeople this month and plotted it into the statistical chart as shown in the figure. The median sales volume of these 20 salespeople this month is __________ units. | 20 | NULL | free_form |
stat21 | /home/yz979/scratch/chengye/math/data/original_set/statset/images/images/21.png | As shown in the figure, a school conducted a survey on students' commuting methods and produced an incomplete pie chart. If the school has a total of 1500 students, estimate how many of them walk to school_______. | 600 | NULL | free_form |
stat210 | /home/yz979/scratch/chengye/math/data/original_set/statset/images/images/210.png | A forestry bureau has created a line chart to display the survival rate of a certain type of transplanted sapling. From the chart, estimate the survival probability of this transplanted sapling (accurate to 0.1). | 0.8 | NULL | free_form |
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