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discrete probability distribution : probability distribution associated with variables that take on a finite or countably infinite number of distinct values
https://openstax.org/books/principles-data-science/pages/3-key-terms
discrete random variable : a random variable where there is only a finite or countable infinite number of values that the variable can take on
https://openstax.org/books/principles-data-science/pages/3-key-terms
empirical probability : a probability that is calculated based on data that has been collected from an experiment
https://openstax.org/books/principles-data-science/pages/3-key-terms
empirical rule : a rule that provides the percentages of data values falling within one, two, and three standard deviations from the mean for a bell-shaped (normal) distribution
https://openstax.org/books/principles-data-science/pages/3-key-terms
event : a subset of the sample space
https://openstax.org/books/principles-data-science/pages/3-key-terms
frequency : a count of the number of times that an event or observation occurs in an experiment or study
https://openstax.org/books/principles-data-science/pages/3-key-terms
frequency distribution : a method of organizing and summarizing a dataset that provides the frequency with which each value in the dataset occurs
https://openstax.org/books/principles-data-science/pages/3-key-terms
independent events : events where the probability of occurrence of one event is not affected by the occurrence of another event
https://openstax.org/books/principles-data-science/pages/3-key-terms
interquartile range (IQR) : a number that indicates the spread of the middle half, or middle 50%, of the data; the difference between the third quartile (Q3Q3) and the first quartile (Q1Q1)
https://openstax.org/books/principles-data-science/pages/3-key-terms
mean (also called arithmetic mean) : a measure of center of a dataset, calculated by adding up the data values and dividing the sum by the number of data values; average
https://openstax.org/books/principles-data-science/pages/3-key-terms
median : the middle value in an ordered dataset
https://openstax.org/books/principles-data-science/pages/3-key-terms
mode : the most frequently occurring data value in a dataset
https://openstax.org/books/principles-data-science/pages/3-key-terms
mutually exclusive events : events that cannot occur at the same time
https://openstax.org/books/principles-data-science/pages/3-key-terms
normal distribution : a bell-shaped distribution curve that is used to model many measurements, including IQ scores, salaries, heights, weights, blood pressures, etc.
https://openstax.org/books/principles-data-science/pages/3-key-terms
outcome : the result of a single trial in a probability experiment
https://openstax.org/books/principles-data-science/pages/3-key-terms
outliers : data values that are significantly different from the other data values in a dataset
https://openstax.org/books/principles-data-science/pages/3-key-terms
percentiles : numbers that divide an ordered dataset into hundredths; used to describe the relative standing of a particular value within a dataset by indicating the percentage of data points that fall below it
https://openstax.org/books/principles-data-science/pages/3-key-terms
Poisson distribution : a probability distribution for discrete random variables used to calculate probabilities for a certain number of occurrences in a specific interval
https://openstax.org/books/principles-data-science/pages/3-key-terms
population data : data representing all the outcomes or measurements that are of interest
https://openstax.org/books/principles-data-science/pages/3-key-terms
population mean : the average for all measurements of interest corresponding to the entire group under study
https://openstax.org/books/principles-data-science/pages/3-key-terms
population size : the number of measurements for the entire group under study
https://openstax.org/books/principles-data-science/pages/3-key-terms
probability : a numerical measure that assesses the likelihood of occurrence of an event
https://openstax.org/books/principles-data-science/pages/3-key-terms
probability analysis : provides the tools to model, understand, and quantify uncertainties, allowing data scientists to make informed decisions from data
https://openstax.org/books/principles-data-science/pages/3-key-terms
probability density function (PDF) : a function that is used to describe the probability distribution of a continuous random variable
https://openstax.org/books/principles-data-science/pages/3-key-terms
probability distribution : a mathematical function that assigns probabilities to various outcomes
https://openstax.org/books/principles-data-science/pages/3-key-terms
probability mass function (PMF) : a function that is used to define the probability distribution of a discrete random variable
https://openstax.org/books/principles-data-science/pages/3-key-terms
quartiles : numbers that divide an ordered dataset into quarters; the second quartile is the same as the median
https://openstax.org/books/principles-data-science/pages/3-key-terms
random variable : a variable where a single numerical value is assigned to a specific outcome from an experiment
https://openstax.org/books/principles-data-science/pages/3-key-terms
range : a measure of dispersion for a dataset calculated by subtracting the minimum from the maximum of the dataset
https://openstax.org/books/principles-data-science/pages/3-key-terms
relative frequency probability : a method of determining the likelihood of an event occurring based on the observed frequency of its occurrence in a given sample or population
https://openstax.org/books/principles-data-science/pages/3-key-terms
sample data : data representing outcomes or measurements collected from a subset or part of a population
https://openstax.org/books/principles-data-science/pages/3-key-terms
sample mean : the average for a subset of the measurements of interest
https://openstax.org/books/principles-data-science/pages/3-key-terms
sample size : the number of measurements for the subset taken from the overall population
https://openstax.org/books/principles-data-science/pages/3-key-terms
sample space : the set of all possible outcomes in a probability experiment
https://openstax.org/books/principles-data-science/pages/3-key-terms
standard deviation : a measure of the spread of a dataset, given in the same units as the data, that indicates how far a typical data value is from the mean
https://openstax.org/books/principles-data-science/pages/3-key-terms
standard normal distribution : a normal distribution with mean of 0 and standard deviation of 1
https://openstax.org/books/principles-data-science/pages/3-key-terms
statistical analysis : the science of collecting, organizing, and interpreting data to make decisions
https://openstax.org/books/principles-data-science/pages/3-key-terms
theoretical probability : a probability that is calculated based on an assessment of equally likely outcomes
https://openstax.org/books/principles-data-science/pages/3-key-terms
trimmed mean : a calculation for the average or mean of a dataset where some percentage of data values are removed from the lower and upper end of the dataset; typically used to mitigate the effects of outliers on the mean
https://openstax.org/books/principles-data-science/pages/3-key-terms
variance : the measure of the spread of data values in a dataset based on the squared deviations from the mean, which is the average of the squared deviations of the observations from the mean
https://openstax.org/books/principles-data-science/pages/3-key-terms
zz-score : a measure of the position of a data value in the dataset, calculated by subtracting the mean from the data value and then dividing the difference by the standard deviation
https://openstax.org/books/principles-data-science/pages/3-key-terms
alternative hypothesis : a complementary statement regarding an unknown population parameter used in hypothesis testing
https://openstax.org/books/principles-data-science/pages/4-key-terms
analysis of variance (ANOVA) : statistical method to compare three or more means and determine if the means are all statistically the same or if at least one mean is different from the others
https://openstax.org/books/principles-data-science/pages/4-key-terms
best-fit linear equation : an equation of the formy^=a+bxy^=a+bxthat provides the best-fit straight line to the(x,y)(x,y)data points
https://openstax.org/books/principles-data-science/pages/4-key-terms
bivariate data : data collected on two variables where the data values are paired with one another
https://openstax.org/books/principles-data-science/pages/4-key-terms
bootstrapping : a method to construct a confidence interval that is based on repeated sampling and does not rely on any assumptions regarding the underlying distribution
https://openstax.org/books/principles-data-science/pages/4-key-terms
central limit theorem : describes the relationship between the sample distribution of sample means and the underlying population
https://openstax.org/books/principles-data-science/pages/4-key-terms
confidence interval : an interval where sample data is used to provide an estimate for a population parameter
https://openstax.org/books/principles-data-science/pages/4-key-terms
confidence level : the probability that the interval estimate will contain the population parameter, given that the estimation process on the parameter is repeated over and over
https://openstax.org/books/principles-data-science/pages/4-key-terms
correlation : a measure of association between two numeric variables
https://openstax.org/books/principles-data-science/pages/4-key-terms
correlation analysis : a statistical method used to evaluate and quantify the strength and direction of the linear relationship between two quantitative variables
https://openstax.org/books/principles-data-science/pages/4-key-terms
correlation coefficient : a measure of the strength and direction of the linear relationship between two variables
https://openstax.org/books/principles-data-science/pages/4-key-terms
critical value : z-score that cuts off an area under the normal curve corresponding to a specified confidence level
https://openstax.org/books/principles-data-science/pages/4-key-terms
dependent samples : samples from one population that can be paired or matched to the samples taken from the second population
https://openstax.org/books/principles-data-science/pages/4-key-terms
dependent variable : in correlation analysis, the variable being studied or measured; the dependent variable is the outcome that is measured or observed to determine the impact of changes in the independent variable
https://openstax.org/books/principles-data-science/pages/4-key-terms
F distribution : a skewed probability distribution that arises in statistical hypothesis testing, such as ANOVA analysis
https://openstax.org/books/principles-data-science/pages/4-key-terms
hypothesis testing : a statistical method to test claims regarding population parameters using sample data
https://openstax.org/books/principles-data-science/pages/4-key-terms
independent samples : the sample from one population that is not related to the sample taken from the second population
https://openstax.org/books/principles-data-science/pages/4-key-terms
independent variable : in correlation analysis, the variable that is manipulated or changed in an experiment or study; the value of the independent variable is controlled or chosen by the experimenter to observe its effect on the dependent variable
https://openstax.org/books/principles-data-science/pages/4-key-terms
inferential statistics : statistical methods that allow researchers to infer or generalize observations from samples to the larger population from which they were selected
https://openstax.org/books/principles-data-science/pages/4-key-terms
least squares method : a method used in linear regression that generates a straight line fit to the data values such that the sum of the squares of the residual is the least sum possible
https://openstax.org/books/principles-data-science/pages/4-key-terms
level of significance (aa) : the maximum allowed probability of making a Type I error; the level of significance is the probability value used to determine when the sample data indicates significant evidence against the null hypothesis
https://openstax.org/books/principles-data-science/pages/4-key-terms
linear correlation : a measure of the association between two variables that exhibit an approximate straight-line fit when plotted on a scatterplot
https://openstax.org/books/principles-data-science/pages/4-key-terms
margin of error : an indication of the maximum error of the estimate
https://openstax.org/books/principles-data-science/pages/4-key-terms
matched pairs : samples from one population that can be paired or matched to the samples taken from the second population
https://openstax.org/books/principles-data-science/pages/4-key-terms
method of least squares : a mathematical method to generate a linear equation that is the “best fit” to the points on the scatterplot in the sense that the line minimizes the differences between the predicted values and observed values for y
https://openstax.org/books/principles-data-science/pages/4-key-terms
modeling : the process of creating a mathematical representation that describes the relationship between different variables in a dataset; the model is then used to understand, explain, and predict the behavior of the data
https://openstax.org/books/principles-data-science/pages/4-key-terms
nonparametric methods : statistical methods that do not rely on any assumptions regarding the underlying distribution
https://openstax.org/books/principles-data-science/pages/4-key-terms
null hypothesis : statement of no effect or no change in the population
https://openstax.org/books/principles-data-science/pages/4-key-terms
p-value : the probability of obtaining a sample statistic with a value as extreme as (or more extreme than) the value determined by the sample data under the assumption that the null hypothesis is true
https://openstax.org/books/principles-data-science/pages/4-key-terms
parametric methods : statistical methods that assume a specific form for the underlying distribution
https://openstax.org/books/principles-data-science/pages/4-key-terms
point estimate : a sample statistic used to estimate a population parameter
https://openstax.org/books/principles-data-science/pages/4-key-terms
prediction : a forecast for the dependent variable based on a specific value of the independent variable generated using the linear model
https://openstax.org/books/principles-data-science/pages/4-key-terms
proportion : a measure that expresses the relationship between a part and the whole; a proportion represents the fraction or percentage of a dataset that exhibits a particular characteristic or falls into a specific category
https://openstax.org/books/principles-data-science/pages/4-key-terms
regression analysis : a statistical technique used to model the relationship between a dependent variable and one or more independent variables
https://openstax.org/books/principles-data-science/pages/4-key-terms
residual : the difference between an observedy-value and the predictedy-value obtained from the linear regression equation
https://openstax.org/books/principles-data-science/pages/4-key-terms
sample mean : a point estimate for the unknown population mean chosen as the most unbiased estimate of the population
https://openstax.org/books/principles-data-science/pages/4-key-terms
sample proportion : chosen as the most unbiased estimate of the population, calculated as the number of successes divided by the sample size:p=xnp=xn
https://openstax.org/books/principles-data-science/pages/4-key-terms
sample statistic : a numerical summary or measure that describes a characteristic of a sample, such as a sample mean or sample proportion
https://openstax.org/books/principles-data-science/pages/4-key-terms
sampling distribution : a probability distribution of a sample statistic based on all possible random samples of a certain size from a population or the distribution of a statistic (such as the mean) that would result from taking random samples from the same population repeatedly and calculating the statistic for each ...
https://openstax.org/books/principles-data-science/pages/4-key-terms
scatterplot (or scatter diagram) : graphical display that shows values of the independent variable plotted on thexx-axis and values of the dependent variable plotted on theyy-axis
https://openstax.org/books/principles-data-science/pages/4-key-terms
standard error of the mean : the standard deviation of the sample mean, calculated as the population standard deviation divided by the square root of the sample size
https://openstax.org/books/principles-data-science/pages/4-key-terms
standardized test statistic : a numerical measure that describes how many standard deviations a particular value is from the mean of a distribution; a standardized test statistic is typically used to assess whether an observed sample statistic is significantly different from what would be expected under a null hypothes...
https://openstax.org/books/principles-data-science/pages/4-key-terms
t-distribution : a bell-shaped, symmetric distribution similar to the normal distribution, though the t-distribution has “thicker tails” as compared to the normal distribution
https://openstax.org/books/principles-data-science/pages/4-key-terms
test statistic : a numerical value used to assess the strength of evidence against a null hypothesis, calculated from sample data that is used in hypothesis testing
https://openstax.org/books/principles-data-science/pages/4-key-terms
Type I error : an error made in hypothesis testing where a researcher rejects the null hypothesis when in fact the null hypothesis is actually true
https://openstax.org/books/principles-data-science/pages/4-key-terms
Type II error : an error made in hypothesis testing where a researcher fails to reject the null hypothesis when the null hypothesis is actually false
https://openstax.org/books/principles-data-science/pages/4-key-terms
unbiased estimator : a statistic that provides a valid estimate for the corresponding population parameter without overestimating or underestimating the parameter
https://openstax.org/books/principles-data-science/pages/4-key-terms
variable : a characteristic or attribute that can be measured or observed.
https://openstax.org/books/principles-data-science/pages/4-key-terms
additive decomposition : time series decomposition into the sum of its components
https://openstax.org/books/principles-data-science/pages/5-key-terms
augmented Dickey-Fuller (ADF) test : statistical test for stationarity of a time series
https://openstax.org/books/principles-data-science/pages/5-key-terms
autocorrelation : measure of correlation between a time series and a shifted copy of itself
https://openstax.org/books/principles-data-science/pages/5-key-terms
autoregressive (AR) model : model or component of a model that captures how the time series depends on its own previous values
https://openstax.org/books/principles-data-science/pages/5-key-terms
cyclic component : large variations in the data that recur over longer time periods than seasonal fluctuations, having no fixed frequency
https://openstax.org/books/principles-data-science/pages/5-key-terms
detrending : one of two complementary operations that separate the trend component from a time series
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differencing : found by taking differences of consecutive terms, that is,xn+1−xnxn+1−xn
https://openstax.org/books/principles-data-science/pages/5-key-terms
error : extent to which predictions differ from actual observations
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exponential moving average (EMA) : type of weighted moving average in which the most recent values are given larger weights and the weights decay exponentially the further back in time the values are in the series
https://openstax.org/books/principles-data-science/pages/5-key-terms
forecasting : making predictions about future, unknown values of a time series
https://openstax.org/books/principles-data-science/pages/5-key-terms
integrative (I) component : component of the ARIMA model that represents the differencing operation
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