Glossary
- Alternative hypothesis
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A working hypothesis that is contradictory to the null hypothesis
- Anecdotal evidence
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Evidence that is based on personal testimony and collected informally
- Association
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A relationship between variables
- Bernoulli trial
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An experiment with the following characteristics:
- There are only two possible outcomes (called “success” and “failure”) for each trial.
- The probability (p) of a success is the same for any trial (so the probability q = 1 − p of a failure is the same for any trial). - Bimodal distribution
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A distribution that has two modes
- Binomial distribution
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A random variable that counts the number of successes in a fixed number (n) of independent Bernoulli trials each with probability of a success (p)
- Bivariate data
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Data consisting of two variables, often in search of an association
- Blinding
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Not telling participants which treatment they are receiving
- Block design study
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Grouping individuals based on a variable into "blocks" and then randomizing cases within each block to the treatment groups
- Case-control study
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A study that compares a group that has a certain characteristic to a group that does not, often a retrospective study for rare conditions
- Center
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The central tendency or most typical value of a dataset
- Central limit theorem (CLT)
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If there is a population with mean μ and standard deviation σ, and you take sufficiently large random samples from the population, then the distribution of the sample means will be approximately normally distributed.
- Class midpoint
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Found by adding the lower limit and upper limit, then dividing by two
- Class width
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The difference in consecutive lower class limits
- Cluster sampling
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A method of sampling where the population has already sorted itself into groups (clusters), and researchers randomly select a cluster and use every individual in the chosen cluster as the sample
- Coefficient of determination
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A numerical measure of the percentage or proportion of variation in the dependent variable (y) that can be explained by the independent variable (x)
- Cohort study
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Longitudinal study where a group of people (typically sharing a common factor) are studied and data is collected for a purpose
- Complement
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The complement of an event consists of all outcomes in a sample space that are NOT in the event.
- Completely randomized study
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Dividing participants into treatment groups randomly
- Conditional probability
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The likelihood that an event will occur given knowledge of another event
- Confidence interval
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An interval built around a point estimate for an unknown population parameter
- Confounding (lurking, conditional) variable
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A variable that has an effect on a study even though it is neither an explanatory variable nor a response variable
- Contingency (two-way) table
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A table in a matrix format that displays the frequency distribution of different variables
- Continuity correction
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When statisticians add or subtract .5 to values to improve approximation
- Continuous random variable
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A random variable (RV) whose outcomes are measured as an uncountable, infinite number of values
- Control group
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A group in a randomized experiment that receives no (or inactive) treatment but is otherwise managed exactly as the other groups
- Controlled (designed) experiment
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Type of experiment where variables are manipulated and data is collected in a controlled setting
- Convenience sampling
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Selecting individuals that are easily accessible and may result in biased data
- Correlation coefficient
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A numerical measure that provides a measure of strength and direction of the linear association between the independent variable x and the dependent variable y
- Critical value
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Point on a distribution that acts as a cut-off value for accepting or rejecting the null hypothesis
- Cross-sectional study
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Data collection on a population at one point in time (often prospective)
- Cumulative distribution function (CDF)
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A function that gives the probability that a random variable takes a value less than or equal to x
- Cumulative relative frequency
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The sum of the relative frequencies for all values that are less than or equal to the given value
- Data
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Actual values (numbers or words) that are collected from the variables of interest
- Data analysis process
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Process of collecting, organizing, and analyzing data
- Degrees of freedom
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The number of objects in a sample that are free to vary
- Descriptive statistics
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Methods of organizing, summarizing, and presenting data
- Designed (controlled) experiment
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Data collection where variables are manipulated in a controlled setting
- Difference in means
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The difference in the means of two independent populations
- Discrete random variable
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A random variable that produces discrete data
- Distribution
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The possible values a variable can take on and how often it does so
- Double-blind study
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The act of blinding both the subjects of an experiment and the researchers who work with the subjects
- Empirical rule
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Roughly 68% of values are within one standard deviation of the mean, roughly 95% of values are within two standard deviations of the mean, and 99.7% of values are within three standard deviations of the mean
- Event
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An outcome or subset of outcomes of an experiment in which you are interested
- Expected value
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Mean of a random variable
- Experimental unit
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Any individual or object to be measured
- Explanatory variable
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The independent variable in an experiment; the value controlled by researchers
- Extrapolation
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The process of predicting outside of the observed x values
- Factors
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Variables in an experiment
- Frequency
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The number of times a value occurs in the data
- Graphical descriptive methods
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Organizing, summarizing, or presenting data visually in graphs, figures, or charts
- Hypothesis testing
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A decision-making procedure for determining whether sample evidence supports a hypothesis
- Independent
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The occurrence of one event has no effect on the probability of the occurrence of another event.
- Individuals
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The person, animal, item, place, etc. about which we collect information
- Inferential statistics
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The facet of statistics dealing with using a sample to generalize (or infer) about the population
- Influential points
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Observed data points that do not follow the trend of the rest of the data and have a large influence on the calculation of the regression line
- Intersection
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The shared or common outcomes of two events (i.e., elements are in both A and B)
- Interval scale level
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Quantitative data where the difference or gap between values is meaningful
- Law of large numbers
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As the number of trials in a probability experiment increases, the relative frequency of an event approaches the theoretical probability
- Levels
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Certain values of variables in an experiment
- Linear regression
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A mathematical model of a linear association
- Longitudinal study
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Collecting data multiple times on the same individuals over a period of time, usually in fixed increments
- Lower class limit
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The lower end of a bin or class in a frequency table or histogram
- Margin of error (MoE)
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How much a point estimate can be expected to differ from the true population value; made up of the standard error multiplied by the critical value
- Matched pairs design
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Very similar individuals (or even the same individual) receive two different treatments (or treatment vs. control), then the results are compared
- Mean (average)
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A number that measures the central tendency of the data
- Measures of location
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A measure of an observation's standing relative to the rest of the dataset
- Median
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The middle number in a sorted list
- Modality
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How many peaks or clusters there appear to be in a quantitative distribution
- Mode
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The most frequently occurring value
- Mutually exclusive (disjoint)
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Two events that cannot happen at the same time; sharing no common outcomes
- Nominal scale level
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Categorical data where the the categories have no natural, intuitive, or obvious order
- Normal (Gaussian) distribution
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A commonly used symmetric, unimodal, bell-shaped, and continuous probability distribution
- Null hypothesis
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The claim that is assumed to be true and is tested in a hypothesis test
- Numerical descriptive methods
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Numbers that summarize some aspect of a dataset, often calculated
- Observational study
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Data collection where no variables are manipulated
- Ordinal scale level
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Categorical data where the the categories have a natural or intuitive order
- Outcome
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A particular result of an experiment
- Outlier
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An observation that stands out from the rest of the data significantly
- p-value
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The probability that an event will occur, assuming the null hypothesis is true
- Parameter
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A number that is used to represent a population characteristic and can only be calculated as the result of a census
- Placebo
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An inactive treatment that has no real effect on the explanatory variable
- Point estimate
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The value that is calculated from a sample used to estimate an unknown population parameter
- Point estimation
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Using sample data to calculate a single statistic as an estimate of an unknown population parameter
- Pooled proportion
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Estimate of the common value of p1 and p2
- Population
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The whole group of individuals who can be studied to answer a research question
- Population mean
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The arithmetic mean, or average, of a population
- Population mean difference
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The mean of the differences in a matched pairs design
- Population proportion
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The number of individuals that have a characteristic of interest divided by the total number in the population
- Power
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The probability of failing to reject a true hypothesis
- Probability
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The study of randomness; a number between zero and one, inclusive, that gives the likelihood that a specific event will occur
- Probability density function (PDF)
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A function that defines a continuous random variable and the likelihood of an outcome
- Probability experiment
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A random experiment where the result is not predetermined
- Probability mass function (PMF)
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A function that gives the probability that a discrete random variable is exactly equal to some value (x)
- Probability model
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A mathematical representation of a random process that lists all possible outcomes and assigns probabilities to each
- Prospective study
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Collecting information as events unfold
- Qualitative data
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Data that describes qualities or puts individuals into categories; also known as categorical data
- Quantile
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Points in a distribution that relate to the rank order of values in that distribution
- Quantitative continuous data
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Data produced by a variable that takes on an uncountable, infinite number of values
- Quantitative data
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Numerical data with a mathematical context
- Quantitative discrete data
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Data produced by a variable that takes on a countable number of values
- Random variable
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A representation of a probability model
- Ratio scale level
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Quantitative data where the difference or gap between values is meaningful AND has a true 0 value
- Relative frequency
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The percentage, proportion, or ratio of the frequency of a value of the data to the total number of outcomes
- Repeated measures
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When an individual goes through a single treatment more than once
- Residual (error)
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A residual measures the vertical distance between an observation and the predicted point on a regression line
- Response variable
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The dependent variable in an experiment; the value that is measured for change at the end of an experiment
- Retrospective study
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Collecting or using data after events have taken place
- Robust
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Not affected by violations of assumptions such as outliers
- Sample
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A subset of the population studied
- Sample mean
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The arithmetic mean, or average, of a dataset
- Sample proportion
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The number of individuals that have a characteristic of interest divided by the total number in the sample, often found from categorical data
- Sample space
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The set of all possible outcomes of an experiment
- Sampling bias
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Bias resulting from all members of the population not being equally likely to be selected
- Sampling distribution
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The probability distribution of a statistic at a given sample size
- Sampling variability
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The idea that samples from the same population can yield different results
- Shape
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The visual appearance of a dataset
- Significance level
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Probability that a true null hypothesis will be rejected, also known as type I error and denoted by α
- Simple random sample (SRS)
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Each member of the population is equally likely to be chosen for a sample of a given sample size and each sample is equally likely to be chosen
- Slope
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Tells us how the dependent variable (y) changes for every one unit increase in the independent (x) variable, on average
- Spread
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The level of variability or dispersion of a dataset; also commonly known as variation/variability
- Standard deviation
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The average distance (deviation) of each observation from the mean
- Standard error
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The standard deviation of a sampling distribution
- Standard normal distribution (SND)
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A normal random variable with a mean of 0 and standard deviation of 1 which z-scores follow; denoted N(0, 1)
- Statistic
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A number calculated from a sample
- Statistical inference
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Using information from a sample to answer a question, or generalize, about a population
- Statistically significant
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Finding sufficient evidence that the observed effect is not just due to variability, often from rejecting the null hypothesis
- Stratified sampling
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Dividing a population into groups (strata) and then using simple random sampling to identify a proportionate number of individuals from each
- Systematic (probability) sampling
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Using some sort of pattern or probability-based method for choosing your sample
- t-distribution
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A family of t–distributions, dependent on degrees of freedom, similar to the normal distribution but with more variability built in
- Test statistic
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A measure of the difference between observations and the hypothesized (or claimed) value
- Treatment combinations (interactions)
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Combinations of levels of variables in an experiment
- Treatments
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Different values or components of the explanatory variable applied in an experiment
- Tree diagram
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Diagram that helps calculate and organize the number of possible outcomes of an event or problem
- Type I error
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The decision is to reject the null hypothesis when, in fact, the null hypothesis is true
- Type II error
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Erroneously rejecting a true null hypothesis or erroneously failing to reject a false null hypothesis
- Uniform distribution
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A probability distribution in which all outcomes are equally likely
- Union
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The set of all outcomes in two (or more) events (i.e., elements are in A or B)
- Upper class limit
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The upper end of a bin or class in a frequency table or histogram
- Values
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Possible observations of the variable
- Variable
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A characteristic of interest for each person or object in a population
- Variance
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The square of the standard deviation; a computational step along the way to calculating the standard deviation
- Variation
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The level of variability or dispersion of a dataset; also commonly known as spread or variability
- Venn diagram
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A diagram that shows all possible relations between a collection of different sets
- y-intercept
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The value of y when x is 0 in a regression equation
- z-score
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A measure of location that tells us how many standard deviations a value is above or below the mean