AP®︎ Statistics: Unit 1 Flashcards
Master key terms and definitions for Unit 1 of AP Statistics – Exploring One-Variable Data and Collecting Data to help you prep for quizzes and the AP exam.
Statistical Study
A study in which data are collected from a sample to answer an investigative question about a larger population
A study in which data are collected from a sample to answer an investigative question about a larger population
The question a statistical study is designed to answer; it has a defined purpose, is answerable by collecting and analyzing data, and anticipates variation
The entire group of items or individuals of interest in a study; its size is the number of items or individuals in the population, denoted by N
A subset of the population from which data are obtained; its size is the number of items or individuals in the sample, denoted by n
A datum is one piece of information about a single item or individual; a data set is the collection of all data obtained in the study
Identifying a statistical result with the corresponding part of the real-world study
The individual or item on which data are recorded
Characteristic that may change from one observational unit to another
A numerical summary that describes a population
A numerical summary that describes a sample
Variable whose values are category names or group labels
Variable whose values are numerical amounts that measure or count something, usually with units
A discrete quantitative variable has a countable number of possible values; a continuous quantitative variable can take any value within a given interval
Table listing each category of one categorical variable and the number of observational units in each category
Table listing each category and the proportion of all included observations in that category
Proportion, relative frequency, and percentage are equivalent part-to-whole summaries of a category's share of the total; a part-to-part ratio compares one category directly to another
A graph for one categorical variable with one bar per category; bar height or length shows frequency, relative frequency, or percentage, and the bars are separated by gaps
A graph that represents the whole data set as a circle; each slice is a category, and the slice’s area as a fraction of the circle equals the category’s relative frequency
Graph of one quantitative variable that groups observations into ordered, nonoverlapping intervals called bins; bar height shows the frequency or relative frequency in each bin, and changing bin width or boundaries can change the appearance
The width of each interval in a histogram, found by subtracting the lower class boundary from the upper class boundary
Graph of one quantitative variable that splits each value into a stem and a leaf, orders stems and leaves from smallest to largest, and includes a key so the values can be read
Graph of one quantitative variable with one dot for each observation placed at its value on a numerical axis; repeated values stack
For a variable, the possible values or categories and how often they occur
A description of the distribution's shape, center, spread, and unusual features in context, including the variable and its units when available
Skewed right means the tail extends farther toward larger values, skewed left means the tail extends farther toward smaller values, and symmetric means the two sides are approximately mirror images
Unimodal means one main peak, bimodal means two prominent peaks, and uniform means frequencies are approximately equal across values or intervals with no prominent peaks
A data point that is unusually small or unusually large relative to the rest of the data
A region between two values in which there are no observed data
A concentration of observations, usually separated from another concentration by a gap or lower-frequency region
Arithmetic average of sample values: x̄ = (Σx_i)/n
Middle value of an ordered data set; for even n, commonly the mean of the two middle values
The minimum is the smallest value in an ordered data set, and the maximum is the largest value
Values that divide ordered data into four parts: Q1 is the median of the lower half, Q2 is the median, and Q3 is the median of the upper half; Q1 and Q3 bound the middle 50%
The pth percentile is the value with approximately p% of the ordered data at or below it
Maximum − minimum
Q3 − Q1; the spread of the middle 50% of the data
Typical distance of sample values from their mean; s = sqrt(Σ(x_i − x̄)² / (n − 1))
The square of the sample standard deviation: s² = Σ(x_i − x̄)² / (n − 1); measured in squared units
If y = a + bx, then mean, median, quartiles, percentiles, minimum, and maximum change by a + b(original); range, IQR, and standard deviation are multiplied by |b|; variance is multiplied by b²
A value is a potential outlier if it is below Q1 − 1.5(IQR) or above Q3 + 1.5(IQR)
A value is a potential outlier by this rule if it is below x̄ − 2s or above x̄ + 2s
A resistant statistic is not greatly affected by outliers or extreme values; a nonresistant statistic can be changed substantially by outliers or extreme values
Minimum, Q1, median, Q3, maximum
Graphical representation of the five-number summary: box from Q1 to Q3 with a line at the median; whiskers extend to the minimum and maximum if there are no outliers, or to the most extreme non-outliers if outliers are plotted separately
In symmetric distributions mean and median are close; in right-skewed mean > median; in left-skewed mean < median
A measure of relative position that tells how many standard deviations a value is above or below the mean; the standardized score most commonly used is the z-score
Collecting data from every member of the population
A study in which the researcher assigns treatments to experimental units to investigate their effects
The observational unit to which a treatment is assigned; when people, often called subjects or participants
The explanatory variable or factor is the variable that may explain or predict changes in the response; its levels are the specific values or categories imposed, and treatments are the conditions imposed, which with one factor are the factor's levels and with multiple factors are combinations of factor levels
The outcome measured or recorded on each unit; in an experiment, it is measured after the treatment is administered
A study in which treatments are not imposed and the researcher records variables as they naturally occur
An observational study in which units are selected at a point in time and data are gathered then and into the future
An observational study in which units are selected at a point in time and information from the past is gathered
An observational study that collects data from people using a standard set of questions
A variable associated with both the explanatory and response variables that provides an alternative explanation for an observed relationship
A sample in which all observational or experimental units are selected from the population using a random mechanism
When units are randomly selected from a population, it is appropriate to generalize results to that population
With replacement means selected units are returned before later selections so the same unit can be chosen more than once; without replacement means selected units are not returned so a unit can be chosen only once
A sample of size n selected so every possible sample of n distinct population units has the same chance of being chosen
Divide the population into nonoverlapping strata, take a random sample from each stratum, and combine the selected units
Divide the population into clusters, randomly select some clusters, and collect data from every observational unit in the selected clusters
Choose a random starting point, then select every kth unit using a fixed interval
Systematic error in the sampling procedure that makes a statistic consistently too high or too low relative to the population parameter
Bias that can occur when the sample consists of people who choose themselves to participate, so volunteers may differ systematically from nonvolunteers
Bias that may occur when part of the population is left out of the sampling frame or has a smaller chance of being selected
Bias that may occur when selected individuals do not respond and respondents differ from nonrespondents in ways related to the study
Bias that occurs when responses or measurements tend to differ from the true value in one direction
Sample chosen because the individuals are easy to reach or readily available
A collection of experimental units created for comparison; may receive no treatment, a placebo, a standard treatment, or another treatment
The difference between the average response to a placebo and the average response to no treatment
An experiment in which one relevant side does not know which treatment is being administered; usually the participants or the researchers who interact with them
An experiment in which neither participants nor the researchers who interact with them know treatment assignments
A variable known or believed to affect the response but not studied as an explanatory variable
Using a random mechanism to assign treatments to experimental units; in a well-designed experiment, it supports a cause-and-effect conclusion
Using enough experimental units in each treatment group so natural variation can be distinguished from treatment effects
Holding extraneous variables constant or accounting for them so treatment groups differ mainly in the explanatory variable
An experimental design in which treatments are assigned to all experimental units completely at random, with no blocks
An extraneous variable believed to affect the response and used to form blocks
A design that first groups units into similar blocks based on a blocking variable, then randomly assigns treatments within each block so every treatment appears in every block
A randomized block design with exactly two treatments, using pairs of similar units or one unit receiving both treatments in random order
Association means two variables tend to vary together, while causation means changes in one variable directly produce changes in the other
