ap stats unit one vocab

A variable that takes on values that are category names or group labels rather than numerical values.

categorical variable

A variable that is measured numerically and can take on a range of values, allowing for mathematical operations and statistical analysis.

quantitative variable

A characteristic that changes from one individual to another in a set of data.

variable

Data that represents categories or groups rather than numerical measurements, such as colors, types, or classifications.

categorical data

A table that displays the number of cases or observations falling into each category.

frequency table

A proportion expressed as a number out of 100, calculated by multiplying the relative frequency by 100.

percentage

A part or share of a whole, expressed as a fraction, decimal, or percentage.

proportion

A ratio that compares two quantities with different units, often used to express frequency or occurrence per unit.

rate

The proportion of observations in a category, expressed as a decimal, fraction, or percentage of the total.

relative frequency

A table that displays the proportion or percentage of cases falling into each category.

relative frequency table

A graph that displays frequencies or relative frequencies for categorical data using rectangular bars, where the height or length represents the count or proportion in each category.

bar chart

A graphical representation using rectangular bars to display the frequency or count of categories in a categorical variable.

bar graph

Data that represents categories or groups rather than numerical measurements, such as colors, types, or classifications.

categorical data

The count or number of observations falling within each category of categorical data.

frequencies

A table that displays the number of cases or observations falling into each category.

frequency table

Visual displays such as bar charts, pie charts, or other graphs used to present data in a visual format.

graphical representations

The proportion of observations in a category, expressed as a decimal, fraction, or percentage of the total.

relative frequency

A variable that can take on infinitely many values that cannot be counted, with infinitely many possible values between any two given values.

continuous variable

A graph that represents the number or proportion of a data set that is less than or equal to a given number.

cumulative graph

A variable that can take on a countable number of values, which may be finite or countably infinite.

discrete variable

A graph that represents each observation as a dot, with position on the horizontal axis corresponding to the data value, with nearly identical values stacked vertically.

dotplot

A graph where the height of each bar represents the number or proportion of observations within an interval, with the ability to alter interval widths to change the appearance.

histogram

A range of values between two boundaries, used to represent a set of outcomes in a normal distribution.

interval

In a stem and leaf plot, usually the last digit of a data value.

leaf

A variable that is measured numerically and can take on a range of values, allowing for mathematical operations and statistical analysis.

quantitative variable

In a stem and leaf plot, the first digit or digits of a data value.

stem

A graphical representation where each data value is split into a stem (first digit or digits) and a leaf (usually the last digit).

stem and leaf plot

A distribution with two prominent peaks.

bimodal

A measure indicating the middle or typical value of a distribution.

center

Concentrations of data usually separated by gaps in a distribution.

cluster

Methods used to summarize and describe the characteristics of a data set without making inferences about a larger population.

descriptive statistics

The pattern of how data values are spread or arranged across a range.

distribution

Regions of a distribution between two data values where there are no observed data.

gap

Data points that are unusually small or large relative to the rest of the data.

outlier

Data that consists of numerical values that can be measured and analyzed mathematically.

quantitative data

The overall form or pattern of a distribution, including characteristics like skewness and modality.

shape

A distribution with a longer tail extending to the left, where the mean is typically less than the median.

skewed left

A distribution with a longer tail extending to the right, where the mean is typically greater than the median.

skewed right

A distribution where the left half is the mirror image of the right half.

symmetric

A distribution where each bar height is approximately the same with no prominent peaks.

uniform

A distribution with one main peak.

unimodal

The spread or dispersion of data values in a distribution.

variability

The median of the lower half of an ordered data set, denoted as Q1, marking the boundary below which 25% of the data falls.

first quartile

A measure of variability calculated as the difference between the third quartile (Q3) and the first quartile (Q1), representing the spread of the middle 50% of data.

interquartile range

The average value of a dataset, represented by μ in the context of a population.

mean

Numerical summaries that describe the central tendency of a data set, including the mean and median.

measures of center

Numerical summaries that describe the location of data values within a distribution, including quartiles and percentiles.

measures of position

Statistical measures that describe how spread out or dispersed data values are in a distribution.

measures of variability

The middle value when data are ordered; for an even number of data points, typically the average of the two middle values.

median

A characteristic of a statistic that is significantly affected or influenced by outliers; also called non-robust.

nonresistant

Data points that are unusually small or large relative to the rest of the data.

outlier

A value such that p% of the data is less than or equal to it, used to describe the position of a data point within a distribution.

percentile

The first quartile; the value below which 25% of the data falls.

Q1

The third quartile; the value below which 75% of the data falls.

Q3

A value that divides an ordered data set into four equal parts; Q1 and Q3 form the boundaries for the middle 50% of values.

quartile

A measure of variability calculated as the difference between the maximum and minimum data values in a dataset.

range

A characteristic of a statistic that is not greatly affected by outliers; also called robust.

resistant

The standard deviation calculated for a sample, denoted by s, using the formula s = √(1/(n-1) ∑(xᵢ-x̄)²).

sample standard deviation

The square of the sample standard deviation, denoted by s², representing variability in squared units.

sample variance

A measure of how spread out data values are from the mean, represented by σ in the context of a population.

standard deviation

Numerical summaries or measures calculated from sample data, such as mean, median, or standard deviation.

statistic

The median of the upper half of an ordered data set, denoted as Q3, marking the boundary below which 75% of the data falls.

third quartile

A graphical representation of the five-number summary showing the distribution of data through a box and whiskers.

boxplot

The median of the lower half of an ordered data set, denoted as Q1, marking the boundary below which 25% of the data falls.

first quartile

A set of five values that describe a dataset: minimum, first quartile (Q1), median, third quartile (Q3), and maximum.

five-number summary

The largest value in a dataset.

maximum

The average value of a dataset, represented by μ in the context of a population.

mean

The middle value when data are ordered; for an even number of data points, typically the average of the two middle values.

median

The smallest value in a dataset.

minimum

Data points that are unusually small or large relative to the rest of the data.

outlier

Data that consists of numerical values that can be measured and analyzed mathematically.

quantitative data

A value that divides an ordered data set into four equal parts; Q1 and Q3 form the boundaries for the middle 50% of values.

quartile

A distribution with a longer tail extending to the left, where the mean is typically less than the median.

skewed left

A distribution with a longer tail extending to the right, where the mean is typically greater than the median.

skewed right

Numerical measures that describe key features of a dataset, such as center, spread, and shape.

summary statistics

A distribution where data is evenly distributed around the center, with the mean and median approximately equal.

symmetric distribution

The median of the upper half of an ordered data set, denoted as Q3, marking the boundary below which 75% of the data falls.

third quartile

Lines extending from the ends of a boxplot that reach to the most extreme data points that are not outliers.

whiskers

A measure indicating the middle or typical value of a distribution.

center

Concentrations of data usually separated by gaps in a distribution.

cluster

Regions of a distribution between two data values where there are no observed data.

gap

Visual displays such as bar charts, pie charts, or other graphs used to present data in a visual format.

graphical representations

A graph where the height of each bar represents the number or proportion of observations within an interval, with the ability to alter interval widths to change the appearance.

histogram

Two or more separate groups of data where the values in one group do not influence or depend on the values in another group.

independent samples

The average value of a dataset, represented by μ in the context of a population.

mean

Data points that are unusually small or large relative to the rest of the data.

outlier

The proportion of observations in a category, expressed as a decimal, fraction, or percentage of the total.

relative frequency

A graphical representation that displays multiple boxplots arranged next to each other to compare the distributions of different groups or samples.

side-by-side boxplots

A measure of how spread out data values are from the mean, represented by σ in the context of a population.

standard deviation

Numerical measures that describe key features of a dataset, such as center, spread, and shape.

summary statistics

The spread or dispersion of data values in a distribution.

variability

A description of data sets that closely follow the pattern of a normal distribution with a mound-shaped, symmetric curve.

approximately normally distributed

A rule stating that for a normal distribution, approximately 68% of observations fall within 1 standard deviation of the mean, 95% within 2 standard deviations, and 99.7% within 3 standard deviations.

empirical rule

The average value of a dataset, represented by μ in the context of a population.

mean

The bell-shaped graph of a normal distribution that is symmetric and mound-shaped.

normal curve

A probability distribution that is mound-shaped and symmetric, characterized by a population mean (μ) and population standard deviation (σ).

normal distribution

A random variable that follows a normal distribution, allowing for the calculation of probabilities for specific intervals.

normally distributed random variable

A numerical summary that describes a characteristic of an entire population.

parameter

A value such that p% of the data is less than or equal to it, used to describe the position of a data point within a distribution.

percentile

The average of all values in an entire population, denoted as μ.

population mean