Starnes/Tabor, The Practice of Statistics for the AP® Course, 7e, Unit 1, English

statistics

The science and art of collecting, analyzing, and drawing conclusions from data.

individual

An object described by a set of data. Individuals can

be people, animals, or things.

variable

Any characteristic of an individual. A variable can take

different values for different individuals.

categorical variable

A variable that assigns labels that place each individual into a particular group, called a category.

quantitative variable

Variable that takes number values that are quantities—counts or measurements.

distribution

Tells what values a variable takes and how often it takes each value.

frequency table

Table that shows the number of individuals having each value.

relative frequency table

Table that shows the proportion or percentage of individuals having each value.

bar graph

Graph used to display the distribution of a categorical variable. The horizontal axis of a bar graph identifies the categories being compared. The heights of the bars show the frequency or relative frequency for each value of the categorical variable. The graph is drawn with blank spaces between the bars to separate the categories being compared.

pie chart

Graph that shows the distribution of a categorical variable as a "pie" whose slices have areas proportional to the category frequencies or relative frequencies. A pie chart must include all the categories that make up a whole.

side-by-side bar graph

Graph used to compare the distribution of a categorical variable in each of two or more groups. For each value of the categorical variable, there is a bar corresponding to each group. The height of each bar is determined by the count or percentage of individuals in the group with that value.

discrete variable

A quantitative variable that takes a countable set of possible values with gaps between them on the number line.

continuous variable

A quantitative variable that can take any value in an interval on the number line.

dotplot

A graph that displays the distribution of a quantitative variable by plotting each data value as a dot above its location on a number line.

roughly symmetric

When the right side of a graph of quantitative data, which contains the half of the observations with the largest values, is approximately a mirror image of the left side.

skewed to the left

When the left side of a graph of quantitative data, which contains the half of the observations with the smallest values, is much longer than the right side.

skewed to the right

When the right side of a graph of quantitative data, which contains the half of the observations with the largest values, is much longer than the left side.

approximately uniform

A distribution in which the frequency (relative frequency) of each possible value is about the same.

stemplot

Graph that displays the distribution of a quantitative variable while including the actual numerical values in the graph. Each data value is separated into two parts: a stem, which consists of the leftmost digits, and a leaf, consisting of the final digit. The stems are ordered from least to greatest and arranged in a vertical column. The leaves are arranged in increasing order out from the appropriate stems.

histogram

Graph that displays the distribution of a quantitative variable by showing each interval of values as a bar. The heights of the bars show the frequencies or relative frequencies of values in each interval.

median

The midpoint of a distribution of quantitative data; the number such that about half the observations are smaller and about half are larger. To find the median, arrange the data values from smallest to largest. If the number n of data values is odd, the median is the middle value in the ordered list. If the number n of data values is even, use the average of the two middle values in the ordered list as the median.

mean

The average of all the individual data values in a distribution of quantitative data. To find the mean, add all the values and divide by the total number of data values.

statistic

Number that describes some characteristic of a sample.

parameter

A number that describes some characteristic of a population.

resistant

A statistical measure that isn’t affected much by extreme values.

range

The distance between the minimum value and the maximum value of a distribution of quantitative data. That is, range = maximum - minimum.

standard deviation

Measures the typical distance of the values in a distribution from the mean. It is calculated by finding an "average" of the squared deviations of the individual data values from the mean, and then taking the square root.

quartiles

The quartiles of a distribution divide an ordered data set into four groups having roughly the same number of values.

first quartile Q1

If the observations in a data set are arranged left to right from smallest to largest, the first quartile Q1 is the median of the data values that are to the left of the median in the ordered list.

third quartile Q3

If the observations in a data set are arranged left to right from smallest to largest, the third quartile Q3 is the median of the data values that are to the right of the median in the ordered list.

interquartile range (IQR)

The distance between the first and third quartiles of a distribution of quantitative data. In symbols, IQR = Q3 - Q1.

five-number summary

The minimum, first quartile 1Q, median, third quartile 3Q, and maximum of a distribution of quantitative data.

boxplot

A visual representation of the five-number summary of a distribution of quantitative data. The box spans the quartiles and shows the variability of the middle half of the distribution. The median is marked with a vertical line segment in the box. Lines extend from the ends of the box to the smallest and largest observations that are not outliers. Outliers are marked with a special symbol such as an asterisk (*).

percentile

The pth percentile of a distribution is the value with p% of observations less than or equal to it.

standardized score (z-score)

For an individual value in a distribution, the standardized score (z-score) tells us how many standard deviations from the mean the value falls, and in what direction.

cumulative relative frequency graph

A cumulative relative frequency graph plots a point corresponding to the percentile of a given value in a distribution of quantitative data. Consecutive points are then connected with a line segment to form the graph.

normal distribution

Distribution described by a normal curve. Any normal distribution is completely specified by two parameters, its mean μ and standard deviation σ. The mean of a normal distribution is at the center of the symmetric normal curve. The standard deviation is the distance from the center to the change-of-curvature points on either side.

normal curve

Important kind of curve that is symmetric, single-peaked, and mound-shaped.

empirical rule

In a normal distribution with mean μ and standard deviation σ (a) about 68% of the values fall within 1 σ of the mean μ, (b) about 95% of the values fall within 2 σ of μ and (c) about 99.7% of the values fall within 3 σ values of μ.

standard normal distribution

Normal distribution with mean 0 and standard deviation 1.