AP Stats: Modeling the World Chapter 3: Displaying and Summarizing Quantitative Data

Distribution

slices up all the possible values of the variable into equal-width bit and gives the number of values (or counts) falling into each bin

Histogram (relative frequency histogram)

uses adjacent bars to show the distribution of a quantitative variable. Each bar represents the frequency (or relative frequency) of values falling in each bin.

Gap

a region of the distribution where there are no values

Stem-and-Leaf Display

shows quantitative data values in a way that sketches the distribution of the data, best described in detail by example.

Dotplot

graphs a dot for each case against a single axis

Shape

to describe this, look for: single vs. multiple modes, symmetry vs. skewness, and outliers and/or gaps

Center

The place in the distribution of a variable that you'd point to if you wanted to attempt the impossible by summarizing the entire distribution with a single number. Measures of this include the mean and the median.

Spread

A numerical summary of how tightly the values are clustered around the center. Measures of this include the IQR and standard deviation.

Mode

A hump or local high point in the shape of the distribution of a variable. The apparent location of this can change as the scale of a histogram is changed.

Unimodal

A distribution having one mode

Bimodal

A distribution with two modes

Multimodal

A distribution with more than two modes

Uniform

A distribution that is roughly flat.

Symmetric

A distribution where two halves on either side of the center look approximately like mirror images of each other

Tails

The parts of a distribution that typically trail off on either side

Skewed

A distribution that is not symmetrical and one tail stretches out further than the other

Outliers

Extreme values that don't appear to belong with the rest of the data. These may be unusual values that deserve further investigation or they may just be mistakes. There's no obvious way to tell. Don't delete these automatically: you have to think about them. These can affect many statistical analyses so you should always be alert for them.

Median

The middle of volume with half of the data above and half below it. If n is even, it is the average of the two middle values. It is usually paired with the IQR.

Range

The difference between the lowest and highest values in a data set

Quartile

a value that divides the data set into four equal parts

Interquartile Range

The difference between the first and third quartiles. It is usually reported along with the median.

Percentile

the number that falls above i% of the data

5-number Summary

Reports the minimum value, quartile 1, the median, quartile 3, and the maximum value

Boxplot

Displays the five number summary as a central box, whiskers that extended to nonoutlying data values, and any outliers shown

Mean

The value found by summing all the data values and dividing by the count. It is usually paired with the standard deviation

Resistant

A calculated summary where outliers have only a small effect on it

Standard Deviation

The square root of the variance, usually reported along with the mean

Variance

The sum of squared deviations from the mean divided by the count minus one