AP Statistics 1.3 - Describing Quantitative Data with Numbers

mean

the average of all the individual data values.

resistant

if it isn't sensitive to extreme values.

median

is the midpoint of a distribution, the number such that about half the observations are smaller and about half are larger.

range

of a distribution is the distance between the minimum value and the maximum value. That is, Range = Maximum - Minimum

standard deviation

measures the typical distance of the values in a distribution from the mean.

variance

the value obtained before taking the square root in the standard deviation calculation.

quartiles

divide the ordered data set into four groups having roughly the same number of values. To find the quartiles, arrange the data values from smallest to largest and find the median.

first quartile Q1

the median of the data values that are to the left of the median in the ordered list.

third quartile Q3

the median of the data values that are to the right of the median in the ordered list.

interquartile range (IQR)

is the distance between the first and third quartiles of a distribution. In symbols: IQR = Q3 − Q1

1.5 x IQR Rule

identifies outliers as an individual value that falls more than 1.5 x IQR above the 3rd quartile or below the 1st quartile.

low outliers

low outliers < Q1 - 1.5 x IQR

high outliers

high outliers > Q3 + 1.5 x IQR

five-number summary

consists of the minimum, the first quartile Q1, the median, the third quartile Q3, and the maximum.

boxplot

a visual representation of the five-number summary.