Chapter 3: Averages and Variation

Section 4: Percentiles and Box-and-Whisker Plots

Measure of Position

• Describes how a data value relates to the other data in a collection of data values.

Percentiles

• The mth percentile is the number that separates the bottom m% of the data from the top (100 – m)% of the data.

• denoted Pm

Quartiles

• Divide data into quarters

• The first quartile Q1 = P25

• The second quartile Q2 = P50 (median)

• The third quartile Q3 = P75

Interquartile Range

• resistant measure of dispersion

• IQR = Q3 - Q1

Box-and-Whisker Plots

• sometimes called box plots

• used to display graphic and numerical features of collections of data

• created using 5 numbers: lowest data value, highest data value and the three quartiles, Q1, Q2, and Q3

Example

• Construct a boxplot for the following data values.

1 2 2 3 3 3 4 5

7 7 9 10 14 20 29 42

Example

0

45

13

6

12

42