3.55 Number SummaryBox Plots

5 Number Summary• The five-number summary is the collection

of•The smallest value•The first quartile (Q1 or P25)

•The median (M or Q2 or P50)

•The third quartile (Q3 or P75)

•The largest value

• These five numbers give a concise description of the distribution of a variable

5 Number Summary●The median

Information about the center of the dataResistant

●The first quartile and the third quartileInformation about the spread of the dataResistant

●The smallest value and the largest valueInformation about the tails of the dataNot resistant

5 Number Summary●Compute the five-number summary for

1, 3, 4, 7, 8, 15, 16, 19, 23, 24, 27, 31, 33, 54

●Calculator●Calculations

The minimum = Q1 =

M = Q2 =

Q3 =The maximum = 54

Boxplot• The five-number summary can be illustrated

using a graph called the boxplot• An example of a (basic) boxplot is

• The middle box shows Q1, Q2, and Q3

• The horizontal lines (sometimes called “whiskers”) show the minimum and maximum

Boxplot●To draw a (basic) boxplot:

Calculate the five-number summaryDraw a horizontal line that will cover all the data from the minimum to the maximum

Draw a box with the left edge at Q1 and the right edge at Q3

Draw a line inside the box at M = Q2

Draw a horizontal line from the Q1 edge of the box to the minimum and one from the Q3 edge of the box to the maximum

Draw a Boxplot• Use the following times from a 5K race to make a

boxplot.• 19.25, 23.25, 23.32, 25.55, 25.33, 26.28, 28.58,

29.12, 30.18, 30.35

Calculator• Using the previous data, make a

boxplot using a calculator.

Better Boxplots!• An example of a more sophisticated boxplot is

• The middle box shows Q1, Q2, and Q3

• The horizontal lines (sometimes called “whiskers”) show the minimum and maximum

• The asterisk on the right shows an outlier (determined by using the upper fence)

Better Boxplots

• Using the previous data, make an outlier boxplot using a calculator.

Box-Plots and Distributions

Comparing Boxplots

●We can compare two distributions by examining their boxplots●We draw the boxplots on the same

horizontal scaleWe can visually compare the centersWe can visually compare the spreadsWe can visually compare the extremes

Review• 5-number summary•Minimum, first quartile, median, third quartile maximum•Resistant measures of center (median) and spread (interquartile range)

• Boxplots•Visual representation of the 5-number summary•Related to the shape of the distribution•Can be used to compare multiple distributions