5 Number Summary Box Plots

The five-number summary is the collection of The smallest value The first quartile (Q 1 or P 25 ) The median (M or Q 2 or P 50 ) The third quartile (Q 3 or P 75 ) The largest value These five numbers give a concise description of the distribution of a variable

● The median  Information about the center of the data  Resistant ● The first quartile and the third quartile  Information about the spread of the data  Resistant ● The smallest value and the largest value  Information about the tails of the data  Not resistant

● Compute the five-number summary for 1, 3, 4, 7, 8, 15, 16, 19, 23, 24, 27, 31, 33, 54 ● Calculator ● Calculations  The minimum =  Q 1 =  M = Q 2 =  Q 3 =  The maximum = 54

The five-number summary can be illustrated using a graph called the boxplot An example of a (basic) boxplot is The middle box shows Q 1, Q 2, and Q 3 The horizontal lines (sometimes called “whiskers”) show the minimum and maximum

● To draw a (basic) boxplot:  Calculate the five-number summary  Draw a horizontal line that will cover all the data from the minimum to the maximum  Draw a box with the left edge at Q 1 and the right edge at Q 3  Draw a line inside the box at M = Q 2  Draw a horizontal line from the Q 1 edge of the box to the minimum and one from the Q 3 edge of the box to the maximum

Use the following times from a 5K race to make a boxplot , 23.25, 23.32, 25.55, 25.33, 26.28, 28.58, 29.12, 30.18, 30.35

Using the previous data, make a boxplot using a calculator.

An example of a more sophisticated boxplot is The middle box shows Q 1, Q 2, and Q 3 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)

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

● We can compare two distributions by examining their boxplots ● We draw the boxplots on the same horizontal scale  We can visually compare the centers  We can visually compare the spreads  We can visually compare the extremes

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