Box and Whisker Plots

and QuartilesSixth Grade

Five Statistical Summary

• When describing a set of data we have seen that we can use measures such as mean and median.

• We can also get a sense of the data’s distribution by examining a five statistical summary.

• (1) minimum, (2) maximum, (3) median (second quartile) , (4) first quartile, and (5) third quartile.

Quartiles

• We know that the median of a set of data separates the data into two equal parts. Data can be further separated into quartiles.

• Quartiles separate the original set of data into 4 equal parts.

• Each of these parts contains one-fourth of the data.

• Quartiles are percentiles that divide the data into fourths.

First Quartile

• The first quartile is the middle (the median) of the lower half of the data. One-fourth of the data lies below the first quartile and three-fourths lies above.

• The 25th percentile.

Second Quartile

• The second quartile is another name for the median of the entire set of data.

• Median of data set = second quartile of data set

• The 50th percentile.

Third Quartile

• The third quartile is the middle (the median) of the upper half of the data. Three-fourths of the data lies below the third quartile and one-fourth lies above.

• The 75th percentile.

• A QUARTILE IS A NUMBER, IT IS NOT A RANGE OF VALUES. A VALUE CAN BE DESCRIBED AS ‘ABOVE’ OR ‘BELOW’ THE FIRST QUARTILE, BUT A VALUE IS NEVER ‘IN’ THE QUARTILE.

Consider the following…

Minimum

65

First quartile

70

Second

quartile

(Median)

80

Third quartil

e

90

Maximum

100

While we do not know every test score, we do know that half of the scores are below 80 and half are above 80. We also know that half of the scores are between 70 and 90. The difference between the third and first quartiles is called the inter-quartile range. IQR = 20.

Find the first, second and third quartiles.

• 1) 4, 3, 6, 5, 2

• 2) 12, 10, 8, 14, 18, 6

• 3) 10, 15, 12, 16, 20

• 4) 5, 2, 3, 8, 7, 12

• 5) 7, 13, 9, 18, 20, 12

Answers

Question First Quartile

Second Quartile

Third Quartile

1 2.5 4 5.5

2 8 11 14

3 11 15 18

4 3 6 8

5 9 13 18

More Practice

• 1) 4, 6, 5, 6, 2, 7, 6, 8

• 2) 17, 14, 20, 29, 12, 24, 10, 19

• 3) 68, 88, 44, 68, 50, 68, 37, 50

• 4) 52, 60, 24, 36, 48, 52, 72

• 5) 102, 78, 312, 170, 250, 40, 52, 38, 125

Answers

Question First Quartile

Second Quartile

Third Quartile

1 4.5 6 6.5

2 13 18 22

3 47 59 68

4 36 52 60

5 46 102 210

Box-and-Whisker Plot

• A five statistical summary can be represented graphically as a box-and-whisker plot. The first and third quartiles are at the end of the box plot, the median is indicated with a vertical line in the interior of the box, and the maximum and minimum are at the ends of the whiskers.

http://www.khanacademy.org/math/probability/descriptive-statistics/Box-and-whisker%20plots/e/creating_box_and_whisker_plots