Draw the box-and-whisker plot for the data; 21, 29, 25, 20, 36, 28, 32, 35, 28, 30, 29, 25, 21, 35, 26, 35, 20, 19

Solution:

We will first find the median and then the lower quartile and the upper quartile using the quartile formula to draw the box and whisker.

Step 1: Arrange the data in ascending order.

19, 20, 20, 21, 21, 25, 25, 26, 28 28, 29, 29, 30, 32, 35, 35, 35, 36.

Step 2: Find the median of the data

M = [(n/2)th term + (n + 1/2)th ]/2

M = [(18/2)th term + (20/2)th ]/2

M = [9th term + 10th ]/2

M = (28 + 28)/2 = 28

M = 28

Step 3: Find the minimum and maximum values of the data.

The minimum is the lowest number in the data set which is 19.

The maximum is the highest number in the data set which is 36.

Step 4: Find the first quartile which lies at 25% of the data and the third quartile which lies at 75% of the data.

The first quartile (Q1) is the median of the lower half of data which lies at 25% of the data.

19, 20, 20, 21, 21, 25, 25, 26, 28.

Q1 = 21

The third quartile (Q3) is the median of the upper half of data which lies at 75% of the data.

28, 29, 29, 30, 32, 35, 35, 35, 36.

Q3 = 32

Step 5: Draw a box and whisker using the data below.

Minimum: 19

First quartile: 21

Median: 28

Third quartile: 32

Maximum: 36

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Draw the box-and-whisker plot for the data; 21, 29, 25, 20, 36, 28, 32, 35, 28, 30, 29, 25, 21, 35, 26, 35, 20, 19

Summary:

Using the values of the median, lower quartile, and upper quartile the box and whisker is drawn.