Question

Calculate the five-number summary of the given data. 11 7 2 17 18 2 13 22 16 1 20 21 20 23 24

Answer 1

Five-number summary

Minimum = 1

First quartile = 7

Median =17

Third quartile = 21

Maximum =24

Explanation :

• ​​​​​The minimum value of the data set is 1.
• The first quartile (or lower quartile or 25th percentile) is the median of the bottom half of the numbers. So, to find the first quartile, we need to place the numbers in value order and find the bottom half.

1   2   2   7   11   13   16   17   18   20   20   21   22   23   24   

So, the bottom half is

1   2   2   7   11   13   16   

The first quartile of the data set is 7.

• The median is the middle number in a sorted list of numbers. So, to find the median, we need to place the numbers in value order and find the middle number.

Ordering the data from least to greatest, we get:

1   2   2   7   11   13   16   17   18   20   20   21   22   23   24   

So, the median is 17 .

The median of the data set is 17.

• The third quartile (or upper quartile or 75th percentile) is the median of the upper half of the numbers. So, to find the third quartile, we need to place the numbers in value order and find the upper half.

1   2   2   7   11   13   16   17   18   20   20   21   22   23   24   

So, the upper half is

18   20   20   21   22   23   24   

The third quartile of the data set is 21.

• The maximum value of the data set is 24.