Question

Obtain the ​five-number summary for the given data. The normal annual precipitation​ (in inches) is given below for 21 different U.S. cities.

39.1
30.2
18.5
32.6
27.1
27.8
8.6
23.9
42.6
30.3
20.6
12.0
5.1
13.5
22.5
10.9
15.8
25.4
17.2
15.5
51.7

Answer 1

The minimum is the smallest value in a data set.

Ordering the data from least to greatest, we get:

5.1   8.6   10.9   12.0   13.5   15.5   15.8   17.2   18.5   20.6   22.5   23.9   25.4   27.1   27.8   30.2   30.3   32.6   39.1   42.6   51.7   

So, the minimum is 5.1.

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.

5.1   8.6   10.9   12.0   13.5   15.5   15.8   17.2   18.5   20.6   22.5   23.9   25.4   27.1   27.8   30.2   30.3   32.6   39.1   42.6   51.7   

So, the bottom half is

5.1   8.6   10.9   12.0   13.5   15.5   15.8   17.2   18.5   20.6   

The median of these numbers is 14.5.

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:

5.1   8.6   10.9   12.0   13.5   15.5   15.8   17.2   18.5   20.6   22.5   23.9   25.4   27.1   27.8   30.2   30.3   32.6   39.1   42.6   51.7   

So, the median is 22.5 .

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.

5.1   8.6   10.9   12.0   13.5   15.5   15.8   17.2   18.5   20.6   22.5   23.9   25.4   27.1   27.8   30.2   30.3   32.6   39.1   42.6   51.7   

So, the upper half is

23.9   25.4   27.1   27.8   30.2   30.3   32.6   39.1   42.6   51.7   

The median of these numbers is 30.25.

The maximum is the greatest value in a data set.

Ordering the data from least to greatest, we get:

5.1   8.6   10.9   12.0   13.5   15.5   15.8   17.2   18.5   20.6   22.5   23.9   25.4   27.1   27.8   30.2   30.3   32.6   39.1   42.6   51.7   

So, the maximum is 51.7.

Hence Five number summary is Min: 5.1, Q1: 14.5, Q2: 22.5, Q3: 30.5 and Max: 51.7