Question

Suppose the data represent the inches of rainfall in April for a certain city over the course of 20 years. Determine the quartiles.

0.240.24	1.691.69	3.283.28	4.664.66
0.370.37	2.122.12	3.463.46	4.774.77
0.490.49	2.322.32	3.713.71	4.914.91
0.930.93	2.622.62	4.094.09	5.225.22
1.241.24	2.892.89	4.224.22	5.65

Q1:

Q2:

Q3:

Q4:

Answer 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.

0.24   0.37   0.49   0.93   1.24   1.69   2.12   2.32   2.62   2.89   3.28   3.46   3.71   4.09   4.22   4.66   4.77   4.91   5.22   5.65   

So, the bottom half is

0.24   0.37   0.49   0.93   1.24   1.69   2.12   2.32   2.62   2.89   

The median of these numbers is 1.465.

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:

0.24   0.37   0.49   0.93   1.24   1.69   2.12   2.32   2.62   2.89   3.28   3.46   3.71   4.09   4.22   4.66   4.77   4.91   5.22   5.65   

As you can see, we do not have just one middle number but we have a pair of middle numbers, so the median is the average of these two numbers:

Median=

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.

0.24   0.37   0.49   0.93   1.24   1.69   2.12   2.32   2.62   2.89   3.28   3.46   3.71   4.09   4.22   4.66   4.77   4.91   5.22   5.65   

So, the upper half is

3.28   3.46   3.71   4.09   4.22   4.66   4.77   4.91   5.22   5.65   

The median of these numbers is 4.44.

The interquartile range is the difference between the third and first quartiles.

The third quartile is 4.44.

The first quartile is 1.465.

The interquartile range = 4.44 - 1.465 = 2.975.