Question

What is the interquartile range for the data set?
4 , 7, 7, 3, 5, 2, 6, 7, 9

Answer 1

Population size:9
Lower quartile (xL): 3.5
Upper quartile (xU): 7

Interquartile range (xU-xL): 3.5

Answer 2

3.5

Explanation:

Given: A data set as 4 , 7, 7, 3, 5, 2, 6, 7, 9

To find: The interquartile range for the data set

Solution: The interquartile range for the data set is the difference of the middle of the first half and the middle of the second half.

So, to find we first need to find the median.

The numbers can be arranged in ascending order as:

2, 3, 4, 5, 6, 7, 7, 7, 9

As, the number of terms is 9, which is odd. So, the median is
`\left ( (9+1)/(2) \right )^(th)` term. So, the median is 6.

So, we have the first half as 2, 3, 4, 5 and the second half as 7, 7,. 7, 9.

Now, the middle of first half is
`(3+4)/(2) =3.5`

middle of second half is
`(7+7)/(2) =7`

Now, interquartile range
`=7-3.5=3.5`

Hence, interquartile range is 3.5.