Question

What is the interquartile range of the following data set?

7.7, 8.4, 9, 8, 6.9

Answer 1

`IQR=8.7-7.3=1.4`

Explanation:

The given data set is:

7.7, 8.4, 9, 8, 6.9

In order to find the Interquartile range, firstly arrange the given data set in ascending order, we have

6.9, 7.7, 8, 8.4, 9

Now, The median is the middle term in the arranged data set that is 8, and The lower half of data is the set below the median that is:

6.9, 7.7

The median for the lower half of data 6.9 , 7.7 is the lower or first quartile that is
`(6.9+7.7)/(2)=(14.6)/(2)=7.3`

And, The upper half of data is the set above the median that is:

8.4, 9

The median for the upper half of data 8.4 , 9 is the upper or third quartile that is
`(8.4+9.0)/(2)=(17.4)/(2)=8.7`.

Now, The interquartile range is the difference between the first quartile 7.3 and the third quartile 8.7 that is:

`IQR=8.7-7.3=1.4`

.

Answer 2

The answer for the statistics question you have above would be 1.4. I got to this answer by arranging the data and finding the median. Then, I divided the data set into 3 parts (Q1, Q2, and Q3). Then I found the average between each median of each quartile and I got 1.39999999986 or 1.4.