Verified Answer :

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.

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Answer:

\(IQR=8.7-7.3=1.4\)

Step-by-step 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 \(\frac{6.9+7.7}{2}=\frac{14.6}{2}=7.3\)

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  \(\frac{8.4+9.0}{2}=\frac{17.4}{2}=8.7\).

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

\(IQR=8.7-7.3=1.4\)

.

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