Question

What is the interquartile range for the data set?

4 7 7 3 5 2 6 7 9
Group of answer choices

9

3.5

7

5.6

Answer 1

To calculate the interquartile range (IQR) for the data set, we first need to organize the numbers in ascending order and then find the first quartile (Q1) and the third quartile (Q3).

**Step 1: Sort the data in ascending order.**
The sorted data set is:
2, 3, 4, 5, 6, 7, 7, 7, 9

**Step 2: Find Q1 and Q3.**
- Q1 is the median of the first half of the data.
- Q3 is the median of the second half of the data.

For this data set, the median (Q2) is the middle number:

- There are 9 numbers, so the median is the 5th number: Q2 = 6.

Now we find Q1 and Q3:
- The first half of the data (before the median): 2, 3, 4, 5
- The second half of the data (after the median): 7, 7, 7, 9

To find Q1:
- We take the first half: 2, 3, 4, 5, and find the median. There are 4 numbers, so Q1 is the average of the 2nd and 3rd numbers:
\[
Q1 = \frac{3 + 4}{2} = 3.5
\]

To find Q3:
- We take the second half: 7, 7, 7, 9, and find the median. Again, there are 4 numbers, so Q3 is the average of the 2nd and 3rd numbers:
\[
Q3 = \frac{7 + 7}{2} = 7
\]

**Step 3: Calculate the interquartile range (IQR).**
\[
IQR = Q3 - Q1 = 7 - 3.5 = 3.5
\]

Thus, the interquartile range for the data set is **3.5**.