Question

Dougie's Donuts tracked the number of donuts each customer ordered for a few weeks.
Number of donuts
0
4
8
12
16
20
What was the interquartile range of the number of donuts ordered?
donuts

Answer 1

To find the interquartile range (IQR) of the number of donuts ordered, we first need to determine the first quartile (Q1) and the third quartile (Q3) from the given data set.

The ordered data is:
0, 4, 8, 12, 16, 20

### Step 1: Find Q1 and Q3

- **Median (Q2)**: Since there are 6 data points, the median is the average of the 3rd and 4th values.
Median \( Q2 = \frac{8 + 12}{2} = 10 \)

- **Q1**: This is the median of the first half of the data (0, 4, 8).
Here, the first half is {0, 4, 8}.
Median of first half: \( Q1 = 4 \) (2nd value in the list)

- **Q3**: This is the median of the second half of the data (12, 16, 20).
Here, the second half is {12, 16, 20}.
Median of second half: \( Q3 = 16 \) (2nd value in the list)

### Step 2: Calculate the interquartile range

Now we can calculate the IQR:
\[
IQR = Q3 - Q1 = 16 - 4 = 12
\]

Thus, the interquartile range of the number of donuts ordered is **12 donuts**.