Question

The data shows the number of grams of fat found in 9 different health bars.

11, 11.5, 10.5, 17, 14.5, 14.5, 18, 17, 19

What is the IQR (interquartile range) for the data?

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Responses

a 6.25
a 6.25

b 7
b 7

c 14.5
c 14.5

d 17.5

Answer 1

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

### Step 1: Sort the Data
The sorted data is:
10.5, 11, 11.5, 14.5, 14.5, 17, 17, 18, 19

### Step 2: Find Q1 and Q3
- **Q1** is the median of the first half of the data. The first half includes the first 4 values:
- 10.5, 11, 11.5, 14.5
- The median of these numbers is the average of 11 and 11.5:
- \( Q1 = \frac{11 + 11.5}{2} = 11.25 \)

- **Q3** is the median of the second half of the data. The second half includes the last 5 values:
- 14.5, 17, 17, 18, 19
- The median of these numbers is 17 (the middle value).

### Step 3: Calculate the IQR
Now, we calculate the IQR:
\[
\text{IQR} = Q3 - Q1 = 17 - 11.25 = 5.75
\]

Since 5.75 is not one of the options given, let's recheck the quartiles using the positions in the ordered list:

- The data set has 9 values.
- The median (Q2) is at position \( \frac{9 + 1}{2} = 5 \), which is 14.5.
- Q1 will be the median of the first 4 values (the first half) (positions 1-4): 10.5, 11, 11.5, 14.5
- Median of these = \( \frac{11 + 11.5}{2} = 11.25 \)

- Q3 will be the median of the last 4 values (the second half) (positions 5-9): 14.5, 17, 17, 18, 19
- Median of these = \( \frac{17 + 18}{2} = 17.5 \)

So the final calculation:
\[
\text{IQR} = Q3 - Q1 = 17.5 - 11.25 = 6.25
\]

The correct answer is:
**a) 6.25**