Question

The typing speeds in words per minute for 9 individuals are given as a dataset.

45, 80, 65, 60, 72, 58, 53, 68, 62

Find the range and the interquartile range of the dataset.

(1 point)
Responses

The range is 35, and the interquartile range is 14.5.

The range is 35, and the interquartile range is 19.

The range is 27, and the interquartile range is 14.5.

The range is 35, and the interquartile range is 12.

Answer 1

To calculate the range and the interquartile range (IQR) of the dataset:

**Dataset:**
45, 80, 65, 60, 72, 58, 53, 68, 62

**Step 1: Calculate the Range**
The range is the difference between the maximum and minimum values in the dataset.

- Maximum value = 80
- Minimum value = 45

\[
\text{Range} = \text{Maximum} - \text{Minimum} = 80 - 45 = 35
\]

**Step 2: Calculate the Interquartile Range (IQR)**
To find the interquartile range, we need to find the first (Q1) and third (Q3) quartiles.

1. **Ordering the Data:**
The ordered dataset is:
45, 53, 58, 60, 62, 65, 68, 72, 80

2. **Finding Q1 and Q3:**
- Q1 is the median of the first half of the data (the lower half):
- Lower half: 45, 53, 58, 60
- Median of the lower half (Q1) = (53 + 58) / 2 = 55.5
- Q3 is the median of the second half of the data (the upper half):
- Upper half: 62, 65, 68, 72, 80
- Median of the upper half (Q3) = (68 + 72) / 2 = 70

3. **Calculating the IQR:**
\[
\text{IQR} = Q3 - Q1 = 70 - 55.5 = 14.5
\]

**Final Results:**
- **Range:** 35
- **Interquartile Range:** 14.5

Thus, the correct response is:

**The range is 35, and the interquartile range is 14.5.**