Question

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Measures of Variation Quick Check
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Question
The heights in inches of six basketball players at a local high school are given as a dataset.

70, 78, 74, 82, 68, 75

Find the range and the interquartile range of the dataset.

(1 point)
Responses

The range is 14, and the interquartile range is 4.5.
The range is 14, and the interquartile range is 4.5.

The range is 14, and the interquartile range is 74.5.
The range is 14, and the interquartile range is 74.5.

The range is 5, and the interquartile range is 8.
The range is 5, and the interquartile range is 8.

The range is 14, and the interquartile range is 8.
The range is 14, and the interquartile range is 8.
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Answer 1

To find the range and the interquartile range (IQR) of the given dataset of heights (70, 78, 74, 82, 68, 75), we will follow these steps:

1. **Find the range:**
- The range is calculated as the difference between the maximum and minimum values in the dataset.
- Maximum height: 82
- Minimum height: 68
- Range = Maximum - Minimum = 82 - 68 = 14

2. **Find the interquartile range (IQR):**
- First, we arrange the dataset in ascending order: 68, 70, 74, 75, 78, 82.
- To find the IQR, we first need to find Q1 (the first quartile) and Q3 (the third quartile).
- Q1 is the median of the first half of the data (68, 70, 74). The median of this half is 70 (the second number).
- Q3 is the median of the second half of the data (75, 78, 82). The median of this half is 78 (the second number).
- Now we can calculate the IQR: IQR = Q3 - Q1 = 78 - 70 = 8.

Thus, we have:
- Range = 14
- Interquartile Range = 8

The correct response is: **The range is 14, and the interquartile range is 8.**