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

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

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

1 answer

To find the range and interquartile range (IQR) of the dataset, we need to first organize the heights in ascending order:

Dataset: 68, 70, 74, 75, 78, 82

Step 1: Calculate the range.

The range is the difference between the maximum and minimum values in the dataset.

  • Maximum value = 82
  • Minimum value = 68

Range = Maximum - Minimum = 82 - 68 = 14

Step 2: Calculate the interquartile range (IQR).

To find the IQR, we need to find the first quartile (Q1), the third quartile (Q3), and then subtract Q1 from Q3.

  1. First quartile (Q1): This is the median of the first half of the data (68, 70, 74). We take the middle value here, which is 70.
  2. Third quartile (Q3): This is the median of the second half of the data (75, 78, 82). The middle value here is 78.

Now we can calculate the IQR:

IQR = Q3 - Q1 = 78 - 70 = 8

Final Results:

  • The range is 14.
  • The interquartile range is 8.

Thus, the correct response is:

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