Measures of Variation Quick Check
5 of 55 of 5 Items
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 8.
The range is 14, and the interquartile range is 8.
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 14, and the interquartile range is 4.5.
The range is 14, and the interquartile range is 4.5.
The range is 5, and the interquartile range is 8.
The range is 14, and the interquartile range is 8.
To find the range, subtract the smallest value in the dataset from the largest value. In this case, the smallest value is 68 and the largest value is 82. So, the range is 82 - 68 = 14.
To find the interquartile range, you need to find the first quartile (Q1) and the third quartile (Q3).
Step 1: Sort the dataset in ascending order: 68, 70, 74, 75, 78, 82.
Step 2: Find the median (Q2), which is the middle value of the dataset. In this case, Q2 is 74.
Step 3: Find the median of the lower half of the dataset (Q1). In this case, Q1 is the median of 68, 70, and 74, which is 70.
Step 4: Find the median of the upper half of the dataset (Q3). In this case, Q3 is the median of 75, 78, and 82, which is 78.
Step 5: Calculate the interquartile range by subtracting Q1 from Q3. In this case, the interquartile range is 78 - 70 = 8.
Therefore, the correct response is: The range is 14, and the interquartile range is 8.