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 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 5, and the interquartile range is 8.
The range is 14, and the interquartile range is 8.
The correct answer is:
The range is 14, and the interquartile range is 8.
To find the range and interquartile range of a dataset, follow these steps:
1. Arrange the dataset in ascending order:
68, 70, 74, 75, 78, 82
2. Calculate the range:
Range = highest value - lowest value
Range = 82 - 68 = 14
3. Determine the quartiles:
a. Find the median, which is the middle value of the dataset:
The median of 6 numbers is the average of the two middle terms: (74 + 75) / 2 = 74.5
b. Find the lower quartile (Q1), which is the median of the lower half of the dataset:
The lower half of the dataset is 68, 70, and 74. The median of these numbers is 70.
c. Find the upper quartile (Q3), which is the median of the upper half of the dataset:
The upper half of the dataset is 75, 78, and 82. The median of these numbers is 78.
4. Calculate the interquartile range:
Interquartile Range (IQR) = Q3 - Q1
IQR = 78 - 70 = 8
Therefore, the correct response is:
The range is 14, and the interquartile range is 8.