The heights of 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 interquartile range of the dataset. (1 point)
To find the range of the dataset, we need to subtract the minimum value from the maximum value:
Range = 82 - 68 = 14
To find the interquartile range of the dataset, we first need to find the first and third quartiles. We have 6 data points, so the first quartile (Q1) is the median of the data points below the median and the third quartile (Q3) is the median of the data points above the median.
First, we need to arrange the data points in ascending order:
68, 70, 74, 75, 78, 82
Since we have an even number of data points, we need to find the median of the lower half (Q1) and the median of the upper half (Q3).
Q1 = (70 + 74) / 2 = 72
Q3 = (75 + 78) / 2 = 76.5
Now, we can calculate the interquartile range by subtracting Q1 from Q3:
Interquartile Range = Q3 - Q1 = 76.5 - 72 = 4.5
Therefore, the range of the dataset is 14 inches and the interquartile range is 4.5 inches.