Explanation:
To calculate the range and semi-interquartile range from the given data/distribution, follow these steps:
Step 1: Sort the given data in ascending order:
8, 10, 12, 13, 15, 15, 16, 26, 28, 31, 34, 72
Step 2: Calculate the range:
Range = Maximum value - Minimum value
Range = 72 - 8
Range = 64
So, the range of the given data is 64.
Step 3: Calculate the quartiles:
To calculate the semi-interquartile range, we first need to find the first quartile (Q1) and third quartile (Q3).
Q1: The median of the lower half of the data set.
Q1 = (12 + 13) / 2
Q1 = 12.5
Q3: The median of the upper half of the data set.
Q3 = (28 + 31) / 2
Q3 = 29.5
Step 4: Calculate the semi-interquartile range:
Semi-Interquartile Range = (Q3 - Q1) / 2
Semi-Interquartile Range = (29.5 - 12.5) / 2
Semi-Interquartile Range = 17 / 2
Semi-Interquartile Range = 8.5
So, the semi-interquartile range of the given data is 8.5.