Question

From the data/distribution below : 26,15,28,31,16,8,13,12, 10,15,34 & 72.... Calculate range & semi-inter quarter range.​

Answer 1

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.