Question

What is the interquartile range of the data set 44,51,56,73,81

Answer 1

To calculate the interquartile range (IQR) of the dataset 44, 51, 56, 73, 81, we subtract the first quartile (51) from the third quartile (73) to find that the IQR is 22.

Step-by-step explanation:

To find the interquartile range (IQR) of the dataset 44, 51, 56, 73, 81, we need to first identify the first (Q1) and third (Q3) quartiles. The IQR is the difference between the third and first quartiles, which can be represented as IQR = Q3 - Q1. As the dataset is already in ascending order, we can proceed directly to find the quartiles.

For a dataset of 5 numbers, the second number is Q1 and the fourth number is Q3:

• Q1 (first quartile) = 51

• Q3 (third quartile) = 73
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Now, we subtract Q1 from Q3 to get the IQR:

IQR = Q3 - Q1 = 73 - 51 = 22

Therefore, the interquartile range of the dataset is 22.