Question

What is the interquartile range of the data? 24, 25, 27, 36, 37, 42, 42, 43, 49, 49, 50, 53, 59, 61, 65 41 7 17 10

Answer 1

The interquartile range is the difference between the third quartile and the first quartile. First, find the median so you can separate the data in half. The median is the middle number. Arrange the numbers from least to greatest and find the number in the middle.

$\sf 24, 25, 27, 36, 37, 42, 42, \boxed{\sf 43}, 49, 49, 50, 53, 59, 61, 65$

Find the medians of these two halves. These will be Quartile 1 and Quartile 3.

$\sf 24, 25, 27, \boxed{\sf 36}, 37, 42, 42$

Quartile 1 is 36

$\sf 49, 49, 50, \boxed{\sf 53}, 59, 61, 65$

Quartile 3 is 53

$\sf IQR=Q3-Q1=53-36=\boxed{\sf 17}$

Answer 2

The interquartile range of the data given the first quartile and the third quartile is 25.

What is the interquartile range?

The interquartile range is the difference between the third quartile and the first quartile.

The data arranged in ascending order is: 7. 10, 17, 24, 25, 27, 36, 37, 41, 42, 42, 43, 49, 49, 50, 53, 59, 61, 65.

• Third quartile = 3/4(n + 1) = 3/4 x 20 = 15th term = 50
• First quartile = 1/4 x (n + 1) = 1/4 x 20 = 5th term = 25
• Interquartile range = 50 - 25 = 25

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