Question

What is the interquartile range (IQR) for the data set? 12, 14, 15, 18, 22, 24, 28, 31, 35

Answer 1

The IQR is 15. To figure this out, we need to do Q1 - Q3. The Q1 = 29.5 and the Q3 = 14.5. 29.5 - 14.5 = 15. 
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Answer 2

Answer:

IQR = 15

Step-by-step explanation:

Data:

N = 9, where

X1 = 12

X2 = 14

X3 = 15

X4 = 18

X5 = 22

X6 = 24

X7 = 28

X8 = 31

X9 = 35

IQR = Q3 - Q1, where

Q1 = First quartile

Q3 = Third quartile

The first quartile will be the subject (N + 1) / 4 = (9 + 1) / 4 = 10/4 = 2.50.

Since it is decimal, the quartile will be a number between X2 = 14 and X3 = 15.

Q1 = X2 + 0.50 (X3-X2) = 14 + 0.50 (15-14) = 14 + 0.50 = 14.50

The third quartile is subject 3 (N + 1) / 4 = 3 (9 + 1) / 4 = 3 (10) / 4 = 30/4 = 7.50.

Since the number is decimal, the quartile will be between X7 = 28 and X8 = 31.

Q3 = X7 + 0.50 (X8-X7) = 28 + 0.50 (31-28) = 28 + 0.50 (3) = 28 + 1.50 = 29.50.

IQR = Q3 - Q1 = 29.50 - 14.50 = 15

 

Hope this helps!