Question

A newspaper regularly reports the air quality index for various areas of Southern California. A sample of air quality index values for Pomona provided the following data:
29, 43, 58, 49, 46, 56, 60, 49, and 51.

Answer 1

The Interquartile range of the distribution which is the difference between the upper and the lower quartile values is 12.5

Arranging the data in ascending order :

• 29, 43, 46, 49, 49, 51, 56, 58, 60

The Interquartile range(IQR) :

IQR = Q3 - Q1

The Lower quartile (Q1) :

0.25(n + 1)th term ; n = number of terms = 9

Q1 = 0.25(10) = 2.5th term

Q1 = (43 + 46) / 2 = 44.5

The Upper Quartile (Q3) :

0.75(n + 1)th term ; n = number of terms = 9

Q3 = 0.75(10) = 7.5th term

Q3 = (56 + 58) / 2 = 57

Therefore, the Interquartile range, IQR = (57 - 44.5) = 12.5

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