Question

Each dot in the following dot plot represents the number of songs on one of Shane's albums. A dot plot has a horizontal axis labeled Number of songs numbered from 6 to 15. Dots are plotted above the following: 6, 15; 9, 2; 10, 3; 11, 1; 12, 2; 14, 1. Find the interquartile range (IQR) of the data in the dot plot.

Answer 1

IQR = 4

Explanation:

You want to know the IQR of the data set having values {6, 9, 10, 11, 12, 14} with frequencies {15, 2, 3, 1, 2, 1}.

Quartiles

There are 24 elements in the data set. The first quartile will be the average of the 6th and 7th data elements. The third quartile will be the average of the 18th and 19th data elements.

Q1 = (6 + 6)/2 = 6

Q3 = (10 +10)/2 = 10

Range

The interquartile range is the difference between Q1 and Q3:

IQR = Q3 -Q1 = 10 -6

IQR = 4

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