Question

each dot in the following dot plot represents the number of songs on one of shanes albums. find the interquartile range (iqr) of the data in the dot plot.

Explanation:

Step1: Count data points

There are 1 + 1+ 3+ 4+ 1+ 2+ 1 = 13 data - points.

Step2: Find the median (Q2)

Since there are 13 data - points, the median is the 7th value when the data is ordered. Counting from the left, the median (Q2) is 10.

Step3: Find the lower half and Q1

The lower half of the data consists of the first 6 values. The median of the lower half (Q1) is the average of the 3rd and 4th ordered values. The 3rd and 4th values in the lower half are 9 and 9, so Q1 = 9.

Step4: Find the upper half and Q3

The upper half of the data consists of the last 6 values. The median of the upper half (Q3) is the average of the 3rd and 4th ordered values in the upper half. The 3rd and 4th values in the upper half are 12 and 12, so Q3 = 12.

Step5: Calculate the IQR

IQR=Q3 - Q1. Substitute Q1 = 9 and Q3 = 12 into the formula: IQR = 12 - 9 = 3.

Answer:

3