The problem asks for the interquartile range (IQR) of the given data set: 45, 40, 23, 34, 95, 57, 62, 48, 50, 44, 51, 47. The IQR is the difference between the third quartile (Q3) and the first quartile (Q1).

1. Problem Description

The problem asks for the interquartile range (IQR) of the given data set: 45, 40, 23, 34, 95, 57, 62, 48, 50, 44, 51,

4

7. The IQR is the difference between the third quartile (Q3) and the first quartile (Q1).

2. Solution Steps

First, we need to sort the data set in ascending order:

23, 34, 40, 44, 45, 47, 48, 50, 51, 57, 62, 95

Next, we find the median (Q2) of the data set. Since there are 12 data points, the median is the average of the 6th and 7th values:

$Q2 = (47 + 48) / 2 = 47.5$

Now, we find the first quartile (Q1), which is the median of the lower half of the data (excluding the median if the number of data points is odd):

Lower half: 23, 34, 40, 44, 45, 47

$Q1 = (40 + 44) / 2 = 42$

Then, we find the third quartile (Q3), which is the median of the upper half of the data:

Upper half: 48, 50, 51, 57, 62, 95

$Q3 = (51 + 57) / 2 = 54$

Finally, we calculate the interquartile range (IQR):

$IQR = Q3 - Q1 = 54 - 42 = 12$

3. Final Answer

B. 12