In the data set below, what is the interquartile range?
12 42 52 62 68 68 72 94 94
To find the interquartile range, we first need to find the values of the first and third quartiles.
First, we need to find the median of the data set. Since we have 9 numbers, the median will be the 5th number in the ordered list:
12 42 52 62 68 68 72 94 94
Median = 68
Now, we divide the data set into two halves, excluding the median:
First half: 12 42 52 62
Second half: 72 94 94
The first quartile (Q1) is the median of the first half of the data set:
Q1 = 52
The third quartile (Q3) is the median of the second half of the data set:
Q3 = 94
Now we can calculate the interquartile range (IQR):
IQR = Q3 - Q1
IQR = 94 - 52
IQR = 42
Therefore, the interquartile range of the data set is 42.