In the data set below, what is the interquartile range?
53 67 84 92 98
To find the interquartile range, we first need to find the first quartile (Q1) and the third quartile (Q3).
To do this, we need to first find the median of the data set.
The median is the middle number, and in this case, it is 84.
Since there are an odd number of values in the data set, Q1 is the median of the first half of the data set, which is 53 and 67.
So, Q1 = 60 (average of 53 and 67).
Similarly, Q3 is the median of the second half of the data set, which is 92 and 98.
So, Q3 = 95 (average of 92 and 98).
Now, the interquartile range (IQR) is calculated by subtracting Q1 from Q3.
IQR = Q3 - Q1
IQR = 95 - 60
IQR = 35
Therefore, the interquartile range of the data set is 35.