Before we can find the range, and interquartile range let's review the definitions of these terms.
Range: the difference between the greatest and least values.
Interquartile Range: the difference between the first quartile and third quartile.
First, we will write the data in numerical order.
12,12,13,13,14,15,17,18
Range
The range is the difference between the greatest and least values.
12,12,13,13,14,15,17, 18
The difference between 18 and 12 is 6.
Interquartile Range
To find the interquartile range, we need to find the median of the lower half, the first quartile, and the median of the upper half, the third quartile.
12,12,13,13, 14,15,17,18
Lower Half Upper Half
We can see that there is an even number of values in the lower half and upper half. The first and third quartiles will be the average of their two middle numbers.
First quartile:& 12+13/2=12.5 [0.7em]
Third quartile:& 15+17/2=16
The difference between the two values is 16-12.5=3.5.
Therefore, the interquartile range is 3.5.
