The range is the difference between the greatest and least values in a set of data. Arranging the data set from least to greatest makes it easier to see the minimum and maximum value.
46, 48, 53, 57, 61, 63, 63, 69, 72
For our exercise, the greatest value is 72 and the least value is 46.
Range: 72- 46= 26
We found that the range of our data set it 26. Let's continue by finding the interquartile range!
Interquartile Range
To find the interquartile range we need to identify the quartiles.
Lower Quartile (Q_1) is the median of the lower half of the data set.
Second Quartile (Q_2) is the median of the data set. It divides the set of data into two halves.
Upper Quartile (Q_3) is the median of the upper half of the data set.
Let's start by recalling the ordered data set from least to greatest value!
46, 48, 53, 57, 61, 63, 63, 69, 72
The median of the set is 61. This value divides the set into two halves. We have two middle values for each half. Thus, we need to calculate the mean of those middle values.
Upper Quartile:& 63+ 69/2=66
Lower Quartile:& 48+ 53/2= 50.5
The last step to calculate the interquartile range is to calculate the difference between the upper and lower quartiles. Let's do it!
Interquartile Range:& 66- 50.5= 15.5
