We want to find the interquartile range of the given data set.
28, 46, 25, 76, 18, 25, 47, 83, 44
To do this, we need to identify the quartiles.
The second quartile (Q_2) is the median of the data set. It divides the set of data into two halves.
The lower quartile (Q_1) is the median of the lower half of the data set.
The upper quartile (Q_3) is the median of the upper half of the data set.
The interquartile range is the difference between the upper and the lower quartiles (Q_3-Q_1).
Let's start by ordering the data set from least to greatest value!
28, 46, 25, 76, 18, 25, 47, 83, 44
⇕
18, 25, 25, 28, 44, 46, 47, 76, 83
Now we can locate the median and the upper and lower quartiles of the data set.
18, 25, 25, 28, 44, 46, 47, 76, 83
There are 9 values in our data set, so the median is easy to find. However, this means that the upper and lower quartiles have 4 values. There are two middle values in each half! We can calculate the means of the middle values to find the quartile values.
Upper Quartile:& 47+ 76/2= 61.5 [0.8em]
Lower Quartile:& 25+ 25/2= 25
The last step to calculate the interquartile range is to find the difference between the upper and the lower quartiles. Let's do it!
Interquartile Range:& 61.5- 25=36.5
The interquartile range of the data set is 36.5.
