The range is 39
The interquartile range is 32
Explanation:
The given data is [tex]57,96,72,63,88[/tex]
Let us arrange the data in ascending order.
Thus, we have,
[tex]57,63,72,88,96[/tex]
We need to determine the range and interquartile range of the data.
Range:
The range of the data is the difference between the highest and the lowest value in the given data.
Highest value = 96
Lowest value = 57
Range = Highest value - Lowest value
= 96 - 57
= 39
Thus, the range of the data is 39
Interquartile range:
The interquartile range is the difference between the upper quartile and the lower quartile in the given data.
From, the given data, we have, 3 quartiles. They are [tex]Q_1 , Q_2[/tex] and [tex]Q_3[/tex]
[tex]Q_2=72[/tex]
[tex]Q_1=\frac{57+63}{2} =60[/tex]
[tex]Q_3=\frac{88+96}{2} =92[/tex]
Interquartile range = [tex]Q_3-Q_1[/tex]
= [tex]92-60[/tex]
= [tex]32[/tex]
The interquartile range is 32
