The Interquartile range for the given data is 4.
What is Interquartile Range?
The interquartile range is a measure of where the “middle fifty” is in a data set. Where a range is a measure of where the beginning and end are in a set, an interquartile range is a measure of where the bulk of the values lie.
Here,
Given data: 23, 24, 25, 27, 27, 28, 29, 30, 30, 31, 32, 37
First Quartile Q₁ = (n-1)/4 th term
Q₁ = (12-1)/4 th term
Q₁ = 11/4 th term
Q₁ = 2.75 th term
Q₁ = 26
Third Quartile Q₃ = 3(n-1)/4 th term
Q₃ = 3 X 11 / 4
Q₃ = 8.25th term
Q₃ = 8th term + 0.25 (9th term - 8th term)
Q₃ = 30 + 0.25 (30 -30 )
Q₃ = 30 + 0
Q₃ = 30
Interquartile range = (Q₃ - Q₁ ) = (30 - 26)
= 4
Thus, the interquartile range = 4.
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