A quartile divides data into three points a lower quartile (Q₁), median (Q₂), and upper quartile (Q₃) to form four groups of the dataset.
a. Quartiles Q₁= 57, Q₂= 59, Q₃= 62
b. Interquartile range, (IQR) = 5
c. 0 and 75 are outlines.
First arrange the given data into increasing order,
We get, 0, 55, 56, 57, 57, 57, 57, 59, 59, 59, 60, 62, 62, 64, 65, 75
Divide into Quartiles,
( 0, 55, 56, 57 ) ( 57, 57, 57, 59) ( 59, 59, 60, 62) ( 62, 64, 65, 75)
Q₁ = [tex]\frac{57+57}{2}=57[/tex]
Q₂ = [tex]\frac{59+59}{2}=59[/tex]
Q₃= [tex]\frac{62 + 62}{2}=62[/tex]
Interquartile range (IQR) = Q₃ - Q₁=62 - 57 = 5
High outliner = 1.5 (IQR) + Q₃
= 1.5(5) + 62
= 69.5
low outliner = Q₁ - 1.5 (IQR)
= 57 - 1.5 (5)
= 49.5
All the values from arrange data set which are lies outside from 69.5 and 49.5 known as outliners.
Here, 0 and 75 are outliners.
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