tate the type of skewness for a frequency distribution whose three quartiles are 21, 18 and 20.
Answers
Given : frequency distribution whose three quartiles are 21, 18 and 20.
To Find : skewness
Solution:
three quartiles are 21, 18 and 20.
Q₁ = 18
Q₂ = 20
Q₃ = 21
Q₃ - Q₂ = 21 - 20 = 1
Q₂ - Q₁ = 20 - 18 = 2
as 1 < 2
Q₃ - Q₂ < Q₂ - Q₁ hence longer tail on left side
Hence Negative skewness , Left Skewed
Coefficient of skewness = ((Q₃ - Q₂ ) - (Q₂ - Q₁) )/(Q₃ - Q₁)
= ( Q₁ + Q₃ - 2Q₂)/(Q₃ - Q₁)
= -1/3
Negative skewness , Left Skewed
Mean < median -ve coefficient skewness
Mean > Median + ve coefficient skewness
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