Question

state the type of skewness for a frequency distribution whose three quartiles are 42,36,40​

Answer 1

Given : frequency distribution whose three quartiles are 42,36,40​

To Find : skewness

Solution:

three quartiles are 42,36,40​

Q₁ = 36

Q₂ = 40

Q₃ = 42

Q₃  - Q₂  = 42 - 40 = 2

Q₂ - Q₁  = 40 - 36  = 4

 as 2 < 4

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)

= -2/6

= - 1/3

Negative skewness ,  Left Skewed

Mean < median  -ve  coefficient skewness

 Mean > Median + ve coefficient skewness

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