third quartile is at a distance of 12.8 from the median in a frequency distribution and its first quartile is at a distribution and its first quartile is at a distance of 11.2 from the median. find skewness and its coefficient
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Answer:
third quartile is at a distance of 12.8 from the median in a frequency distribution and its first quartile is at a distribution and its first quartile is at a distance of 11.2 from the median. find skewness and its coefficient
Given : Third quartile is at a distance of 12.8 from the median in a frequency distribution and
first quartile is at a distance of 11.2 from the medium.
To Find : the skewness and its coefficient.
Solution:
Third quartile is at a distance of 12.8 from the median
=> Q₃ - Q₂ = 12.8
first quartile is at a distance of 11.2 from the medium.
=> Q₂ - Q₁ = 11.2
as 11.2 < 12.8
Q₂ - Q₁ < Q₃ - Q₂ hence longer tail on right side
Hence Positive skewness , Right Skewed
Coefficient of skewness = ((Q₃ - Q₂ ) - (Q₂ - Q₁) )/(Q₃ - Q₁)
= ( 12.8 - 11.4)/(Q₂+ 12.8 -(Q₂- 11.4))
= 1.4/ (24.2)
= 14/242
= 7/121
positive skewness , Right Skewed , coefficient = 7/121
Mean < median -ve coefficient skewness
Mean > Median + ve coefficient skewness
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