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Question
For a data set, sum of upper and lower quartiles is 100, difference between upper and lower quartiles is 40 and median is 50. Find the coefficient of skewness.
Solution
Given, Q3 + Q1 = 100 ...(i)
Q3 − Q1 = 40 ...(ii)
Median = Q2 = 50
Adding (i) and (ii), we get
2Q3 = 140
∴ Q3 = `140/2` = 70
Substituting the value of Q3 in (i), we get
70 + Q1 = 100
∴ Q1 = 100 − 70 = 30
Skb = `("Q"_3 + "Q"_1 - 2"Q"_2)/("Q"_3 - "Q"_1)`
= `(70+30-2(50))/40`
= `(100-100)/40`
∴ Skb = 0
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