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For a distribution, Bowley’s coefficient of skewness is 0.6. The sum of upper and lower quartiles is 100 and median is 38. Find the upper and lower quartiles. - Mathematics and Statistics

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Sum

For a distribution, Bowley’s coefficient of skewness is 0.6. The sum of upper and lower quartiles is 100 and median is 38. Find the upper and lower quartiles.

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Solution

Given, Skb = 0.6, Q3 + Q1 = 100,
Median = Q2 = 38

Skb = `("Q"_3 + "Q"_1 - 2"Q"_2)/("Q"_3 - "Q"_1)`

∴ 0.6 = `(100 - 2(38))/("Q"_3 - "Q"_1)`

∴ 0.6(Q3 – Q1) = 100 – 76 = 24

∴ Q3 – Q1 = `24/0.6`

∴ Q3 – Q1 = 40             ....(i)
Q3 + Q1 = 100             ....(ii) (given)
Adding (i) and (ii), we get
2Q3 = 140

∴ Q3 = `140/2` = 70
Substituting the value of Q3 in (ii), we get
70 + Q1 = 100
∴ Q1 = 100 – 70 = 30
∴ upper quartile = 70 and lower quartile = 30.

Concept: Measures of Skewness - Bowley’s Coefficient of Skewness
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