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Question
Find Skb for the following set of observations:
18, 27, 10, 25, 31, 13, 28.
Solution
The given data can be arranged in ascending order as follows:
10, 13, 18, 25, 27, 28, 31.
Here, n = 7
∴ Q1 = value of `(("n" + 1)/4)^"th"` observation
= value of `((7 + 1)/4)^"th"` observation
= value of 2nd observation
∴ Q1 = 13
Q2 = value of `2(("n" + 1)/4)^"th"` observation
= value of `2((7 + 1)/4)^"th"` observation
= value of (2 × 2)th observation
= value of 4th observation
∴ Q2 = 25
Q3 = value of `3(("n" + 1)/4)^"th"` observation
= value of `3((7 + 1)/4)^"th"` observation
= value of (3 × 2)th observation
= value of 6th observation
∴ Q3 = 28
Coefficient of skewness,
Skb = `("Q"_3 + "Q"_1 - 2"Q"_2)/("Q"_3 - "Q"_1)`
= `(28 + 13 - 2(25))/(28 - 13)`
= `(41 - 50)/15`
= `- 9/15`
∴ Skb = – 0.6
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