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Question
For a data set with upper quartile equal to 55 and median equal to 42. If the distribution is symmetric, find the value of lower quartile.
Solution
Upper quartile = Q3 = 55
Median = Q2 = 42
Since the distribution is symmetric.
∴ Skb = 0
Skb = `("Q"_3 + "Q"_1 - 2"Q"_2)/("Q"_3 - "Q"_1)`
∴ 0 = `("Q"_3 + "Q"_1 - 2"Q"_2)/("Q"_3 - "Q"_1)`
∴ 0 = Q3 + Q1 − 2Q2
∴ Q1 = 2Q2 – Q3
∴ Q1 = 2(42) – 55
∴ Q1 = 84 – 55
∴ Q1 = 29
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