Question

Suppose, we have 6 observations such that 33, 22, 22, 28, 115, 107.Calculate 10th, 50th and 100th percentiles? ​

Answer 1

Solution :-

→ 6 observations are :- 22, 22, 28, 33, 107, 115 .

10th percentile :-

→ 0.10 * (6 + 1) = 0.70 ≈ 1 st observation

So,

→ 10 th percentile = 22 (Ans.)

50th percentile :-

→ 0.50 * (6 + 1) = 3.5 th observation

So,

→ 3rd observation + 0.5 (4th - 3rd observation)

→ 28 + 0.5(33 - 28)

→ 28 + 0.5 * 5

→ 28 + 2.5

→ 30.5 (Ans.)

Or,

→ 50th percentile = Median

since observations are even .

→ Median = [3rd observation + 4th observation] / 2

→ Median = [28 + 33]/2

→ Median = 61/2

→ Median = 30.5 (Ans.)

100th percentile :-

→ 100th percentile = Highest observation

→ 100th percentile = 115 (Ans.)

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