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Question
Calculate the mean, mode and median for the following data:
22, 15, 10, 10, 24, 21
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Solution
Arranging in ascending order: 10, 10, 15, 21, 22, 24
Mean = `"Sum of all observations"/"Number of observations"`
= `(10 + 10 + 15 + 21 + 22 + 24)/6`
= `102/6`
= 17
Here n = 6, even
∴ Medain = `1/2{("n"/2)^"th" "term" + ("n"/2 + 1)^"th" "term"}`
= `1/2{(6/2)^"th" "term" + (6/2 + 1)^"th" "term"}`
= `1/2{3^"th" "term" + 4^"th" "term"}`
= `1/2{15 + 21}`
= `1/2(36)`
∴ Median = 18
Clearly the data 10 occurs maximum number of times and so 10 is the mode.
∴ Mode = 10
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