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Question
Find the mean deviation about the mean for the data.
38, 70, 48, 40, 42, 55, 63, 46, 54, 44
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Solution
Arithmetic mean `overline x = (38 + 70 + 48 + 40 + 42 + 55 + 63 + 46 + 54 + 44)/10 = 500/10 = 50`
`sum |x_i - overline x| = |38 - 50| + |70 - 50| + |48 - 50| + |40 - 50| + |42 - 50| + |55 - 50| + |63 - 50| + |46 - 50| + |54 - 50| + |44 - 50|`
= 12 + 20 + 2 + 10 + 8 + 5 + 13 + 4 + 4 + 4 + 6
= 84
∴ MD `(overline x) = (sum |x_i - overline x|)/n`
= `84/10`
= 8.4
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