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A variable x takes values 1,2,3,4,5 with corresponding frequencies 1,2,3,4,5. Then the mean deviation of x from mean?

A variable x takes values 1,2,3,4,5 with corresponding frequencies 1,2,3,4,5. Then the mean deviation of x from mean?
 

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Grade:12

1 Answers

Samyak Jain
333 Points
5 years ago
Values of x are 1,2,3,4,5 and corresponding frequencies are 1,2,3,4,5.
Mean deviation of x from mean is [∑ |xi – \mu|.fi] / [∑ fi ], where \mu is mean, f is frequency.
Now, mean, \mu = ∑ xifi / ∑ fi  =  (1.1 + 2.2 + 3.3 + 4.4 + 5.5) / (1 + 2 + 3 + 4 + 5) = 55/15 = 11/3.
∑ |xi – \mu|.fi = |1 – 11/3|.1 + |2 – 11/3|.2 + |3 – 11/3|.3 + |4 – 11/3|.4 + |5 – 11/3|.5
                 = 8/3 + 10/3 + 6/3 + 4/3 + 20/3  =  (8 + 10 + 6 + 4 + 20)/3 = 48/3 = 16.
\therefore [∑ |xi – \mu| fi] / [∑ fi ] = 16 / 15 = mean deviation of x from mean.

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