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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?

Samyak Jain
333 Points
2 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$\dpi{100} \mu$|.fi] / [∑ fi ], where $\dpi{100} \mu$ is mean, f is frequency.
Now, mean, $\dpi{100} \mu$ = ∑ xifi / ∑ fi  =  (1.1 + 2.2 + 3.3 + 4.4 + 5.5) / (1 + 2 + 3 + 4 + 5) = 55/15 = 11/3.
∑ |xi$\dpi{100} \mu$|.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.
$\dpi{100} \therefore$ [∑ |xi$\dpi{100} \mu$| fi] / [∑ fi ] = 16 / 15 = mean deviation of x from mean.