1.

Calculate the mean deviation from the mean for the following data :(i) 4, 7, 8, 9, 10, 12, 13, 17(ii) 13, 17, 16, 14, 11, 13, 10, 16, 11, 18, 12, 17(iii) 38, 70, 48, 40, 42, 55, 63, 46, 54, 44

Answer»

(i) 4, 7, 8, 9, 10, 12, 13, 17

We know that,

MD = 1/n ∑ni=1|di|

Where, |di| = |xi – x|

So, let ‘x’ be the mean of the given observation.

x = [4 + 7 + 8 + 9 + 10 + 12 + 13 + 17]/8

= 80/8

= 10

Number of observations, ‘n’ = 8

xi|di| = |xi – 10|
46
73
82
91
100
122
133
177
Total24

MD = 1/n ∑ni=1|di|

= 1/8 × 24

= 3

∴ The Mean Deviation is 3.

(ii) 13, 17, 16, 14, 11, 13, 10, 16, 11, 18, 12, 17

We know that,

MD = 1/n ∑ni=1|di|

Where, |di| = |xi – x|

So, let ‘x’ be the mean of the given observation.

x = [13 + 17 + 16 + 14 + 11 + 13 + 10 + 16 + 11 + 18 + 12 + 17]/12

= 168/12

= 14

Number of observations, ‘n’ = 12

xi|di| = |xi – 14|
131
173
162
140
113
131
104
162
113
184
122
173
Total28

MD = 1/n ∑ni=1|di|

= 1/12 × 28

= 2.33

∴ The Mean Deviation is 2.33.

(iii) 38, 70, 48, 40, 42, 55, 63, 46, 54, 44

We know that,

MD = 1/n ∑ni=1|di|

Where, |di| = |xi – x|

So, let ‘x’ be the mean of the given observation.

x = [38 + 70 + 48 + 40 + 42 + 55 + 63 + 46 + 54 + 44]/10

= 500/10

= 50

Number of observations, ‘n’ = 10

xi|di| = |xi – 50|
3812
7020
482
4010
428
555
6313
464
544
446
Total84

MD = 1/n ∑ni=1|di|

= 1/10 × 84

= 8.4

∴ The Mean Deviation is 8.4.


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