What is the sum of deviations of the variate values 73, 85, 92, 105, 120 from their mean?

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NDA (Held On: 18 Apr 2021) Maths Previous Year paper
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  1. -2
  2. -1
  3. 0
  4. 5

Answer (Detailed Solution Below)

Option 3 : 0
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Concept:

For the observations \(\rm x_1 ,x_2 ,x_3 ,..........,x_n\)

Mean (\(\rm\overline x\)) = \(\rm {x_1 +x_2 + x_3 +..........+x_n\over n}\)

Deviation of the observation from the mean = xi - \(\rm\overline x\)

where i ∈ [1, n]

Calculation:

Mean = \(\rm {73+85+92+105+120\over 5}\)

\(\rm\overline x\) = \(\rm {475\over 5}\) = 95

Value Mean Deviation of the value
73 95 73 - 95 = -22
85 95 85 - 95 = -10
92 95 92 - 95 = -3
105 95 105 - 95 = 10
120 95 120 - 95 = 25

 

The sum of the deviation = -22 +(-10) + (-3) + 10 + 25 = 0

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