Question Bank - Mathematics

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What is the algebraic sum of the deviations of the same set of values measured from 99?

A.
0
B.
10
C.
20
D.
40

Solution:

Concept:Mean = (Sum of all the observations/Total number of observations)Deviation = ? |X “ µ|Here, ? represents the addition of valuesX represents each value in the data setµ represents the mean of the data setCalculation:We know that the sum of observationsx1 + x2 + x3 + ....... + xn = 1980 ----(1)And the total number of observationsn = 20 ----(2)Sum of the deviations x1, x2, x3 ...... xn, from 99 is given by(x1 - 99) + (x2 - 99) + (x3 - 99) + ......... +(xn - 99)? x1 + x2 + x3 + .......... + xn - 99n Putting the value of equations (1) and (2) in equation (3), we get,1980 - 99 × 20 = 1980 - 1980 = 0? The Sum of the deviations is 0.

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