Question Bank - Mathematics

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If the algebraic sum of the deviations of the same set of values measured from y is 180, then what is the value of y ?

A.
80
B.
85
C.
90
D.
95

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 y is 180(x1 - y) + (x2 - y) + (x3 - y) + ......... +(xn - y) = 180? x1 + x2 + x3 + .......... + xn - ny = 180 Putting the value of equation (1) and (2) in above equation, we get,? 1980 - 20 × y = 180? 1980 - 180 = 20y? 1800 = 20y? y = 90? The value of y is 90.

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