Question

If the sum of the deviation of a set of values x1, x2, x3,..... xn measured from 50 is ( - 10 ) and the sum of deviation of the values from 46 is 70. Then find its mean.

PLEASE ANSWER IT I HAVE TO GIVE MY BOARD EXAM ON 7 MARCH.

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Answer 1

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Sum of the deviations x1, x2, x3, � xn from 50 is -10.

So, (x1 - 50) + (x2 - 50) + (x3 - 50) � + (xn - 50) = -10

Or x1 + x2 + x3 �+ xn - 50n = -10

Or x1 + x2 + x3 �+ xn = 50n - 10 � (1)

Sum of deviations of the values from 46 is 70

So, (x1 - 46) + (x2 - 46) + (x3 - 46) � + (xn - 46) = 70

Or x1 + x2 + x3 �+ xn - 46n = 70

Or 50n - 10 - 46n = 70 [Using (1)]

Or 4n = 80

Or n = 20

That is total number of observations is 20.

So, sum of observations = x1 + x2 + x3 �+ xn = 50 � 20 - 10 = 990

And hence, mean of the data is 990/20 = 49.5

Answer 2

Answer:

Step-by-step explanation:

The deviations of x1, x2,... xn from 50 are x1 - 50 , x2 - 50 ,... xn -50

Hence the sum is

(x1 - 50 ) + (x2 - 50 ) + ...... (xn - 50) = -10

(x1 + x2 + ....xn) - 50 n = -10 ...(1)

similarly we have

(x1 + x2 + .....xn) - 46n = 70 ...(2)

equation (2) - (1) gives

-4n = -80

n = 20

substituting the value of n in (1)

(x1 + x2 + ....xn) - 50 (20) = -10

(x1 + x2 + ....xn) = 990

Hence the mean

(x1 + x2 + ....xn) /n = 990/20 = 49.5

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