# The mean of a data is 10. If each observation is multiplied by 5 and then 1 is added to each result , find the mean of the new observations so obtained

1
by anudeepd2

2015-04-22T20:24:52+05:30

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Let the data set be :  Di , for i = 1, to 10,  ie.,  D₁, D₂, ... D₁₀
mean μ of N observations = 10.
So total of the N observations = 10 N

The new data set contains :  5 Di + 1,  ie.,  5 D₁+1, 5 D₂+2,..., 5 D_N+1
Sum of the new data set =  5 (D₁ + D₂ + D₃ ... D_N ) + (1+1+...N times)
=  5 * 10 N  +  N
= 51 N
So mean of the new data set = 51 N / N = 51

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If each data item is multiplied by x then the mean is also multiplied by  x.
If each data item is added by x  then the mean is also added by x.

If each item is multiplied by a and b is added to each item, then the mean becomes a times plus b.