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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

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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

======================== 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.