Question

The mean of n observation is x bar. If each observation is increased by 5, what will be the new mean?

Answer 1

Answer:

The new mean will be x(bar) + 5

Step-by-step explanation:

Suppose there are "n" observations, denoted as:

x1, x2, x3, ....xn

then,

x(bar) = (x1 + x2 + .....+xn)/n

x(bar) is the OLD mean

Let us define a new variable Y such that

y1 = x1 + 5; y2 = x2 + 5; etc.

Let y(bar) denote the mean of y1, y2, .....yn

Hence y(bar) is the NEW mean

y(bar) = (y1 + y2 + .....+yn)/n

But y1 = x1 + 5, and so on,

Hence:

y(bar) = [(x1 + 5) + (x2 + 5) + .....+ (xn + 5)]/n

          = [(x1 + x2 + .... +xn) + (5 + 5 + .....n times)]/n

          = [(x1 + x2 + .... +xn) + (5n)]/n

           = (x1 + x2 + .... +xn)/n + (5n/n)

            = x(bar) + 5

y(bar) = x(bar) + 5

=> New mean = x(bar) + 5

In general, if each observation is increased by 5,the new mean also increases by 5.

More explanation:

In Step 4 of the calculation of y(bar) we have used the rule:

(a + b)/c = a/c + b/c

Also, 5 + 5 + 5 + ...n times = 5xn = 5n

Answer 2

Step-by-step explanation:

xbar + 5

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