Question

The mean of 10 numbers is 5. When an eleventh number is added to the original ten, the new mean is 7.What was the eleventh number?

Answer 1

Let:

S = Sum of the sample

N = Sample size

M = Mean

Where:

Mean = 5 for N=10

and

Mean = 7 for N = 11

M = S/N

5 = S/10

Solving for S:

S = 50

So:

(S + x)/11 = 7

Where:

x = eleventh number

(50 + x)/11 = 7

Solving for x:

50 + x = 77

x = 77 - 50

x = 27