Question
Sun December 16, 2012 By:

The mean of 20 numbers is 18. If 18 is added to each of the first ten numbers,find the mean of new set of 20 numbers.

Expert Reply
Sun December 16, 2012

We know that,

Sum of observations = Mean × Number of observation, n

? Sum of 20 observation = 18 × 20

x 1x x +.......x 8 + x 9 + x 10 + x 11 + x 12 +..........+x 20 = 360 ...(1)

when 18 is added to first 10 observation, then

Sum of new observations

= (x 1 + 18) + (x 2 + 18) + (x 3 + 18) +......+ (x 8 + 18) + (x 9 + 18) + (x 10 + 18) + x 11 x 12 +..........+ x 20.

= (x 1 + x + ...... + x 20) + 18 × 10

= 360 + 180 (Using (1))

= 540

So, mean of new observations = 540/20 = 27

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