# The mean of 20 numbers is 18. If 3 is added to each of the first ten numbers, find the mean of the new set of 20 numbers.

@kmr.rv: Good answer!Keep posting!

Let the 20 observations be x1, x2, x3,.......,x8, x9, x10, x11, x12,..........,x20.

We know that,

Sum of n observations = Mean × Number of observation, n

∴ Sum of 20 observation = 18 × 20

⇒  x1+ x2 + x3 +.......x8 + x9 + x10 + x11 + x12 +..........+x20 = 360   ...(1)

when 3 is added to first 10 observation, then

Sum of new observations

= (x1 + 3) + (x2 + 3) + (x3 + 3) +......+ (x8 + 3) + (x9 + 3) + (x10 + 3) + x11 + x12 +..........+ x20.

= (x1 + x2 + ...... + x20) + 3 × 10

= 360 + 30         (Using (1))

= 390

Thus, the mean of new observations is 19.5.

• 17

LET SUM OF TERMS BE "S".

18 = S/20

S =1820 = 360

SINCE 3 IS ADDED TO FIRST 10 TERMS

S' = 360+310

S' = 360+30=390

MEAN OF NEW SET = S'/20 =390/20

= 19.5

• 2

S =1820 = 360

SINCE 3 IS ADDED TO FIRST 10 TERMS

S' = 360+310

S' = 360+30=390

MEAN OF NEW SET = S'/20 =390/20

=

19
• 1
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