# 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.

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

• 1

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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