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 *x*_{1}, *x*_{2}, *x*_{3},.......,*x*_{8}, *x*_{9}, *x*_{10}, *x*_{11}, *x*_{12},..........,*x*_{20}.

We know that,

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

**n**∴ Sum of 20 observation = 18 × 20

⇒ *x*_{1}+ *x*_{2 }+ *x*_{3 }+.......*x*_{8} + *x*_{9} + *x*_{10} + *x*_{11} + *x*_{12 }+..........+*x*_{20} = 360 ...(1)

when 3 is added to first 10 observation, then

Sum of new observations

= (*x*_{1} + 3) + (*x*_{2} + 3) + (*x*_{3} + 3) +......+ (*x*_{8} + 3) + (*x*_{9} + 3) + (*x*_{10} + 3) + *x*_{11 }+ *x*_{12 }+..........+ *x*_{20}.

= (*x*_{1} + *x*_{2 }+ ...... + *x*_{20}) + 3 × 10

= 360 + 30 (Using (1))

= 390

Thus, the mean of new observations is 19.5.

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