State true or false.

The mean of 20 numbers is 18. If 3 is added to each of the first ten numbers, then the mean of the new set of 20 numbers will be 18.5.

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True

False

answer is B.

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Detailed Solution

Given that,
Mean of 20 numbers= 18.
We have to check if 3 is added to each of the first ten numbers, then the mean of the new set of 20 numbers will be 18.5.
We know that,

Mean= Sum of all observations Number of observations

Calculating the sum of all observations,

Sum of all numbers 20 = 18 Sum of all numbers = 20 × 18 = 360

Note that the same number, that is, 3 is added to the first 10 numbers.

⇒ 3 × 10 = 30

Hence, the new of sum will be,
= 360 + 30 = 390
Calculating the new mean after 3 is added to each of the first ten numbers using the above formula,

39020 = 19.5

.
So, if the mean of 20 numbers is 18 and 3 is added to each of the first ten numbers, then the mean of the new set of 20 numbers will be 19.5.
Thus the statement is false.
Therefore, option 2 is correct.

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