The mean of a set of numbers is 20. If each number is multiplied by 2, then find the mean of the new set

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answer is A.

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Detailed Solution

Given that mean of a set of numbers is 20. Each number is multiplied by 2.
The value of the mean of a given data set is the average of a given set of numbers.
Suppose the set of numbers be

x 1, x 2, x 3 … … .. x n

Thus, the mean of set is,

x ¯ = x 1 + x 2 + x 3 … … . x n n

Now, if each number is multiplied by k, then new numbers will be

k x 1, k x 2, k x 3 … … . k x n

The mean of new set is,

⇒ X ¯ = k x 1 + k x 2 + k x 3 … … k x n n ⇒ X ¯ = k x ¯

Substituting the values, we get,

X ¯ = 2 × 20 ⇒ X ¯ = 40

So, the new mean is 40.
Therefore, option (1) is correct.

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