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The mean of $75$ numbers is $35$ . If each number is multiplied by $4$ , find the new mean.

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140

280

answer is A.

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Detailed Solution

It is given that the mean of

75

numbers is

35

. We need to find the new mean if each number is multiplied by

4

.
We know that,

Mean = \frac{Sum of observations}{Number of observations}

\Rightarrow 35 = \frac{a_{0} + a_{1} + a_{2} + . . . . . + a_{74}}{75}

\Rightarrow a_{0} + a_{1} + a_{2} + . . . . . + a_{74} = 35 \times 75

\Rightarrow a_{0} + a_{1} + a_{2} + . . . . . + a_{74} = 2625

— (1)
Let

x

be the new mean when each term is multiplied by

4

\Rightarrow x = \frac{4 a_{0} + {4 a}_{1} + {4 a}_{2} + . . . . . + {4 a}_{74}}{75}

\Rightarrow x = \frac{4 (a_{0} + a_{1} + a_{2} + . . . . . + a_{74})}{75}

Substituting eq (1) in the above equation,

\Rightarrow x = \frac{4 \times 2625}{75}

\Rightarrow x = 140

Thus the new mean when each term is multiplied by

4

140

.
Hence, the correct option is 1.

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