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The mean of $10$ observations is $15$ . If $15$ is added, then the new mean is

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15.9

11

10

15

answer is A.

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Detailed Solution

It is given that the mean of

10

observations is

15

. We need to find the new mean if

15

is added to the given observations.
We know that,

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

\Rightarrow 15 = \frac{x_{1} + x_{2} + . . . . . + x_{100}}{10}

{\Rightarrow x}_{1} + x_{2} + . . . . . + x_{100} = 15 \times 10

{\Rightarrow x}_{1} + x_{2} + . . . . . + x_{100} = 150

15

is added to the given data, then

{\Rightarrow x}_{1} + x_{2} + . . . . . + x_{100} + 15 = 150 + 15

{\Rightarrow x}_{1} + x_{2} + . . . . . + x_{100} + 15 = 175

Therefore,

New mea n = \frac{x_{1} + x_{2} + . . . . . + x_{100} + 15}{11}

\Rightarrow New mean = \frac{175}{11}

\Rightarrow New mean = 15.9

Thus the new mean of the given data is

15.9

.
Hence, the correct option is 1.

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