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The mean of $5$ numbers is $27$ . If one more number is included, then the mean is $25$ . Find the included number.

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-15

5

- 8

answer is A.

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Detailed Solution

It is given that the mean of

5

numbers is

27

. It is given that if one more number is included, then the mean is

25

. We have to find the included number.
Let the five numbers be

a, b, c, d, e

.
By data,

Mean = 27

We know that,

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

\Rightarrow 27 = \frac{a + b + c + d + e}{5}

\Rightarrow 27 \times 5 = a + b + c + d + e

\Rightarrow a + b + c + d + e = 135

— (1)
Let the included number be

f

.
Then,

Mean = 25

We know that,

Mean = \frac{Sum of the observations}{N umber of the observations}

\Rightarrow 25 = \frac{a + b + c + d + e + f}{6}

\Rightarrow 25 \times 6 = a + b + c + d + e + f

\Rightarrow a + b + c + d + e + f = 150

— (2)
Subtracting eq(1) from eq(2),

\Rightarrow (a + b + c + d + e + f) - (a + b + c + d + e) = (150) - (135)

\Rightarrow f = - 15

Thus, the included number is

- 15

.
Hence, the correct option is 1.

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