Question

The mean of 12 numbers is 11. If three numbers 2, 5 and 6 are replaced by 6, 5 and 2
respectively, then the new mean is
a)10 b)11 c)12 d) 13
please answer fast!!!

Answer 1

Given:

The mean of $12$ numbers = $11$

The numbers $2,5,6$ are replaced by $6, 5, 2$

To find:

The new mean

Formula:

$Mean\;=\;\frac{Sum\;of\;all\;observations}{Number\;of\;observations}$

Step-by-step explanation:

The sum of observations of both sets of numbers are given below:

$2+5+6\;=\;13\\\\6+5+2\;=\;13$

Since the sum of both set of numbers are equal, there will be no change in the existing mean value $11$

Answer:

Therefore, the new mean is option (b) $11$

Answer 2

SOLUTION

TO CHOOSE THE CORRECT OPTION

The mean of 12 numbers is 11. If three numbers 2, 5 and 6 are replaced by 6, 5 and 2 respectively, then the new mean is

a) 10

b) 11

c) 12

d) 13

EVALUATION

Here it is given that the mean of 12 numbers is 11.

Sum of 12 numbers

= 12 × 11

= 132

Now 2, 5 and 6 are replaced by 6, 5 and 2 respectively

Sum of 2, 5 and 6

= 2 + 5 + 6

= 13

Sum of 6, 5 and 2

= 6 + 5 + 2

= 13

New sum of 12 numbers

= 132 - 13 + 13

= 132

Since sum of 12 numbers is unchanged

So mean of 12 numbers will be unchanged

Hence the required mean

$\displaystyle \sf{ = \frac{132}{12} }$

= 11

FINAL ANSWER

Hence the correct option is b) 11

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