Question

The mean of 9 numbers is x. If one number is included which is 3x, then the new mean is​

Answer 1

SOLUTION

GIVEN

• The mean of 9 numbers is x

• one number is included which is 3x

TO DETERMINE

The new mean

EVALUATION

Here it is given that the mean of 9 numbers is x

∴ The sum of the 9 numbers = 9x

Now one number is included which is 3x

∴ Total number of observations = 9 + 1 = 10

∴ Sum of the 10 numbers

= 9x + 3x

= 12x

∴ The new mean

$= \displaystyle \sf{ \frac{12x}{10} }$

$= \displaystyle \sf{1.2x }$

FINAL ANSWER

The new mean = 1.2x

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Answer 2

Given :  

The mean of 9 numbers = x

one number is included = 3x

To find : The new mean

Solution :  

Mean = sum of all observations/Total number of observations

x = sum of 9 observations/9

Sum of 9 observations = 9 × x

Sum of 9 observations = 9x

When one number is included which is 3x, then total number of observations is  (9 + 1) = 10

New Mean = sum of 10 observations/10

New Mean = (9x + 3x)/10

New Mean = 12x/10

New Mean = 1.2x

Hence, the new mean is 1.2x.  

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