Question

the mean of 6 numbers is 12 if 2 numbers are excluded the new mean is 11 find the mean of excluded numbers


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Answer 1

Answer :

The mean of excluded numbers = 14

Step-by-step explanation :

Given :

• the mean of 6 numbers is 12
• if 2 numbers are excluded the new mean is 11

To find :

the mean of excluded numbers

Solution :

$\boxed{\longrightarrow \tt Mean=\dfrac{sum \ of \ observations}{number \ of \ observations}}$

Given, mean of 6 numbers is 12

   $\sf 12=\dfrac{sum \ of \ six \ numbers}{6} \\\\ \sf sum \ of \ six \ numbers=12 \times 6 \\\\ \sf \longrightarrow sum \ of \ six \ numbers=72$

If 2 numbers are excluded, then number of observations = 4

 new mean = 11

   $\sf 11=\dfrac{sum \ of \ four \ numbers}{4} \\\\ \sf sum \ of \ four \ numbers=11 \times 4 \\\\ \sf \longrightarrow sum \ of \ four \ numbers=44$

The sum of the two excluded numbers is equal to the difference between sum of six numbers and sum of four numbers.

➣ The sum of the two excluded numbers = (sum of six numbers) - (sum of four numbers)

➣ The sum of the two excluded numbers = 72 - 44

➣ The sum of the two excluded numbers = 28

Now, we have to find the mean of excluded numbers.

 $\sf Mean=\dfrac{sum \ of \ the \ two \ excluded \ numbers}{2} \\\\ \sf mean=\dfrac{28}{2} \\\\ \underline{ \sf Mean=14}$

Therefore, the mean of excluded numbers is 14.