Question

The arithmetic mean of a set of 10 values is 100. If a value 155 is added, the
arithmetic mean of these 11 values is *

Answer 1

Step-by-step explanation:

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Answer 2

Answer:

The arithmetic mean of the 11 values is 105

Step-by-step explanation:

Arithmetic mean:

• The mean or the average of the data is given by the ratio of the sum of all the values of the data to the total number of the elements in the data.

       $\overline x=\dfrac{\Sigma x}{n}$      

       where n is the number of the elements.

Given the mean of a set of 10 values is 100.

So, here $n=10$ and $\overline x=100$

From the formula of mean, we get

$100=\dfrac{\Sigma x}{10} \implies\Sigma x=100\times 10=1000$

Hence, the sum of all the 10 numbers is 1000.

Given a value 155 is added as 11th number.

Thus, the new mean of 11 numbers is,

$\overline x=\dfrac{\Sigma x+155}{11}$

  $=\dfrac{1000+155}{11}=\dfrac{1155}{11}=105$  

Therefore, the arithmetic mean of the 11 values is 105.

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