Question

The mean of a sample of size $10$ is $15$. If the value of each item is reduced by $2$, the mean of the sample will be_____.

• A. $15$
• B. $13$
• C. $11$
• D. $22$

Answer 1

The correct option is B $13$

Mean refers to the average amount in a given group of data. So arithmetic mean can be calculated by adding the first term and the last term of the series and then dividing the sum by 2. In the given series the first term 'a' is decreased by 2 and the last term 'b' is also decreased by 2 , so the

Mean = {(a-2)+ (b-2)} /2

= (a+b-4) /2

= {(a+b)/2} - 4/2

= {(a+b)/2} - 2

Therefore, the mean is also decreased by 2. So,if the mean was 15 then now it will be 13.