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Maths-

General

Easy

Question

If 5 is added to each and every item of a data, then the A.M is

5 times to the first A.M.
increased by 5 to the first A.M.
equal to the first A.M.
decreased by 5 to the first A.M.

The correct answer is: increased by 5 to the first A.M.

Let $X subscript i$ be the original observations of the data.
Let there are total n number of observations in the data.
Sum of original observation = n X original mean
$begin inline style stack rightwards double arrow sum X subscript i space equals n x with minus on top with blank below end style$ , where $top enclose x$ is original mean of data.
Since 5 is added to each and every item of the data

Each observations of new data is of type $left parenthesis X subscript i space end subscript plus 5 right parenthesis$ .
Sum of new observations = $begin inline style sum for blank of end style X subscript i plus 5$
$N e w space M e a n space equals fraction numerator sum for blank of X subscript i plus space 5 over denominator n end fraction space equals space fraction numerator sum for blank of X subscript i plus space sum for blank of 5 over denominator n end fraction equals space fraction numerator n top enclose x plus space 5 n over denominator n end fraction space equals space fraction numerator n left parenthesis space top enclose x plus space 5 right parenthesis over denominator n end fraction equals space top enclose x plus 5$

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