Maths-
General
Easy

Question

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

  1. 5 times to the first A.M.    
  2. increased by 5 to the first A.M.    
  3. equal to the first A.M.    
  4. 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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