Question

The mean of ungrouped data is 13.If each observation is doubled then find the mean of the new data.

Answer 1

Solutions :
 Let the number of Observations = n
  Let the observations in ungrouped data be x1+x2+...+xn
   Therefore mean = Sum of Observations / Number of Observations
                       Mean1 =  x1+x2+----+xn / n .......(Ist)

Now According to question ,
Each observation is doubled ,
Therefore Sum of Observations becomes = 2*x1+2*x2 + .. + 2*xn
                                                            = 2 (x1+x2+---+xn)
Number of Observations = n
Therefore,  Mean2  = Sum of Observations / number of Observations
                       =  2 (x1+x2+---+xn)/n  (Using Equation 1st)
                     Mean2 = 2 * mean1
we know that ,
mean1 = 13 (Given)
Hence mean2 = 2*13 = 26
Hope this helps you!!

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