Question

The mean of the data x₁,x₂,x₃,.........xn is 102.Find the mean of the data 5x₁,5x₂,5x₃,..........5x n.

Answer 1

Mean (Let it be M)= Sum of observations (Let it be S) / Total no. (Let it be n)
Therefore, M1=S/n
Given, M1=102
Therefore, x1+x2+x3+...+xn/n =102
Now, Mean of 5x1,5x2...,5xn=?
M2= 5x1+5x2+5x3+...+5xn/n
Taking 5 as common,
5(x1+x2+x3+...+xn)/n
=5M1 (5 times the new mean)
=5x102=510

Answer 2

$data\ are\ x_1,\ x_2,\ x_3,\ x_4,\ ....\ x_n.\\ mean,\ \bar x=102\\ \\ \Rightarrow 102= \frac{x_1+x_2+....+x_n}{n} \\ \\now\ we\ need\ to\ find\ mean\ of\ x_1,\ x_2,\ x_3,\ x_4,\ ....\ x_n.\\ \\ \bar x' = \frac{5x_1+5x_2+5x_3+....+5x_n}{n}\\ \\ \Rightarrow \bar x' = \frac{5(x_1+x_2+x_3+....+x_n)}{n}\\ \\ \Rightarrow \bar x' =5 \times \frac{x_1+x_2+x_3+....+x_n}{n}\\ \\ \Rightarrow \bar x' =5 \times 102=510\\ \\ The\ mean\ is\ 510.$