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2015-03-10T13:33:01+05:30

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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
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2015-03-10T14:21:19+05:30

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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.
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