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2015-11-08T18:44:22+05:30

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[If 'n' is added to each observation then'n' should also be added to the mean.]
therefore:
             mean of 20 numbers = 59
 {When 3 is added to each observation,the mean = 59+3}
                                                                        = 62
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[If 'n' is multiplied to each observation then'n' should also be multiplied to the mean.]
2)  mean of 12 numbers= 48
{when each observation is multiplied by 4,then mean= 48*4
                                                                            = 192
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2015-11-08T19:29:34+05:30

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mean = \mu =\frac{1}{N} \Sigma_{i=1}^N\ x_i\\\\(1)Each\ observation\ x_i'=x_i+3 * 1\\\\\mu'=\frac{1}{N} \Sigma_{i=1}^N\ x_i'=\frac{1}{N} \Sigma_{i=1}^N\ x_i+\frac{1}{N}\Sigma_{i=1}^N\ 3\\\\=\mu+3.\\\\ \\(2) x_i'=4*x_i\\\\\mu'=\frac{1}{N} \Sigma_{i=1}^N\ x_i'=\frac{1}{N} \Sigma_{i=1}^N\ 4 * x_i=\frac{1}{N} *4*\Sigma_{i=1}^N\ x_i\\\\=4*\mu.


Thus when 3 is added to each number in the population having a mean of 59, the mean becomes 59 + 3 = 62.

Thus when each number in the population is multiplied by 4, then mean is multiplied by 4 ie., mean = 48 * 4 = 192

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