Question

(4) If a constant value 5 is subtracted from each of a set of numbers,
the mean of the set of numbers will be:
increased by 5
O 5
decreased by 5
O is not affected
Ooh​

Answer 1

Answer:

Variance is the mean of the squares of the deviations from the mean. Therefore, if a constant value that is 15 is subtracted from each observations of the set, then the variance will not be altered as the effect of such a act will be managed at the time of calculating the deviations of the series. 

Answer 2

Given,

If a constant value 5 is subtracted from each of a set of numbers,

the mean of the set of numbers will be:

Solution,

Assume that the mean of n numbers is M.

$\[ \Rightarrow \frac{{{x_1} + {x_2} + - - - - + {x_n}}}{n} = M\]$

Now, subtract five from each term.

$\[\begin{array}{l} \Rightarrow \frac{{\left( {{x_1} - 5} \right) + \left( {{x_2} - 5} \right) + - - - - + \left( {{x_n} - 5} \right)}}{n}\\ \Rightarrow \frac{{\left( {{x_1} + {x_2} + - - - - {x_n}} \right) - \left( {n5} \right)}}{n}\\ \Rightarrow \frac{{\left( {{x_1} + {x_2} + - - - - {x_n}} \right)}}{n} - \frac{{n5}}{n}\\ \Rightarrow M - 5\end{array}\]$

Hence, the correct option is (c) i.e.  decreased by five.