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Q.
The mean of a set of numbers is $\bar{x}$. If each item is decreased by $4$, then mean of new observations (set) is
Statistics
Solution:
Let the n numbers are $x_1$, $x_2$, $x_3$, ..., $x_n$
$\therefore $ New items are $x_{1} - 4$, $x_{2} - 4$, $x_{3} - 4$ ,..., $x_{n} - 4$
$\therefore $ New mean $= \frac{\left(x_{1}-4\right)+\left(x_{2}-4\right)+... + \left(x_{n}-4\right)}{n}$
$= \frac{x_{1}+x_{2}+... x_{n}-4n}{n}$
$= \frac{x_{1}+x_{2}+... x_{n}}{n}- 4 = \bar{x} - 4$
So, new mean is reduced by $4$ units in $\bar{x}$