Explain, by taking a suitable example, how the arithmetic mean al… - Vidyadip

Question

Explain, by taking a suitable example, how the arithmetic mean alters by:
$i.$ Adding a constant $k$ to each term.
$ii.$ Subtracting a constant $k$ from each term.
$iii.$ Multiplying each term by a constant $k.$
$iv.$ Dividing each term by non-zero constant $k.$

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Answer

Let say numbers are $3, 4, 5$
$\therefore$ mean$=\frac{\text{Sum of numbers}}{\text{Total numbers}}$
$=\frac{ 3+ 4+5}{3}$
$=4$
$i.$ Adding constant term $k = 2$ in each term.
New numbers are $= 5, 6, 7$
$\therefore$ mean$=\frac{\text{Sum of numbers}}{\text{Total numbers}}$
$=\frac{ 5+ 6+7}{3}$
$\therefore$ New mean will be $2$ more than the original mean.
$ii.$ Subtracting constant term $k = 2$ in each term.
New numbers are $= 1, 2, 3$
$\therefore$ mean$=\frac{\text{Sum of numbers}}{\text{Total numbers}}$
$=\frac{ 1+ 2+3}{3}$
$\therefore$ New mean will be $2$ less than the original mean.
$iii.$ Multiplying by constant term $k = 2$ in each term.
New numbers are $= 6, 8, 10$
$\therefore$ mean$=\frac{\text{Sum of numbers}}{\text{Total numbers}}$
$=\frac{ 6+ 8+10}{3}$
$=8=4\times2$
$\therefore$ New mean will be $2$ times of the original mean.
$iv.$ Divide the constant term $k = 2$ in each term.
New numbers are $= 1.5, 2, 2.5.$
$\therefore$ mean$=\frac{\text{Sum of numbers}}{\text{Total numbers}}$
$=\frac{ 1.5+ 2+2.5}{3}$
$=2=\frac{4}{2}$
$\therefore$ New mean will be half of the original mean.

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