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 and (iv) dividing each term by non-zero constant k.
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 $=\frac{\text { Sum of numbers }}{\text { Total numbers }}$
$=\frac{5+6+7}{3}$
∴ 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 $=\frac{\text { sum of numbers }}{\text { total numbers }}$
$=\frac{1+2+3}{3}$
∴ 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 × 2
∴ 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 = 4/2
∴ new mean will be half of the original mean.