Explain, by taking a suitable example, how the arithmetic mean alters

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 and (iv) dividing each term by non-zero constant k.

Solution:

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.