Explain, by taking a suitable example, how the arithmetic mean alters by: 1. Adding a constant k to each term. 2. Subtracting a constant k from each term. 3. Multiplying each term by a constant k. 4. Dividing each term by non-zero constant k.

Let say numbers are 3, 4, 5 = Sum of numbers Total numbers = 3+ 4+5 3 =4 1. Adding constant term k = 2 in each term. New numbers are = 5, 6, 7 = Sum of numbers Total numbers = 5+ 6+7 3 New mean will be 2 more than the original mean. 2. Subtracting constant term k = 2 in each term. New numbers are = 1, 2, 3 = Sum of numbers Total numbers = 1+ 2+3 3 New mean will be 2 less than the original mean. 3. Multiplying by constant term k = 2 in each term. New numbers are = 6, 8, 10 = Sum of numbers Total numbers = 6+ 8+10 3 =8=4 2 New mean will be 2 times of the original mean. 4. Divide the constant term k = 2 in each term. New numbers are = 1.5, 2, 2.5. = Sum of numbers Total numbers = 1.5+ 2+2.5 3 =2=4 2 New mean will be half of the original mean.

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

Download App

Question

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

Adding a constant k to each term.
Subtracting a constant k from each term.
Multiplying each term by a constant k.
Dividing each term by non-zero constant k.

✓

Answer

Let say numbers are 3, 4, 5$\therefore\text{Mean}=\frac{\text{Sum of numbers}}{\text{Total numbers}}$
$=\frac{ 3+ 4+5}{3}$
$=4$

Adding constant term k = 2 in each term.

New numbers are = 5, 6, 7
$\therefore\text{Mean}=\frac{\text{Sum of numbers}}{\text{Total numbers}}$
$=\frac{ 5+ 6+7}{3}$
$\therefore$ New mean will be 2 more than the original mean.

Subtracting constant term k = 2 in each term.

New numbers are = 1, 2, 3
$\therefore\text{Mean}=\frac{\text{Sum of numbers}}{\text{Total numbers}}$
$=\frac{ 1+ 2+3}{3}$
$\therefore$ New mean will be 2 less than the original mean.

Multiplying by constant term k = 2 in each term.

New numbers are = 6, 8, 10
$\therefore\text{Mean}=\frac{\text{Sum of numbers}}{\text{Total numbers}}$
$=\frac{ 6+ 8+10}{3}$
$=8=4\times2$
$\therefore$ New mean will be 2 times of the original mean.

Divide the constant term k = 2 in each term.

New numbers are = 1.5, 2, 2.5.
$\therefore\text{Mean}=\frac{\text{Sum of numbers}}{\text{Total numbers}}$
$=\frac{ 1.5+ 2+2.5}{3}$
$=2=\frac{4}{2}$
$\therefore$ New mean will be half of the original mean.