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Measures Of Central Tendency — Maths STD 9 — Question

Gujarat BoardEnglish MediumSTD 9MathsMeasures Of Central Tendency5 Marks
Question
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.
✓

Answer

Let say numbers are 3, 4, 5

$\therefore\text{Mean}=\frac{\text{Sum of numbers}}{\text{Total numbers}}$

$=\frac{ 3+ 4+5}{3}$

$=4$

  1. 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.

  1. 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.

  1. 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.

  1. 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.

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