Question

If 5 is subtracted from each observation of some certain item then its co- efficient of variation is 10% and if 5 is added to each item then its coefficient of variation is 6%. Find original coefficient of variation.​

Answer 1

write both equations and divide to get x and substitute in one of the eqn to get 'sigma' and then find coefficient of variation using both.

Answer 2

Answer:

Option B : 7.5%

Step-by-step explanation:

For coefficient of variation = 10%

$\frac{∝}{x + 5} * 100 = 10$ .............................. (Equation 1)

For coefficient of variation = 6%

$\frac{∝}{x - 5} * 100 = 6$ ................................. (Equation 2)

Now,

Divide Equation 1 and Equation 2,

We get,

∴ $\frac{x + 5}{x - 5} = \frac{10}{6}$

∴ $\frac{x + 5}{x - 5} = \frac{5}{3}$

∴ 3x + 15 = 5x - 25

∴ 5x - 3x = 15 + 25

∴ 2x = 40

∴ x = 20

Now,

put x = 20 in equation 1

$\frac{∝}{20 - 5} * 100 = 10$

∝ = $\frac{10 * 15}{100}$

∝ = 1.5

Now,

Coefficient of variation is

$\frac{1.5 }{20} * 100$ = 7.5

∴ Coefficient of variation is 7.5%

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