An economic researcher recorded the price per bag of cocoa (in thousands of Naira) across … — JAMB UTME

An economic researcher recorded the price per bag of cocoa (in thousands of Naira) across five key agricultural markets as $₦14$ , $₦18$ , $₦20$ , $₦22$ , and $₦26$ . What is the coefficient of variation of these cocoa prices?

$20\%$ Answer
B
$16\%$
C
$80\%$
D
$4\%$

Answer

The coefficient of variation of the cocoa prices is

20\%

The coefficient of variation measures relative dispersion and is obtained by dividing the standard deviation by the mean and multiplying by

100\%

. With a mean of

20

and a standard deviation of

4

, the coefficient of variation is

\frac{4}{20} \times 100\% = 20\%

Step-by-Step Solution

Calculate the mean (

\bar{x}

) of the prices

\bar{x} = \frac{14 + 18 + 20 + 22 + 26}{5} = \frac{100}{5} = 20

The mean is required to determine deviations and as the denominator for coefficient of variation.

Calculate the sum of squared deviations from the mean

(14-20)^2 + (18-20)^2 + (20-20)^2 + (22-20)^2 + (26-20)^2 = 36 + 4 + 0 + 4 + 36 = 80

Determining the total squared deviations is necessary to calculate variance.

Compute the variance (

\sigma^2

) and standard deviation (

\sigma

)

\sigma^2 = \frac{80}{5} = 16

, so

\sigma = \sqrt{16} = 4

Variance is the average squared deviation, and standard deviation is its square root.

Calculate the coefficient of variation (

CV

)

CV = \frac{\sigma}{\bar{x}} \times 100\% = \frac{4}{20} \times 100\% = 20\%

Coefficient of variation measures relative dispersion as the ratio of standard deviation to mean expressed as a percentage.

Key Concept

Coefficient of Variation

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