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Calculate the Coefficient of Variation (CV) of individual wages and state which firm is more consistent.

Mathematics

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b) Calculate the Coefficient of Variation (CV) of individual wages and state which firm is more consistent.

The Coefficient of Variation (CV) is a measure of relative variability. It is calculated as the ratio of the standard deviation to the mean, expressed as a percentage.

CV=σμ×100%CV = \frac{\sigma}{\mu} \times 100\%

Where σ\sigma is the standard deviation and μ\mu is the mean (average monthly wages).
The standard deviation (σ\sigma) is the square root of the variance.

For Firm A:

  1. Identify the given values for Firm A.

    Average monthly wages (μA\mu_A) = Sh. 1860
    Variance of the distribution = 81

  2. Calculate the standard deviation for Firm A.

    σA=Variance=81=9\sigma_A = \sqrt{\text{Variance}} = \sqrt{81} = 9

  3. Calculate the Coefficient of Variation for Firm A.

    CVA=σAμA×100%CV_A = \frac{\sigma_A}{\mu_A} \times 100\% CVA=91860×100%CV_A = \frac{9}{1860} \times 100\% CVA=0.0048387×100%CV_A = 0.0048387 \times 100\% CVA≈0.4839%CV_A \approx 0.4839\%

    For Firm B:

  4. Identify the given values for Firm B.

    Average monthly wages (μB\mu_B) = Sh. 1750
    Variance of the distribution = 100

  5. Calculate the standard deviation for Firm B.

    σB=Variance=100=10\sigma_B = \sqrt{\text{Variance}} = \sqrt{100} = 10

  6. Calculate the Coefficient of Variation for Firm B.

    CVB=σBμB×100%CV_B = \frac{\sigma_B}{\mu_B} \times 100\% CVB=101750×100%CV_B = \frac{10}{1750} \times 100\% CVB=0.0057143×100%CV_B = 0.0057143 \times 100\% CVB≈0.5714%CV_B \approx 0.5714\%

  7. Compare the CVs and determine consistency.

    CVA≈0.4839%CV_A \approx 0.4839\%
    CVB≈0.5714%CV_B \approx 0.5714\%
    Since CVA<CVBCV_A < CV_B, Firm A has less relative variability in its wages, meaning its wages are more consistent.

    The Coefficient of Variation for Firm A is 0.48%\boxed{0.48\%} and for Firm B is 0.57%\boxed{0.57\%}. Firm A is more consistent.

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