MATH STATISTICS.pptx university level students
- 1. CONT… Calculate the coefficient of variation CV=SD µ SD =0.50709 AND SD =1.192037 ₁ ₂ µ =7.2 AND µ =7.325 ₁ ₂ CV =0.50709 X 100% AND CV =1.92037 X 100% ₁ ₂ 7.2 7.325 CV =7.04% AND CV =26.22% ₁ ₂ NOTE; A higher CV indicates greater variability relative to mean. A lower CV indicates less variability relative to the mean.
- 2. USES OF COEFFICIENT OF VARIATION 1. Comparing risk or volatility In finance used to compare the risk (standard deviation) of different investment relative to their expected returns. A lower CV indicates a better risk-return trade-off 2.Comparing Variability Across Datasets When comparing datasets with different units or scales (e.g comparing variability in test scores vs income), CV standardizes the comparison. 3. Quality Control In manufacturing, CV helps assess consistency or variability in production process. A lower CV means more consistent product quality.
- 4. MEANING Coefficient of variation is a type of relative measure of dispersion expressed as a ratio of standard variation to the mean OR Is a statistical measure of a relative variability of a data set. It is defined as the ratio of standard deviation to the mean often expressed as a percentage. CV=STANDARD DEVIATION (∂) X 100% MEAN (µ) Where standard deviation = √VARIANCE VARIANCE= (X-µ)² N
- 5. EXAMPLES 1 1.Business product sales Product A Mean monthly sales = 1000 units Standard deviation = 100 units CV = (100/1000) X 100 =10% Product B Mean monthly sales = 500 units Standard deviation = 150 units CV = (150/500) X 100 = 30% Interpretation; Product A has more consistent sales than Product B
- 6. EXAMPLE 2 STORE 1 STORE 2 6.5 4.2 6.7 5.4 6.8 6.2 7.2 7.7 7.3 7.7 7.4 8.4 7.8 9.2 7.9 9.8