Solve the following questions based on the average wage rates and standard deviation of two similar company X and Y as represented in the table. [3+2] Company Average wage rate Standard deviation :…

Part 1: Coefficient of Variation and Consistency of Wage Rates

1. Coefficient of Variation (CV) for Each Company

The coefficient of variation (CV) is calculated using the formula: $$CV=\left(\frac{\text{Standard Deviation}}{\text{Average}}\right)\times 100$$

For Company X: $$C{V}_X=\left(\frac{13}{40}\right)\times 100=32.5\%$$

For Company Y: $$C{V}_Y=\left(\frac{14}{50}\right)\times 100=28\%$$

2. Which Company’s Wage Rate is More Consistent?

The coefficient of variation (CV) measures the relative variability of data. A lower CV indicates greater consistency (less dispersion relative to the mean).

• Company Y has a lower CV (28%) compared to Company X (32.5%).
• This means Company Y’s wage rates are more consistent because the standard deviation is smaller relative to its average wage.

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Part 2: Paasche’s Price Index (Alternative Question)

Step 1: Calculate the Paasche Price Index Formula

The Paasche Price Index (PPI) is calculated as: $$PPI=\left(\frac{\sum (P_1\times Q_1)}{\sum (P_0\times Q_1)}\right)\times 100$$ where:

• $P_0$ = Base year (2020) prices
• $P_1$ = Current year (2024) prices
• $Q_1$ = Current year (2024) quantities

Step 2: Compute the Numerator ($\sum P_1\times Q_1$)

Step 3: Compute the Denominator ($\sum P_0\times Q_1$)

Step 4: Calculate the Paasche Index

$$PPI=\left(\frac{900}{644}\right)\times 100=140.06$$

Interpretation

• The Paasche Index is 140.06, meaning prices in 2024 are 40.06% higher than in 2020.
• This indicates inflation in the given commodities between 2020 and 2024.