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 :…

Solution to the First Question

1. Coefficient of Variation (CV) for Each Company

The coefficient of variation (CV) is a statistical measure that indicates the relative variability of data points in a dataset. It is calculated using the formula:

$$CV=\left(\frac{\sigma }{\bar{x}}\right)\times 100$$

where:

• $\sigma$ = standard deviation
• $\bar{x}$ = average wage rate

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) helps determine the consistency of wage rates. A lower CV indicates greater consistency (less variability relative to the mean).

• Company X has a CV of 32.5%.
• Company Y has a CV of 28%.

Since 28% < 32.5%, Company Y’s wage rate is more consistent than Company X’s. This means that the wage rates in Company Y are more stable and less dispersed compared to those in Company X.

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Solution to the Second Question (OR)

1. Index Number Using Paasche’s Method

Paasche’s index number is calculated using the formula:

$$P_{01}=\left(\frac{\sum (p_1{q}_1)}{\sum (p_0{q}_1)}\right)\times 100$$

where:

• $p_0$ = price in the base year (2020)
• $p_1$ = price in the current year (2024)
• $q_1$ = quantity in the current year (2024)

Calculations:

$$P_{01}=\left(\frac{892}{644}\right)\times 100=138.51$$

2. Interpretation of the Result

The Paasche’s index number is 138.51, which means that the price level in 2024 is 138.51% of the price level in 2020. In other words, there has been a 38.51% increase in prices from 2020 to 2024. This indicates inflationary pressure in the economy.