Question 1175111: The number of patients in two hospitals A and B, the average wage of employees and the variances of wages are given below:
Hospital A Hospital B
No. of employees 50 100
Mean wage 120 85
Variance 9 6
In which hospital is the variation in the distribution of wages greater and why
Answer by CPhill(1959)   (Show Source):
You can put this solution on YOUR website! To determine which hospital has greater variation in the distribution of wages, we need to compare their **coefficients of variation (CV)**. The coefficient of variation measures the relative variability of data and is calculated as:
CV = (Standard Deviation / Mean) * 100%
**1. Calculate the Standard Deviation**
* Standard deviation is the square root of the variance.
* Hospital A: Standard Deviation (s_A) = √9 = 3
* Hospital B: Standard Deviation (s_B) = √6 ≈ 2.449
**2. Calculate the Coefficient of Variation (CV)**
* Hospital A: CV_A = (3 / 120) * 100% = 2.5%
* Hospital B: CV_B = (2.449 / 85) * 100% ≈ 2.88%
**3. Compare the Coefficients of Variation**
* CV_B (2.88%) > CV_A (2.5%)
**Conclusion**
The variation in the distribution of wages is greater in **Hospital B**.
**Why?**
While Hospital A has a higher absolute variance (9 vs. 6), Hospital B has a higher coefficient of variation. This means that relative to the mean wage, the spread of wages is larger in Hospital B. In other words, the wages in Hospital B are more dispersed relative to their average wage compared to the wages in Hospital A.
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