A contract employs three types- Class A , Class B and class c. to class A workers, he pays an average monthly salary of $ 400, to class B workers, he pays an average monthly salary of $ 320 and to class C workers he pays an average monthly salary of $ 150. The combined average salary paid by the contractor is $ 225. If the number of class A and class B is 10 each. find the number of class C workers!
B) the standard deviaton of class A , class B and Class C workers is 15, 7 and 12 respectively. calculate the cofficient of variation of class A, B and class C workers.
c) comment on the variability in the salaries of the class A, B and C workers
To find the number of Class C workers, we need to calculate the total monthly salary paid by the contractor and subtract the combined salaries of Class A and Class B workers.
Let's calculate the total monthly salary paid by the contractor:
Total Salary = (Number of Class A Workers * Average Salary of Class A) + (Number of Class B Workers * Average Salary of Class B) + (Number of Class C Workers * Average Salary of Class C)
Total Salary = (10 * $400) + (10 * $320) + (Number of Class C Workers * $150)
Given that the combined average salary is $225, we can set up the following equation:
($225) * (10 + 10 + Number of Class C Workers) = (10 * $400) + (10 * $320) + (Number of Class C Workers * $150)
Simplifying the equation, we have:
$2250 + 2250 + 225 * Number of Class C Workers = $4000 + $3200 + $150 * Number of Class C Workers
Combining like terms, we get:
4500 + 225 * Number of Class C Workers = 7200 + 150 * Number of Class C Workers
Rearranging the equation to isolate the Number of Class C Workers, we have:
225 * Number of Class C Workers - 150 * Number of Class C Workers = 7200 - 4500
75 * Number of Class C Workers = 2700
Number of Class C Workers = 2700 / 75
Number of Class C Workers = 36
Therefore, there are 36 Class C workers.
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To calculate the coefficient of variation for each class of workers, we need the standard deviation and mean for each class.
The coefficient of variation is calculated using the formula:
Coefficient of Variation = (Standard Deviation / Mean) * 100
For Class A workers:
Standard Deviation of Class A = 15
Mean of Class A = $400
Coefficient of Variation for Class A = (15 / 400) * 100 = 3.75
For Class B workers:
Standard Deviation of Class B = 7
Mean of Class B = $320
Coefficient of Variation for Class B = (7 / 320) * 100 = 2.1875
For Class C workers:
Standard Deviation of Class C = 12
Mean of Class C = $150
Coefficient of Variation for Class C = (12 / 150) * 100 = 8
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Regarding the variability in the salaries of Class A, B, and C workers:
- Class A workers have the highest coefficient of variation (3.75), indicating a moderate level of variability in their salaries. The salaries of Class A workers can range more widely compared to their mean.
- Class B workers have the lowest coefficient of variation (2.1875), indicating a lower level of variability in their salaries. The salaries of Class B workers are relatively closer to their mean compared to Class A workers.
- Class C workers have a coefficient of variation of 8, indicating a higher level of variability in their salaries. The salaries of Class C workers can vary more compared to their mean.
Overall, the salaries of Class C workers show the highest variability among the three classes.