The mean salary of the female employees of one company is $29,525. The mean salary of the male employees of the same company is $33,470. Can
the mean salary of all employees of the company be obtained by finding the
mean of $29,525 and $33,470? Explain your thinking. Under what conditions would the mean of $29,525 and $33,470 yield the mean salary of all employees of the company?
Your reasoning is valid only if the number of employees of males and females is the same.
I will explain with a simple example:
group A : 100,200,200,300
average = sum/4 = 200
group B = 50, 100,200,250
avg = sum/4 = 150
true average = total of all 8/8 = 175
avg by taking the average of the two averages
= (200+150)/2 = 175
Now I will add another 200 to group A
group A: 100,200,200,200,300
avg = sum/5 = 200
true average of all 9 is now
= total of all 9 numbers/9 = 1600/9 = 177.8
while with "your method" the anwer would still be 175
Well, well, well, looks like we've got ourselves a math problem! So, the average salary of the female employees is $29,525, while the average salary of the male employees is $33,470. Can we just take the average of these two numbers and call it a day? Let's find out!
To answer your question, we need to consider the number of employees in each group. If the number of female employees is significantly different from the number of male employees, then simply averaging their salaries won't give us the mean salary of all employees.
Let me put it in perspective. If you have a party with 10 people, and one person has a giant pizza while the other nine have tiny sandwiches, then averaging the pizza and sandwich won't give you the mean snack consumption of all the party-goers. It will heavily skew towards the pizza eater!
Similarly, if there are more male employees than female employees (or vice versa), then the average salary will be influenced more by the group with more employees. So, in order to obtain the mean salary of all employees, we need to take into account the number of employees in each group. That's the only way to get an accurate picture of the overall salary distribution.
To sum it up, simply finding the mean of $29,525 and $33,470 won't necessarily yield the mean salary of all employees. We need to consider the relative sizes of the male and female employee groups. Only then can we get our hands on the true average salary.
Now, if the number of male and female employees is equal or very close, then averaging their salaries could give us a reasonable approximation of the mean salary of all employees. But if the numbers are way off, then a simple average won't cut it.
I hope my funny explanation gave you a clearer understanding! If you have more math-doubts or need a good laugh, feel free to ask!
No, the mean salary of all employees of the company cannot be obtained simply by finding the mean of the salaries of female and male employees. This is because the mean of $29,525 and $33,470 does not take into account the number of employees in each gender category.
To obtain the mean salary of all employees, we need to consider the total number of employees and the salary distribution within each gender group. If the number of male and female employees is roughly equal and their salary distributions are similar, then finding the mean of the two groups may yield the mean salary of all employees. However, if there is a significant difference in the number of employees or their salary distributions, then combining the means of the two groups will not accurately represent the mean salary of all employees.
To determine if the mean salary of all employees of the company can be obtained by finding the mean of $29,525 and $33,470, we need to consider the distribution and the number of employees for each gender.
Calculating the mean by taking the average of $29,525 and $33,470 would assume that the number of male and female employees is equal, and that their salaries are distributed evenly. If these assumptions hold true, then finding the mean of $29,525 and $33,470 would give you the mean salary of all employees of the company.
However, if the number of male and female employees is unequal, or if their salaries are not evenly distributed, then finding the mean of these two numbers would not accurately represent the mean salary of all employees.
To obtain the mean salary of all employees, you would need to consider the number of male and female employees and their respective salaries. The general formula for calculating the mean is to sum up all the salaries and divide it by the total number of employees.
For example, if the company has 100 female employees, each earning $29,525, and 200 male employees, each earning $33,470, the total sum of salaries would be (100 * $29,525) + (200 * $33,470). The total number of employees would be 100 + 200. To find the mean salary, you would divide the total sum of salaries by the total number of employees.
In summary, finding the mean of $29,525 and $33,470 can represent the mean salary of all employees under the condition that the number of male and female employees is equal, and their salaries are distributed evenly.