Question

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?

Answer 1

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