Posted by Rena on Friday, December 10, 2010 at 8:16am.
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?

Math  Reiny, Friday, December 10, 2010 at 10:14am
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
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