Question

 The mean salary of all female workers is $35,000. The mean salary of all male workers is $41,000. What must be true about the mean salary of all workers?

a. It must be $38,000.
b. It must be larger than the median salary.
c. It could be any number between $35,000 and $41,000.

d. It must be larger than $38,000.
e. It cannot be larger than $40,000.

Answer 1

Answer c.

Comments

Could you possibly give a bit of an explanation on why the other answers are incorrect? Thank you!

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Yes, Cleo, I think I can. Imagine an all-male workforce, then the mean would be $41000. If all are female workers, the mean would be $35000. So the mean of mixed male and female workers has to be somewhere in between. It can’t be outside the limits, and without knowing how many of each gender there are, no unique figure can be calculated.

Let’s do an example of a workforce of 10 people.

1. 5 male and 5 female: mean=(5m+5f)/10=5(41000)+5(35000)=(205000+175000)/10=$38000.

2. 7 male and 3 female: mean=(7m+3f)/10=7(41000)+3(35000)=(287000+105000)/10=$39200.

3. 3 male and 7 female: mean=(3m+7f)/10=3(41000)+7(35000)=(123000+245000)/10=$36800.

All these results are between $35000 and $41000. Predominantly male gives a mean of a little less than $41000 and predominantly gives a mean a little more than $35000. Instead of a fixed number of workers we can use percentages: mean is $38000 for 50% male; $39200 for 70% male; $36800 for 30% male.

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Thank you!!