Data Sufficiency

dferm wrote:At a certain company, the average (arithmetic mean) number of years of experience is 9.8 years for the male employees and 9.1 years for the female employees. What is the ratio of the number of the company's male employees to the number of the company's female employee?

(1) There are 52 male employees at the company
(2) The average number of years of experience for the company's male and female employees combined is 9.3 years.

Please explain the equation setup..

I got this question correct but need a little more light on the problem..

here's a general fact, without the numbers at first:
for a weighted average
* if you know the fractions of the population corresponding to the different data points, then you can find the weighted average (regardless of whether you know the actual # of individuals in the population) --
see this
https://www.beatthegmat.com/averages-t10427.html#42150

* if there are only two different data points and you know the weighted average, then you can figure out the fractions of the population that correspond to the two different data points.

the latter of these two points is the one that applies here: if you know that there are only two data points (9.1 and 9.8), and you know the weighted average of those data points (9.3), then you can find the fractions of the population corresponding to 9.1 and 9.8. for data sufficiency, it doesn't matter what those fractions are, so you're done as soon as you make that realization.

--

here's how to actually find the fractions (in case you have a problem solving problem, say):

1) figure out the distance between the weighted average and each of the 2 data points
in this problem, those distances are 0.2 (between 9.1 and 9.3) and 0.5 (between 9.8 and 9.3).

2) find the ratio of those distances
the ratio in this case is 5:2

3) the ratio of those distances is the same as the ratio of the parts into which the population is divided. assign the greater part of the ratio to whichever data point is closer to the average -- yes, i know that wording is somewhat awkward, but this isn't an easy concept to put into words
in this case, the ratio of women to men must be 5:2, because the women's average (9.1) is closer to the overall average, meaning that there are more women.

a ratio of 5:2 means that 5/7 of the workers are women and the other 2/7 of the workers are men.

mmslf75 wrote:Ron ,,,, u rock man..!!!

superb explanation..!!

thanks.