Aaron Han W. answered • 05/31/21
Engineering Grad for Math and Science Tutoring
For A)
You can determine the weighted mean finding the following:
- Sum of scores multiplied by the weights
- The total weights
- Your weighted mean will then be: Sum of Scores * Weights / Total Weights.
In this case, we get:
(4 * 2 + 2 * 2 + 5 * 3 + 5 * 3 + 4 * 1) / (2 + 2 + 3 + 3 + 1) = 4.18
The regular mean is the same steps except we treat the weights as 1 for each.
In this case, we get:
(4 + 2 + 5 + 5 + 4) / (5) = 4
For B)
We can see that the weighting increases how much each individual score category affects / improves the weighted average. The categories with the highest weights would have a larger impact on the weighted average. This means that the companies most value Interpersonal Skills and Communication Skills.
Thanks,
- Aaron
Aaron Han W.
Hi Gary, good question! It depends on what they are asking the mean to be of. If they were asking for the mean scores across the applicants, in this case where we only have 1 applicant, we would use 1 instead of 5 as the count. I believe the question is asking for the regular mean score for this one application across the 5 categories. In that case, we are taking the average across is 5 scores and hence the count would be 5 instead. Thanks, - Aaron05/31/21
Gary H.
ohh okay thank you so much Aaron very good explanation, and also in this case the sample mean would be used? (I know population & sample mean give the same results, but just want to make sure)05/31/21
Aaron Han W.
Hi Gary, I think this is also an interesting question. If we were taking the average across all applicants, I would say we are doing a sample mean. The reason being that we are likely calculating the mean from a sample of all applicants that are available as opposed to the mean from the entire population. In the case that we are taking the average across these 5 categories, since we know that these are the only 5 categories being evaluated and that these are all the categories that are available, I think it would be reasonable to use the population mean. However, as you mentioned the resulting value would be the same. Thanks! - Aaron05/31/21
Gary H.
that makes sense, thank you again Aaron!05/31/21
David W.
Sorry, no! The regular mean is simply the arithmetic average of this applicant's five scores [4.0]. The weighted mean of this applicant's five scores is the weighted arithmetic average of this applicant's five scores [4.18]. The population mean score [over all categories] is somewhere 5<mean<25 [note: yes, could be converted to 1<mean<5 when divided by 5 to make sense for a 1-5 rating system]. The weighted population mean [over all categories] is somewhere 15<wmean<25 [or, also,1<wmean<5 when converted], but it is NOT NECESSARILY THE SAME as the weighted mean [over all categories] FOR THIS ONE SAMPLE; it could be anywhere in that range [note: suppose all other 99 applicants got five ones as their score].06/01/21
Gary H.
thank you, but for the regular mean, wouldn't it be 1 instead of 5 because of the one applicant? And also you would use sample mean in this case.05/31/21