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I have been given a dataset and been tasked with calculating the average wage for different job titles. The data includes a mix of ranges (min-max) and values.

If we assume for the job title, Developer, these are the wages:

1. $80K - 120K
2. $90K
3. $120K - 150K
4. $95K
5. $50K
6. $200K - 225K
7. $100K
8. $100 – 150K
9. $50K - 120K
10. $85K 

How should I calculate the average wage for a Developer?

My thoughts are to first excluded wage information for 5, 6 and 9 as these look like outliers. I would then take the average of each range and add these together with the other wages, and then divide by the number of wages.

This would give:

(100 + 90 + 135 + 95 + 100 + 125 + 85)/7 = $104K

I would then conclude that the average wage for a Developer at Company is 104K, with the range 80K to 150K.

Is this approach correct?

EDIT

80K-120K means that there's one person whose income is somewhere in that range.

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  • $\begingroup$ What does 80K-120K mean? Does it mean there's one person whose income is somewhere in that range and we're not sure where? or does it mean there's a group of people, one making 80K, one making 120K, the others making somewhere in between? If it's a group, then when you average you should weight the salary by the number of people in the group. $\endgroup$ – Gerry Myerson Mar 22 at 0:38
  • $\begingroup$ @GerryMyerson Thanks for the reply. Please see my edit which answers your question. $\endgroup$ – tigertommy Mar 22 at 0:52
  • $\begingroup$ @tigertommy: I'm sorry but I don't understand why are you not using all the data. If you fear that outliers may contaminate the mean, perhaps you should use the median. Other than that, I think it's a good idea to use the range mid-point whenever you don't know the exact value of the salary. $\endgroup$ – Ertxiem Mar 22 at 1:09
  • $\begingroup$ @Ertxiem Thanks. That's a fair point. How should I determine if I should use the median instead of the mean? $\endgroup$ – tigertommy Mar 22 at 1:14
  • $\begingroup$ @tigertommy: There if no computation that can answer that. It really depends on the aims of the study and how do you wish to deal with the outliers. $\endgroup$ – Ertxiem Mar 22 at 1:19
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Your decision as to what constitutes an outlier is a very subjective one and has no place in analytics. There is no reason to suspect that salaries should follow a normal, or similarly shaped, distribution. It is completely understandable to have a junior developer just out of uni on a wage several standard deviations less than the average and experienced managerial level developers many times above. I have a feeling a real distribution would be at least bi-modal.

Please don't exclude outliers without a solid justification for doing so, but apart from that your approach is completely correct.

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  • $\begingroup$ Thank you. That's a fair point. I eliminated those data points in a subjective manner. I did so as I believe they may skew the mean or as @Ertxiem wrote: "contaminate the mean". Do you think it would be better to use the median instead of the mean? $\endgroup$ – tigertommy Mar 22 at 1:12
  • $\begingroup$ As he/she says, it depends on the objectives of the study. Some continuous distributions do not have a finite mean and in such a case measuring a value is meaningless. For your underlying distribution it may be that the mean isn't a quantity that is meaningful to a reader who is unfamiliar with statistics that do not follow a bell shaped curve. If your audience is more advanced you could report skew and potentially kurtosis, or if you get more data a graph of the distribution. Good data visualisation can help the least experienced understand your findings. $\endgroup$ – Paul Childs Mar 22 at 1:32
  • $\begingroup$ If you are giving the range, the median won't provide any extra information. The mode can be useful but you likely don't have enough data for an accurate determination of one. Another approach to determining the mode is to fit a representive curve and find the peak. $\endgroup$ – Paul Childs Mar 22 at 1:33

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