Add Up Data First, Then Take the Average? Or Take the Averages First, Then Add?
Date: 01/20/2010 at 12:36:21 From: brenda Subject: Confused when trying to find the sum of a ratio Hi, I have a database with data on 100 companies. I have a column for sales and a column for employees. I want to work out total sales per employee. However, I am confused about whether I should sum the sales for all 100 companies first, like so ... sales for firm 1 + sales for firm 2 + sales for firm 3 + ... etc. ... and then divide by the sum of the employees for all 100 companies ... employees for firm 1 + employees for firm 2 + employees for firm 3 + ... etc. ... or whether I should work out sales per employee for each individual company first, like so ... sales for firm 1 / employees for firm 1 sales for firm 2 / employees for firm 2 sales for firm 3 / employees for firm 3 ... etc. ... and then total all those averages. I thought I would get the same answer doing it either way, but this is not the case, and I'm not sure which method I should be using. Also, if I do the latter method and then take the average of that, what does that figure mean?
Date: 01/20/2010 at 13:55:06 From: Doctor Peterson Subject: Re: Confused when trying to find the sum of a ratio Hi, Brenda. These are just two different calculations; you have to decide which one is what you want. Since you phrase your intention as "TOTAL sales per employee," without mention of companies, I presume the number you want is the total sales, divided by the total number of employees. That calculation pays attention to each employee equally. If, instead, you want to focus attention on each company equally, you would find the sales per employee for each company, and then average those. To see what is going on, take an extreme example. Say we have two companies, one with 10 employees and the other with 100; and each has sales of $1000. Here are the two calculations, in table form: company sales employees sales/emp ------- ----- --------- --------- A $1000 10 $100 } B $1000 100 $10 } average: $55 ----- ----- --- ---- Total $2000 110 average: $18.18 The average sales per employee overall is 1000 + 1000 2000 ----------- = ---- = 18.18 10 + 100 110 The average per company is 100 + 10 110 -------- = --- = 55 2 2 That $55 per company average is bigger because both companies are treated equally, giving the small company (with its larger sales per employee) as much influence, or "weight," as the other. The average of sales per employee, $18.18, gives every employee the same weight, making the larger company (with its smaller sales per employee) more influential. These are two different weighted averages, with different weightings. Both calculations might make sense for different purposes. - Doctor Peterson, The Math Forum http://mathforum.org/dr.math/
Date: 01/21/2010 at 05:19:00 From: brenda Subject: Thank you (Confused when trying to find the sum of a ratio) Thank you so much for your answer. It has really helped clarify things for me. I didn't expect such a prompt reply, either. It's very much appreciated. Regards Brenda
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