AboutWarren D. Miller, CFA, ASA, CMA, CPA Expertise My in-depth knowledge of economics is confined to three sub-disciplines: Austrian economics, industrial organization, and evolutionary economics. Other questions dealing with macroeconomics, the traditional neoclassical paradigm, labor economics, environmental economics, agricultural economics, health economics, and so on should go to those who have the appropriate expertise.
N.B.: I DO NOT ANSWER QUESTIONS MARKED 'PRIVATE' because I believe that knowledge should be shared, not hoarded. I also believe that such questions are likely to come those trying to cheat. Similarly, as one who was a full-time academic for half a decade, I can recognize test and homework questions several time zones away. Therefore, please do not demean yourself by submitting such questions to me. Those who do so are cheating, pure and simple, and I WILL call you out publicly if I believe you are doing so. I have a zero-tolerance policy where cheating and dishonesty are concerned.
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Finally, please DO NOT ask for investment advice. I am not licensed to provide such advice. If you want such advice, check with your financial planner or other financial adviser.
Experience I work with Austrian economics (which is different in major respects from the traditional neoclassical model), industrial organization (which is about industry structure, conduct, and performance), and evolutionary economics (almost, but not quite, the economic analog of its biological counterpart) everyday in my work. I appraise closely-held businesses, provide exit-planning services, and offer high-level strategic analysis, advice, and clients to CEOs and owners of mid-sized businesses. Understanding, applying, and writing about these disciplines is an essential part of how I have made my living since 1993.
Organizations CFA Institute, Strategic Management Society, American Society of Appraisers, Institute of Management Accountants, Academy of Management, Culver Legion
Publications CFA Magazine, Strategic Finance, Valuation Strategies, Value Examiner, Journal of Advanced Property Economics, Harvard Business Review, American Fly Fisher, CFA Digest, CPA Expert, and Business Valuation Review, among others
Education/Credentials MBA - Oklahoma State (1991)
BBA - U. of Oklahoma (1975)
Chartered Financial Analyst designation (2006)
Accredited Senior Appraiser (2006)
Certified Management Accountant (1992)
Certified Public Accountant (1992)
Fisrt of all I want to thank you for being here and giving us an opportunity to share the problems and get answers from such professionals like you.
I would be so grateful if you help me with the question that I have.
I am student and my major is Environmental studies but as we all know Economics is important in every field. I am doing my research on Newspaper coverage of environmental issues. Currently I am on the step of identifying the prominence it means how many articles in front and back pages.However I was asked to find out the weighted average of the articles in pages. For example during the 1990 to 1992 there are 10 articles in 1 pages, 20 articles in 2 pages and so one. Not having the economic knowledge make me spent a lot of time in this issue that I don't have since not so much time for deadline. I would be grateful if you help me with questions:
1) What will give me the calculation of the weighted average of the articles in pages
2) what formula can be used for it?
I have read a lot about it but I would be happy to hear you explanation with regard to this specific issue.
Thank you very much in advance,
Looking forward to your soon response,
Kindly,
Loona
ANSWER: Hi, Loona--
Thank you for your questions, and thank you for using AllExperts.com. Your questions are terrific. Let me respond.
As you recognize, there is a difference between an "average" and a "weighted average." I'm going to set up a sample fact pattern and show you the difference.
Fact Pattern: 10 articles with 1 page each, 22 articles with 2 pages each, 12 with 3 pages, 1 with 8 pages, and 1 with 15. (I know it's unlikely that a newspaper would carry an article that was 8 or 15 pages long, but I have those in there to illustrate!)
1. AVERAGE LENGTH (/ means "divided by):
(1 + 2 + 3 + 8 + 15)/5 = 5.8 pages.
2. WEIGHTED AVERAGE LENGTH (x means "times" or "multiply):
As you can see "weighted" takes into account the number of articles for each page length. A simple average just averages the length of the articles without regard to how often they occurred.
Let's do another one, just to illustrate again:
Fact Pattern: Let's assume that the age distribution of the 150 people in a movie theater is as follows: 14 people are 18 years old, 1 is 19, 4 are 20, 28 are 21, 32 are 22, 42 are 24, 17 are 27, 11 are 32, and 1 is 87.
1. AVERAGE AGE:
(18+19+20+21+22+24+27+32+87)/9 = 270/9 = 30.0 years.
(232+19+80+576+704+1,008+459+352+87)/(150) = 3,517/150 = 23.45 years.
In statistics, the weighted average is called "the mean." It is represented either by the Greek letter "mu" or by an "x" with a line above it (pronounced "x-bar"). The "mu" is for an entire population of whatever is being analyzed; x-bar is for a sample drawn randomly from that population.
I hope this isn't more than you wanted to know. :-)
Please do me a favor by completing the 'rate-the-expert' email you'll receive on the heels of this reply. Your ratings and comments help me do a better job of helping people like you who ask such interesting questions!
Thanks again, Loona--
Warren
---------- FOLLOW-UP ----------
QUESTION: Dear Mr. Warren D. Miller
I am so so grateful to you for the prompt,clear and great explanation. Of course it is great pleasure for me to rate for you and I have already done it. :)
However I think I made a mistake in my question. I am so sorry. Just in order to clarify I would be happy to know your comment about it.
I wrote 10 articles in 1 pages that can be understood as if there is 10 articles in 1 page length. However what i mean is First, Second, Third .. pages.
Just like during the years from 1992-1997 the total number of articles that published in First pages of newspapers are 10 (means some editions could not have article on first page or second but could have on third pages).
I just wanted to ask is the same formula can be used in this case too?
I think my question is somehow confusing :) sorry again,
Thank you very much in advance,
Kindly,
Loona
ANSWER: Thank you for your kind words and very positive evaluation of my response. I wish everyone were as prompt and as generous in their responses as you. Thank you so much.
Now, let me see if I'm understanding your question. Instead of the number of pages in each article, you're wanting to take a weighted average of the "page number of the first page." Is that correct?
If it is, then you should use the same formula. However, the one thing I would do is round the result to a full page number. It wouldn't make any sense to say, for instance, "The weighted average page number on which the typical article began was p. 3.72." Better to say, "Articles do not begin on fractional pages. Therefore, we rounded our result. Of the [how many, Loona] articles in our sample, the weighted average number of the page on which the typical article began was up. 4."
I do hope this helps. Please let me know if I'm understanding your question this time. Sorry I didn't get it right the first time.
All the best--
Warren
---------- FOLLOW-UP ----------
QUESTION: Dear Mr. Warren D. Miller
Thank you very much again for the time you share to respond to my question. I am so grateful. And please, you got everything right in the first time.It was me who made a mistake.
I would like to share some details of the research I am doing in order to make it clear. Currently I am doing analysis of the prominence of the articles means calculating how many articles placed in first, second, third and fourth pages during the years 1986 - 2008. I am taking four front pages to analyze.
During this years for example:
10 articles placed in first pages (means 1 article on 1993, Saturday edition, September 20, first page, another article Monday edition, April 3, first page etc)
40 articles placed in second ( means 1 article on 1994 Thursday edition January 19 second page etc)
50 in third pages (the same here with third pages)
30 in fourth pages (the same here for fourth pages)
After counting I have got the numbers mentioned above.
I got this results and was asked to find out weighted average and I did have very few information about it and what it can give me. Why I have to do it? To find what?(may be it sounds funny but "why" is always following me. :)) You greatly explained in your first answer. The case I describe here is little different from the one of my first message. :) Thus I thought may be there is some difference in calculation too in comparison with the first case.
I hope I am not confusing you again this time :)
May be my English is not so good. I am sorry.
Thank you very very much,
Kindly,
Loona
Answer Loona, my friend, your English is a WHOLE LOT BETTER than my Japanese! Don't apologize, please. You are delightful to work with, and I'm glad I can help you.
I do not see any reason to change the advice I gave you "in the first case," Loona. Not at all. It's still good, accurate advice.
There is one thing, though, that I think might be worth your consideration. Instead of doing the analysis "longitudinally"--that means combining all the years and getting one "weighted average"--try making the calculations year-by-year instead. In other words, there would be a weighted average for 1986, another for 1987, another for 1988, etc. You would end up with 23 weighted averages for each year, 1986-2008.
Why do it this way? Well, because on a year-by-year basis, you would see what the trend is in the placement of stories about the environment? You could also see the trend in HOW MANY stories there were each year. That information would be far more useful and meaningful, I think, than just a single weighted average for the 23-year period, inclusive.
You could input the information in Excel in a table. Label the horizontal axis with Year, beginning with 1986 on the left and having another numbered year shown @ 1990, 1995, 2000, 2005, and 2008. No need to have all 23 numbered years shown - that would just be "visual clutter."
Label the vertical axis on the left with Page Number. Label another vertical axis on the right with Number of Articles. Then have Excel make a histogram for the Page Number data and a line graph for the Number of Articles.
The way to make the graph have even more impact is to label the vertical axis on the left in DEscending page-number order from the top. In other words, have p. 1 at the top on the left side, 2 below it, 3 below 2, etc. The right side would be just the opposite. Label it in AScending order - lower number at the bottom, higher numbers going up.
I'm betting that the histogram trend would be towards p. 1 and the line graph trend would be towards more articles. And with the labeling scheme I've described, the histogram trend would be UP (towards p. 1), and the line graph would ALSO be UP (towards a greater number of articles).
Now THAT, Loona, would be VERY useful information. Why do I say that? Well, most people, at least in America, are intimidated by math of any kind. I think that is much less the case in Japan, though I certainly do not know for certain, of course. Still, regardless of your audience, the "picture"--the graph--will convey more information faster and better than writing it on paper or in Word EVER would.
Trust me on this one. This is the kind of problem I have to wrestle with in my work. There is an old saying, "A picture is worth a thousand words." When it comes to math and statistics, it's not "a thousand words." It's "a million words," at least.
Take care. I do hope you find this helpful. You can use the Help screens in Excel to guide you through setting the table up to produce the graph I've described. You can also get help on-line and through the Excel tutorials that are available free on-line. Here are several links for you:
I hope this is helpful, Loona. I highly, highly recommend using the graph in Excel the way I have described. EVEN IF YOU DON'T TURN IT IN FOR ACADEMIC CREDIT, you will learn so much about how to present data visually. And THAT is far more important than the 'weighted average' calculations that I helped you with initially.
Please let me know if there's anything else I can do to help you, either with these issues or with different ones. And, of course, please do me the favor of completing the rate-the-expert email once again. Your ratings and, especially, any comments you care to make, are SO very helpful to me.
Take care, and good luck, Loona. You are a pleasure to help and to work with.
