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.
In addition, please don't imitate the businessman who posted a request for help in August 2008. He expressly denied that he was seeking "investment advice" and said that his query was for, and I quote, "educational and informational purposes." Later, he allowed as how his questions related to the possible purchase of a $500K piece of equipment. I said I thought he had misrepresented himself. Bottom line: high-end business consulting is how I make my living. I am the sole support for my family. Please respect that fact and don't try to get for free what our clients pay for. If your company is big enough to have a sophisticated problem, it's big enough to pay for the kind of expert advice we provide. Beckmill Research, LLC, is a 95-octane firm. We're small, but we've been at this for nearly 18 years. We know what we're doing.
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.
