Wikipedia:Reference desk/Archives/Mathematics/2009 May 24

= May 24 =

Margin vs Markup
I'm having some problems wrapping my head around the difference between margin and markup. I understand that margin is the percentage of the sale price that's profit and that markup is the percentage of the cost to make up the selling price. I know this information but I'm having difficulty comprehending it.

If the cost of an item is $100 and I want to make 50% profit, do I calculate the margin or markup? If I calculate markup I get a $150 selling price while calculating margin gives me a $200 selling price. In other words, does that 50% refer to margin or markup?

I'm pretty confused. Help! - Pyro19 (talk) 04:12, 24 May 2009 (UTC)


 * To me, "50% profit" sounds as if the profit is 50% of the selling price, so that you have a 50% margin, or equivalently, a 100% markup. Michael Hardy (talk) 11:03, 24 May 2009 (UTC)


 * Usually, profit is calculated from invested capital, so it would amount to markup in this context. This is the usual interpretation, in Economics or Accountings. However, people may call "profit" the margin over total sales. It all depends on what you are referring to with "to make 50% profit". Do you mean to recover 50% of the money you have used to buy inventory? Then charge 150. The other way, you want your net income to be half of your total sales: Charge 200. :) Pallida  Mors  04:46, 25 May 2009 (UTC)
 * I think you are mistaking this with IRR and NPV - I suggest with respect that the OP ignores the above comment, as it will only confuse them. 89.241.155.179 (talk) 18:57, 25 May 2009 (UTC)


 * Markup - you buy goods for your shop (or store I think in American english) for the wholesale price of £2. If your policy is to mark up everything by say 75% (over-simplifying you want to get a "profit" of 75% of the wholesale cost), then the retail price (the price you sell it to customers at) will be £2 plus 75% of £2, making £3.50. Often, mark-ups are much higher than this. In reality, you would probably decide the retail price of each product line individually, choosing the retail price that you thought would make you the most money. In that situation you would know the wholesale price and the retail price, and then you could calculate the mark-up. Eg wholesale price (WP) £1, retail price (RP) £5, then your mark-up would be (RP/WP - 1) x 100 = 400%


 * Margin - if you're saying that the "profit" is simply the difference between the retail price and the wholesale price, then yes, the amounts in £s of the margin and the mark-up would be the same. But the %s would be different because you calculate the margin as a percentage of the retail sale price (as far as I recall). Going back to the earlier example, the retail price is £3.50. The purchase cost is £2. By your simple definition of profit, then the "profit" is £1.50. To get the margin, you calculate the percentage of £3.50 that £1.50 is. I make it about 43%. So the margin is 43%


 * Other more common (and realistic) definitions of profit would deduct other costs also from the retail price, such as fixed and variable overheads, and so the margin will vary with your definition of profit. In accounting there are many different definitions of profit, it depends which one you use. 89.241.155.179 (talk) 18:57, 25 May 2009 (UTC)


 * With due respect, I know pretty well what profit, IRR and NPV are: I was just trying to answer the OP's question. That was about how to compute a profit ratio. I can't see how your example differs from mine. The OP is planely asking whether the ratio has the total revenue or the invested money ("wholesale price" if you wish) as denominator. Both your answer and mine seem to agree that both ways are possible. Pallida  Mors  21:02, 25 May 2009 (UTC)
 * When you wrote 'profit' and 'invested capital' I assumed you were referring to the capital of the whole enterprise and its fully prepared management accounts. But if you only meant the cost of the stock, and by profit you meant what I would normally call 'contribution' (because it contributes to overheads and profit), then yes we have been describing the same thing. 89.242.123.98 (talk) 22:10, 25 May 2009 (UTC)

value of pi
What is the value of pi?--Lightfreak (talk) 08:35, 24 May 2009 (UTC)
 * Check Pi. — JAO • T • C 08:57, 24 May 2009 (UTC)
 * The value of pi is approximately:


 * 3.14159265358979323846264338327950288419716939937510


 * See this site for a value of pi to a greater degree of accuracy. Let me note that the value of pi to a finite number of decimal places is really not of much interest, except of course for computational problems. In that case however, a calculator or a computer is used. In other words, the value of pi has no real mathematical meaning, but rather there are some interesting properties of pi. These properties of pi can be determined without knowing the value of pi. According to normal number for example, it is not known whether pi is a normal number. In other words, if you give me a finite string of digits, is it true that this finite string appears consecutively in the decimal expansion of pi? Although this is thought to be true, no proof exists. There are other properties of pi, however, which are known and are relatively simple to derive. For example, pi is not an algebraic number and it is irrational. Proving such facts has a much greater merit than computing the value of pi. However, if you search "value of pi" on google, you should get relevant values, or even click on the link suggested by JAO above. I hope that this answers your question. -- PS T  09:09, 24 May 2009 (UTC)


 * If you just type pi as a query to google it gives a value to 8 decimal places at the start of the results. You can also convert units and do other simple maths these, e.g. 1+sqrt(2). Dmcq (talk) 12:34, 24 May 2009 (UTC)

Nonlinear Homogeneous Differential Equations
Can a differential equation be nonlinear but is still homogeneous? --Yanwen (talk) 15:19, 24 May 2009 (UTC)
 * What's your definition of homogeneous differential equation? If you mean, for instance: "a differntial equation such that for all solution u(t) and any real number λ, the function λu(t) is also solution", consider e.g. ű(t)=f(u,u') where f(x,y) is a nonlinear function on R2 and 1-homogeneous, that is f(λx,λy)=λf(x,y), like for instance f(x,y) = xy2/(x 2 + y2).--84.221.81.90 (talk) 17:05, 24 May 2009 (UTC)
 * I meant the definition given here; an equation of the form $$a_n(x) D^n y(x) + a_{n-1}(x)D^{n-1} y(x) + \cdots + a_1(x) D y(x) + a_0(x) y(x) = 0$$--Yanwen (talk) 20:34, 24 May 2009 (UTC)


 * Ahh! Sorry, I misunderstood because homogeneous without linear may have other meanings. Well, in general a linear equation is one of the form Lx=a with L a linear operator, and the corresponding homogeneous equation is Lx=0, that is, the special case of the datum a=0. But the distinction really makes few sense if L is not linear. If L is not linear, the case a=0 has not a particular role among the equations L(x)=a. On the other hand every equation can be written in the form L(x)=0, if you allow L to be nonlinear (just move everything on the LHS).--84.221.81.90 (talk) 21:26, 24 May 2009 (UTC)
 * Also see Homogeneous differential equation. -- Meni Rosenfeld (talk) 19:05, 25 May 2009 (UTC)

Plus-or-minus range
This is not a homework question. There are 2,351 Magic: The Gathering players registered with the DCI in Ontario. Of these, 2,198 are in known cities, and 392 are known to be in the cities I'm interested in. By assuming that players in unknown cities follow the same geographic distribution as those in known cities, I've estimated the total number in the cities of interest to be 419. What's my plus-or-minus range with 95% confidence? Neon Merlin  21:15, 24 May 2009 (UTC)

Update: I have also estimated, based on the figure of 6 million total players in a Wizards of the Coast press release and a total of only 221,748 registered players, that the total number of players in Toronto is actually 11,345. What's my plus-or-minus range for this figure, if we make the simplifying assumption that the figure from the press release is exact and up-to-date and neglect the "more than"? Neon Merlin  21:52, 24 May 2009 (UTC)


 * For the first question - a registered player in a known city has a $$392/2198$$ probability of being in an interesting city. There are 153 players in an unknown city, and by your assumption, each also has a $$392/2198$$ probability of being in an interesting city. We also assume that the locations are independent, so the number of such players is distributed binomially with $$n = 153$$ and $$p = 392/2198$$. So this value is between 18 and 36 with probability >95%. This puts your goal between 410 and 428, which is $$\pm2.15%$$ of your estimated value, with 95% confidence.
 * For the second question this should be a similar calculation, perhaps easier because for these large numbers, you can safely approximate the binomial distribution with a normal one. -- Meni Rosenfeld (talk) 19:03, 25 May 2009 (UTC)
 * I don't think the second question can be approached by quite the same method, since we're estimating the size of a superset of the known-size set rather than a subset. Also, the +/- range from the first question needs to be propagated into the second question (although if what I was taught in high-school physics is correct, this just means converting the two +/- ranges to percentages, adding them together and converting back). Neon  Merlin  01:06, 26 May 2009 (UTC)