Talk:Rate (mathematics)

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—Yamara ✉ 23:10, 5 May 2008 (UTC)

Discussion

hello i want to see a table of reactivity --193.195.198.254

You should ask for this on Talk:Reactivity. --Toby Bartels 15:35, 2 March 2007 (UTC)

Definition

I do not see that 'meters' and 'seconds' are the same unit, what would in fact be a 'ratio'. That definition differs completely from that e.g. in the Oxford Dictionary.HJJHolm (talk) 13:43, 15 July 2008 (UTC)

Your point regarding that the two measurements is taken. They can be the same unit or different units.+mt 14:33, 15 July 2008 (UTC)

Is Rate is all about time ?

Rate is a measure of something over time. And the article should say that. Re-write. Paul Beardsell (talk) 07:23, 1 March 2009 (UTC)

Your claim is incorrect. A rate is simply a ratio of something per something used in a particular context. The denominator is often time, but it doesn't need to be. Examples of rates that are not "something over time" include exchange rate, inflation rate, unemployment rate. +mt 17:59, 1 March 2009 (UTC)

Inflation rate is the change in prices per unit time. The rate of change is always (I contend) per unit time. Where you are correct is when "rate" is used instead of "ratio", often incorrectly. Unemployment rate is a proportion and really unemployment ratio. The growth in unemployment is unemployment rate. Like it or not, in maths a "ratio" is a fraction or a proportion and is often dimensionless. "Rate" is usually change per unit time. Paul Beardsell (talk) 23:13, 1 March 2009 (UTC)

English is imprecise. And there is room for a disambiguation page and, what do you know, there is one: See rate. But the name of this article is "Rate (mathmatics)". Reverting. Please do not revert back to what I think is a poorly written and imprecise version of the article. Thanks. Paul Beardsell (talk) 23:13, 1 March 2009 (UTC)

We agree that this is a mathematics article, but variables and dimensions are usually treated generically in math, so this doesn't help your case. My calculus textbook (Adams, Robert A. (1995). Calculus: A Complete Course (3rd ed.). Addison-Wesley Publishers Ltd. pp. 129, 135. ISBN 0-201-82823-5.) has all sorts of examples that describe rates that are not "per time", such as "the rate of change of the area of a circle with respect to the radius" in one example or "the rate of change in gravitational force with respect to distance from Earth", etc. Yes, this book also provides many "per time" examples as well. Search for "rate" in derivative and evaluate the context in which it is used. The formal definition of the "rate of change" in my textbook (p.129), (added to front page) does not assume "per time" anywhere since it is an unnecessary limitation. In an applied use, a gradient rarely has rates in units "per time" (usually it is a spatial dimension). Still not convinced? Look for the definition of "rate" at these links: [1], [2], [3], [4], [5]. I'm all for improvements in this article and I'll agree that the prior version was mismanaged, but you completely modified the definition to what you thought it was, which is why I revered your work (also, consider the use of a spell-checker). The content of your edits are not wrong, but your assumption of always "per time" is not correct and is not supported by references. Terms like "unemployment rate", "tax rate", "exchange rate" are not wrong, since this terminology sits fine with the formal definition that I'm showing you. +mt 05:41, 2 March 2009 (UTC)

You're right. Sorry to be disruptive. But the default "per unit" is "per unit time". If you don't say then the rate of something is the rate per unit time. Notice also the project template (how I hate those). Paul Beardsell (talk) 08:27, 2 March 2009 (UTC)

I'm not convinced that the default should be "per unit time". All percentages are rates and they are mostly not per unit time. For example, the percentage of people divorced is the ratio of divorced people to total population. It's better not to think of it as a rate since the "divorce rate" means the percent of marriages that end in divorce. This is a rate that is not "per unit time". — Preceding unsigned comment added by Dlawyer (talk • contribs) 03:15, 24 November 2015 (UTC)

I've thought about this some more and I think that in Physics "per unit time" should be the default. But now I'm proposing a new title for this article that will resolve this problem: "Rates and ratios (mathematics)"David S. Lawyer 01:40, 25 November 2015 (UTC) — Preceding unsigned comment added by Dlawyer (talk • contribs)

Proposed addition: Averages of rates and ratios

I'm proposing a major addition to this article which will show how to find various means of rates (ratios). I first thought I might put it in the Harmonic mean article (which has many examples) but now think it belongs in this article. Here's what I wrote in Talk: Harmonic Mean#Taking an average of ratios(rates). New article?

The harmonic mean is sometimes used to take "true' averages of ratios. In many cases, weighting is required. In some cases, only the arithmetic mean is needed and gives the same results as the harmonic mean (since different weightings were used). Shouldn't this (or another article) explain how to do this in general. A formula showing weights is given in this Harmonic mean article, but no rules for determining weights. I've formulated this and it's really pretty simple. What one often wants to determine when averaging ratios Ai/Bi (i terms from 1 to N) is (SumAi)/(SumBi) = "Ratio of averages" (both numerator and denominator are divided by N to get an "average" but the two N's cancel out). Let Ri = Ai/Bi, the ratios to be averaged. If one knows only the Ri's and Bi's, then to get the "ratio of averages" one takes the arithmetic mean of the Ri's using the Bi's as weights (the denominator of the ratios). If one knows only the Ri's and Ai's then one uses Ai's as weights and takes the harmonic mean. The sum of the weights must add to 1 so each Ai weight is divided by sumAi. Likewise for Bi's. These rules show how to determine the weights. Proving these rules takes only several lines and is very simple algebra.

There are rates that are functions of time distance, etc. For example velocity v(z) where z is distance or time. One can use integration for them instead of summation. Should this be covered also, regarding taking the arithmetic or harmonic mean using integrals? It will directly follow from the rules for summation mentioned above.David S. Lawyer 00:53, 25 November 2015 (UTC)

I went ahead and created this section and it soon got deleted on Jan.3, 2016 (reverted) since it was claimed to be WP:OR (unsourced), and too specific).

I was planning to add a couple of so-so references from the I-net but really wanted to find it in a textbook. I think the subject is very important since it shows when to uses the arithmetic mean and when to use the harmonic mean, and in addition shows what weights to use in finding such means. There were a few typos and it could be explained better than I did it. I'll try to improve on it in my sandbox and re-revert it (with some improvements). I'll also add some examples.

Taking averages of rates are fairly common situations. If one divides a transportation trip into segments and goes at speed Vi on the ith segment (of length Xi), what is the average speed of the trip? It's the harmonic mean weighted by the normalized Xi (adjusted so they add up to 1). Example: I go half way at 0 mi/hr and go 100 mi/hr on the 2nd half of the trip. Arithmetic mean= 50 but harmonic mean = 0 (the correct average speed since I never get to my destination). Another example is finding the average efficiency of an automobile engine on a trip where one knows the efficiency at each time segment of the trip. It's not the efficiencies weighted by time but the efficiencies weighted by input power times time where input power is the fuel flow times the heat value of the fuel. The simple rule I show: weight by the denominator of rates uses the arithmetic mean, but weight by the numerator uses the harmonic mean, helps to solve the above problems. This proposed section will be used by reference for both the Arithmetic mean and Harmonic mean articles and should become an important part of these articles. But since it pertains to both articles and involves ratios/rates, I think it's best put here. I think that the harmonic mean is mainly used for certain cases of ratios. So I suggest that you give me a few months to fix my contribution and if I don't have time to follow thru, then try to fix my contribution.David S. Lawyer 07:12, 9 January 2016 (UTC)

David S. Lawyer 07:12, 9 January 2016 (UTC)

Proposed name change: Rates and ratios (mathematics)

This would solve the argument as to whether a certain ratio is a rate. For example, I'm not sure if the percent of the population that is under 16 is really a rate, but it most definitely is a ratio. Then create a lot of redirects to this new name: ratio, ratios, rate, rates (math), etc.David S. Lawyer 00:18, 25 November 2015 (UTC) — Preceding unsigned comment added by Dlawyer (talk • contribs)

I browsed the Internet for discussions on whether rates and ratios are the same. It seems a majority of people think they are not exactly the same, but differ in their views as to just how "rates" are different from "ratios". "Ratios" seems to be the broader term.David S. Lawyer 08:35, 26 November 2015 (UTC) — Preceding unsigned comment added by Dlawyer (talk • contribs)

Can anyone make sense of the 1st and 3rd paragraphs in the Introduction section?

The sentence in the first paragraph of the section that begins "For example" contains the word "tracity", not in any dictionary I've checked. It has more left parentheses than right parentheses. It mentions a subset of a route, but only sets have subsets; since when is a route a set?

The third paragraph refers to "a set of ratios (i =0,N)". In this set, is N supposed to range over the positive integers, so that (0,2) is a member of the set? According to the lead in the Ratio article, ordered pairs can be ratios. Does the set then consist of ratios like 0∶2, 0∶3, etc.? The paragraph also refers to "the set of v_i s mentioned above" though no v_i s have been mentioned. The first paragraph, if I guess correctly concerning its parentheses, says that v is a function of i, so maybe the reference should be to the values of v(i ) rather than to the v_i s? Either way, what are these values? We're told that the i 's can be assigned to political subdivisions so, OK, I hereby assign 43 to Idaho since it was the 43rd state to join the United States. Now, what is v(43) or v₄₃?

Peter Brown (talk) 01:16, 3 November 2019 (UTC)

Rates and what they are

These are some basic questions about rates that must be answered.

I believe that "per" means a rate. I believe percentages are rates constructed out of 100 unites.

All rates must have two and only two variables as an equation must have two sides. There are two types of rates. One type is constructed out of dependent variables and the other type is constructed out of independent variables.

If I say 10% am I saying "10 parts per 100 parts" or "10 parts of 100 parts"? This is a most important question for an understanding of the distinction between "of" and "per" is essential.

Is 10 parts per 90 parts equal to 100 parts? Is 10 parts per 100 parts equal to 110 parts? Rates constructed out of dependent variables have a commonality of units. When I say parts I of course am talking about common unites.

Can one average percentages? Can one average rates?

If one has a container with 10% alcohol in it and mixes a container with 50% alcohol in it can one know the percentage of alcohol in the mixed container?

The answer to this is true for all rates and percentages are rates.

If I am wrong please correct me.

Mwdar (talk) 18:46, 3 January 2020 (UTC) mwdar — Preceding unsigned comment added by Mwdar (talk • contribs)