# Help Me Understand These Numbers **URL:** \ **Category:** Factual Questions\ **Created:** [January 10, 2020, 3:12pm UTC](https://boards.straightdope.com/t/help-me-understand-these-numbers/846220 "2020-01-10T15:12:17Z")\ **Posts on this page:** 16\ **Page:** 1
**Author:** ![Paul\_in\_Qatar](https://avatars.discourse-cdn.com/v4/letter/p/ccd318/32.png) [@Paul\_in\_Qatar](https://boards.straightdope.com/u/Paul_in_Qatar)\ **Post date:** [January 10, 2020, 3:12pm UTC](https://boards.straightdope.com/t/help-me-understand-these-numbers/846220/1 "2020-01-10T15:12:17Z")
From an article in _The Economist_ on racial distribution of students in the best New York City high schools, **…show that whites are 80% more likely than black students to take part in programmes for the gifted and Asians are three times as likely.** I think this is poorly written. Maybe I am dumb. Maybe it means: 100 black students 180 white students 300 Asian students What do you think? ---
**Author:** ![Cheesesteak](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/cheesesteak/32/3694_2.png) [@Cheesesteak](https://boards.straightdope.com/u/Cheesesteak)\ **Post date:** [January 10, 2020, 3:14pm UTC](https://boards.straightdope.com/t/help-me-understand-these-numbers/846220/2 "2020-01-10T15:14:46Z")
I’d say it’s more: Out of every 1000 students of each race… 100 of the black students would take part 180 white students 300 asian students ---
**Author:** ![Crane](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/crane/32/3495_2.png) [@Crane](https://boards.straightdope.com/u/Crane)\ **Post date:** [January 10, 2020, 3:22pm UTC](https://boards.straightdope.com/t/help-me-understand-these-numbers/846220/3 "2020-01-10T15:22:41Z")
The numbers simply record participation, not ability. ---
**Author:** ![Chronos](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/chronos/32/134_2.png) [@Chronos](https://boards.straightdope.com/u/Chronos)\ **Post date:** [January 10, 2020, 3:24pm UTC](https://boards.straightdope.com/t/help-me-understand-these-numbers/846220/4 "2020-01-10T15:24:57Z")
I would take the same interpretation as **Cheesesteak** (with the caveat, of course, that we don’t know what the common denominator is that leads to 100 black students, 180 white students, and 300 Asian students). ---
**Author:** ![Paul\_in\_Qatar](https://avatars.discourse-cdn.com/v4/letter/p/ccd318/32.png) [@Paul\_in\_Qatar](https://boards.straightdope.com/u/Paul_in_Qatar)\ **Post date:** [January 10, 2020, 3:30pm UTC](https://boards.straightdope.com/t/help-me-understand-these-numbers/846220/5 "2020-01-10T15:30:07Z")
Surely\* it would mean out of every 580 students I could expect those numbers from each group. But why the heck didn’t they just use a percentage? \*I mean I guess, I do not understand this. ---
**Author:** ![brossa](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/brossa/32/3040_2.png) [@brossa](https://boards.straightdope.com/u/brossa)\ **Post date:** [January 10, 2020, 4:00pm UTC](https://boards.straightdope.com/t/help-me-understand-these-numbers/846220/6 "2020-01-10T16:00:49Z")
Given the wording from the OP, “% more likely…to take part in programmes”, I would parse it as: If _x_% of Black students take part - the baseline likelihood - then 1.8(_x_)% of White students take part, and 3.0(_x_)% of Asian students take part. So for example 5% of Black students, 9% of White students, and 15% of Asian students. Or 2%, 3.6%, and 6%. But we aren’t given what _x_ actually is, so we can’t yet say how many students out of 1000 of each race. Nor do we know what the the baseline demographics are to say what the demographics of the gifted program is. If there are 10000 Black students, 5000 White students, and 1000 Asian students in the school system, then under my interpretation the gifted program will have (for _x_=0.05) 500 Black, 450 White, and 150 Asian students. ---
**Author:** ![Thudlow\_Boink](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/thudlow_boink/32/320_2.png) [@Thudlow\_Boink](https://boards.straightdope.com/u/Thudlow_Boink)\ **Post date:** [January 10, 2020, 4:05pm UTC](https://boards.straightdope.com/t/help-me-understand-these-numbers/846220/7 "2020-01-10T16:05:23Z")
I, also, agree with **Cheesesteak** ’s interpretation. Assuming it’s correct, the OP is guilty of the [Base Rate Fallacy](https://en.wikipedia.org/wiki/Base_rate_fallacy). The percentage of black students who take part in programs for the gifted is **not** the same thing as the percentage of students in programs for the gifted who are black. ---
**Author:** ![Paul\_in\_Qatar](https://avatars.discourse-cdn.com/v4/letter/p/ccd318/32.png) [@Paul\_in\_Qatar](https://boards.straightdope.com/u/Paul_in_Qatar)\ **Post date:** [January 10, 2020, 4:55pm UTC](https://boards.straightdope.com/t/help-me-understand-these-numbers/846220/8 "2020-01-10T16:55:59Z")
I do not like how this was written. ---
**Author:** ![CookingWithGas](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/cookingwithgas/32/485_2.png) [@CookingWithGas](https://boards.straightdope.com/u/CookingWithGas)\ **Post date:** [January 10, 2020, 8:06pm UTC](https://boards.straightdope.com/t/help-me-understand-these-numbers/846220/9 "2020-01-10T20:06:19Z")
> [@Paul\_in\_Qatar](#): > > I do not like how this was written. Neither do I, and I am surprised it came from _The Economist_. ---
**Author:** ![Ignotus](https://avatars.discourse-cdn.com/v4/letter/i/ecc23a/32.png) [@Ignotus](https://boards.straightdope.com/u/Ignotus)\ **Post date:** [January 10, 2020, 9:23pm UTC](https://boards.straightdope.com/t/help-me-understand-these-numbers/846220/10 "2020-01-10T21:23:05Z")
I think it’s fairly straightforward, much along with **Cheesesteak** : for every black student in the programmes there are on an average 1.8 white and 3 Asian. The stupid part is, of course, the underlying assumption that students/people can be divided into the non-overlapping categories “Black”, “White” and “Asian”…! ---
**Author:** ![scr4](https://avatars.discourse-cdn.com/v4/letter/s/59ef9b/32.png) [@scr4](https://boards.straightdope.com/u/scr4)\ **Post date:** [January 10, 2020, 9:39pm UTC](https://boards.straightdope.com/t/help-me-understand-these-numbers/846220/11 "2020-01-10T21:39:18Z")
> [@Ignotus](#): > > I think it’s fairly straightforward, much along with **Cheesesteak** : for every black student in the programmes there are on an average 1.8 white and 3 Asian. No, that’s totally different. The numbers are about what percentage of each race participates in the program. That’s totally different from the percentages of each race in the program. Let’s say the school’s students are 50% white, 30% black, 10% Asian. (10% other) If each race participated in the special program at the same rate, the program participants will also be 50% white, 30% black, 10% Asian, 10% other. But instead, Asians are 3x more likely than black to participate, and whites 80% more. Which means the program participants is something like 54% white, 18% black, 18% Asian, 10% other. In other words, the white:black ratio in the special program is 3:1 instead of 1.66:1 (i.e. 80% higher than in the whole school), and asian:black ratio is 1:1 instead of 1:3 (i.e. 3 times higher). ---
**Author:** ![Paul\_in\_Qatar](https://avatars.discourse-cdn.com/v4/letter/p/ccd318/32.png) [@Paul\_in\_Qatar](https://boards.straightdope.com/u/Paul_in_Qatar)\ **Post date:** [January 13, 2020, 8:24am UTC](https://boards.straightdope.com/t/help-me-understand-these-numbers/846220/12 "2020-01-13T08:24:42Z")
I am not certain any of us can figure this out. ---
**Author:** ![penultima\_thule](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/penultima_thule/32/3833_2.png) [@penultima\_thule](https://boards.straightdope.com/u/penultima_thule)\ **Post date:** [January 13, 2020, 10:39am UTC](https://boards.straightdope.com/t/help-me-understand-these-numbers/846220/13 "2020-01-13T10:39:11Z")
I reckon **scr4** has nailed it. ---
**Author:** ![Chronos](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/chronos/32/134_2.png) [@Chronos](https://boards.straightdope.com/u/Chronos)\ **Post date:** [January 13, 2020, 3:15pm UTC](https://boards.straightdope.com/t/help-me-understand-these-numbers/846220/14 "2020-01-13T15:15:49Z")
**scr4** has the meaning of what the article is actually saying. It may be that the writer of the article didn’t understand what he was saying and phrased it wrong, but we have no evidence of that. This is a much more useful piece of information than simply telling the composition of the gifted program, since the composition of the gifted program would be meaningless without knowing the composition of the school as a whole. Though, of course, the best reporting would have been to give the raw numbers. ---
**Author:** ![DSYoungEsq](https://avatars.discourse-cdn.com/v4/letter/d/c6cbf5/32.png) [@DSYoungEsq](https://boards.straightdope.com/u/DSYoungEsq)\ **Post date:** [January 13, 2020, 5:04pm UTC](https://boards.straightdope.com/t/help-me-understand-these-numbers/846220/15 "2020-01-13T17:04:46Z")
Here is a link to the article in question: [A battle over gifted education is brewing in America](https://www.economist.com/united-states/2020/01/09/a-battle-over-gifted-education-is-brewing-in-america). It’s probably behind a paywall, sadly (I subscribe, so I can’t tell). The quote is from the introductory portion of the article, a relevant portion of which I will quote here: > [@](#): > > The debate over whether education of gifted children segregates them on the basis of pre-existing privilege rather than cognitive ability is neither new nor uniquely American. The number of selective, state-run grammar schools in Britain reached its zenith in 1965, before the Labour government of Harold Wilson embarked on a largely successful effort “to eliminate separatism in secondary education”. The three-tiered German education system—which sorts children on the basis of ability at the age of ten into either university-preparatory schools or vocational ones—has always been criticised for fostering social segregation. The fact that the children of Turkish migrants are now disproportionately sorted into lower-tier secondary schools instead of selective Gymnasien adds a disquieting racial divide. > > In America the debate is kicking up anew. The issue is national: the most recent statistics \*\*show that whites are 80% more likely than black students to take part in programmes for the gifted, and Asians are three times as likely. \*\*But the principal battleground has been New York City. (Bolded the part that is the subject of the thread) Unfortunately, the way in which this is referenced leaves ambiguity as to the author’s intention (there is no ambiguity as to meaning). ---
**Author:** ![Mama\_Zappa](https://avatars.discourse-cdn.com/v4/letter/m/71e660/32.png) [@Mama\_Zappa](https://boards.straightdope.com/u/Mama_Zappa)\ **Post date:** [January 14, 2020, 6:57pm UTC](https://boards.straightdope.com/t/help-me-understand-these-numbers/846220/16 "2020-01-14T18:57:52Z")
> [@Ignotus](#): > > I think it’s fairly straightforward, much along with **Cheesesteak** : for every black student in the programmes there are on an average 1.8 white and 3 Asian. > > The stupid part is, of course, the underlying assumption that students/people can be divided into the non-overlapping categories “Black”, “White” and “Asian”…! I don’t read it that way at all. I think it’s a relative percentage. If black students participate at a rate of 10%, and you have 1000 black students, that’s 100 black students in the program. If you have 10000 black students, then 1000 are in the program. Then you’d expect 18% of white students to participate, and 30% of asian students. If black students participate at a rate off 1%, then 1.8% of white students and 3%of asian students participate. Multiply each of those percentages by the number of students in that category. So if you have a district that is largely black, then the vast majority of students in the programs will be black. They’re just a smaller subset of their originating category than the other categories. I agree though, it’s poorly phrased. So: black students 100,000, white students 1000, asian students 100. In the program, you have 1000 black students, 18 white, and 3 asian. Black students 1000, white 10000, asian 5000, you’ll have 10 black, 180 white, and 150 asian. All with those same ratios relating to their originating groups.