Gifted Issues Discussion homepage Forums General Discussion Some statistics help?

Maybe it's just late, maybe it's because I never actually took statistics, maybe my math brain cells are fried, but I've been trying to figure out the chances my dd's teacher has had a child in her class at the same level as dd and I can't wrap my brain around the problem. Here's what I know:

1. This is dd's teacher's 4th year of teaching
2. Class size is around 25 students
3. There are 1300 3rd graders in the entire district.
4. Of those 1300, 50 are placed in the full-day gifted program.
5. Assuming my dd is among the top 10 students on the waitlist for the full-day gifted class, and the remaining 1250 3rd graders are distributed evenly into classes of 25, how likely is it that her teacher would have 1 or more of the top 10 waitlisted students in her class each of her 4 years? Or even one of the top 25?

And for extra credit:

We're in a good suburban district, with plenty of techies and high achievers. But even so, how likely is it that there are 50/1300 3rd graders that would have IQs in the 140+ range? Or even the 130+ range? If you can't tell, I'm trying to bolster my argument that dd belongs in the full day program.

Thanks!

OK, I'll take a crack at this one.

The train leaving Penn Station was traveling at an average speed of 85mph and served each of its passengers 2.75 sandwiches, arriving at Central Station at 7:05am.

Was I close?

Sorry -- let me try that again.

I'll let someone who actually took statistics work the numbers, but no matter the answer, I wouldn't hang too much on the stats involved to get your daughter into the class. While I know nothing about the teachers or admins involved, I'd safely bet that their eyes would roll waaaaay back into their heads if you approached them with any sort of raw statistical argument.

Your daughter could be 1/1,000,000, but I doubt any district would drop an enrolled GT student just because someone more statistically rare comes along.

I suppose you could argue about your daughter's ranking on the waiting list, but without knowing the intimate details of all the other waiting students, you'd be fighting that battle rather blindly.

Assuming your daughter's placement on the waiting list indicates meeting some particular standard for the program, I think the bulk of your work in getting her into the GT class is done. As such, your energies are probably best directed at obtaining some sort of accommodation within your daughter's current classroom.

Oh, I know it's a long shot, but I did hear that they sometimes leave a spot or two open in the class, in case someone transfers in from out of district. But you're right, our best bet at this time is getting some sort of accomodation in her regular class. We have a meeting with the school guidance team coming up in a couple of weeks, since her teacher didn't feel she could make any changes on her own.

I'm anticipating, among other arguments, dd's teacher claiming that (#1) she's had numerous kids in her class like dd, and they didn't need anything different and (#2) if dd's so smart, why didn't she make it into the full day program in the first place? For #2, I'd like to be able to say, "That's a great question. Statistically, it seems kind of weird that they would deny our appeal after seeing these test scores. Do you think they might have discriminated against her because of her ADHD?"

I've heard that one of the people on the team is a real number cruncher--you have to show her the hard data to convince her of anything. I just want to go in armed with as many different arguments as possible so I can pull out whichever one I need for the situation.

Plus, I figured there had to be someone here that would appreciate a math problem first thing in the morning.

Here is the math, assuming a random distribution of students:
1250 student/25 students per class=50 classes per year
50 class*4 years=200 classes over four years for a third grade teacher
200 classes/40 students over four years (if the waitlist is 10 for each grade)= 1 in 5 chance (if only 10 for all grades, 1 in 20--200/10)
It is unlikely, but possible--even more possible if students are ability-grouped in her class right now.

Ability grouping? I wish! No, they make an effort to spread the high and low achievers out between classes.

So let me be sure I understand. It doesn't matter how long a teacher has been teaching--a 5-year teacher will have the same chance of having had a top 10 student in her class as a 25-year teacher? And the chance of having two of the top 10 students in a class would be 1 in 25, the chance of having 3 in a class would be 1 in 125 (though in reality, it probably wouldn't happen at all because of aforementioned spreading)?

Oooo, can I play?

The probability in any one year that 1 of the top 10 wait-listed students is in one the 50 3rd grade classrooms is 1/5 = 20%. (assuming random distribution)
For each subsequent year, the probability increases that you've had one at least once.
Year 2 = 36%
Year 3 = 48.8%
Year 4 = 59.04%
Year 5 = 67.23%
...
Year 25 = 99.62%

For one of the top 25 wait-listed students:
Year 1 = 50%
Year 2 = 75%
Year 3 = 87.5%
Year 4 = 93.75%
Year 5 = 96.88%
...
Year 25 = 100% (almost!)

Now, the chance of having 2 of the top 10 in one year is 4%. After 4 years, the chance of her having had 2 of the top ten at least once is 15%.
3 of top ten in one year .8%, after 4 years 3.2%.


Extra Credit:

With normal distribution, you would expect approx. 1/44 people to have IQ 130+. So of 1300 kids, 30 should be 130+. Approx. 1/261 have 140+. 5 of 1300.

Most likely a higher percentage than above in your area, but still not 50 kids 140+.

HTH. Either way, it sure was fun!