I need a project for my students that involves taking data and calculating z-scores and percentiles so I need examples of real bell curve distributions. However it needs to be high-school student appropriate so no IQ testing. Height would work considering separate bell curves for men and women. Weight I know would work too. What are other examples of real bell curves that a student could use to do this project. Note it does not have to be a bell curve related to humans. Suppose daily high temperatures are distributed according to a bell curve; then they could use that as well.
The results of repeated trials of rolling multiple dice will fall along a bell curve. Just a pair of regular old six-sided dice will suffice to demonstrate the concept.
Yes, I know that the Central Limit Theorem gives me bell curve galore. I’m looking more for bell curves in the wild that students can use to get out and do measurements. Like shoe size. Does that follow a bell curve distribution?
Any kind of human performance or competition should produce bell curves if you use a broad enough data set.
ETA: I misread I think - you want them to generate the data themselves rather than using existing sets, yes? So ideally something that can be done fairly easily and with enough repetitions to create a reasonable distribution?
Temperatures are going to vary with the season. You want something that has a fixed nominal value, but which has some variation. When we were making measuring devices, we included a tabulator that measured and plotted the actual measured values in a histogram. Over lots of measurements, it made a great Bell Curve.
So if you have access to a digital scale and, say, a big stash of pennies, you could measure the weights of the pennies and record the values on an Excel sheet, then generate the hizstogram. You could weigh any kind of coin or standardized product. The digital scale is good because it minimizes operator bias – If you had people using calipers to measure the diameter of a penny you might get operator bias, unless it;s a digital scale.
A quick and dirty way to generate a pseudo-normal distribution is to add together twelve random numbers (that fall between 0 and 1), subtract 6, and divide by 12. Do this a lot of times. The numbers this generated will pretty closely follow a Bell Curve that is centered at zero and have a width of 1. You can use this to launch a discussion of the Central Limit Theorem, which is ultimately the reason that the Bell Curve occupies such an important part of this kind of statistics.
Central Limit Theorem (CLT): Definition and Key Characteristics.
Edited to add: Sorry about the CLT – when I wrote tyhis, the posts about the CDEntral Limit Theorem hadnb’t yet been posted.
No. They will use an existing bell curve and measure against it. Like shoe size: use the existing bell curve and you are a male size 10, your z-score is X and are in the Yth percentile.
Careful with that one. Human ability often falls on a Pareto curve, not a bell curve. You’re better off measuring a characteristic like height or weight than performance.
So you’re looking for either downloadable sets of data or for published graphs of [whatever] such that both a) the [whatever] data represents a normal distribution, and b) the kids have a way of generating a sample [whatever] value to plot versus the statistical data?
Tallish order, especially if their individual sample data has to be something they have or can measure, versus just making up test value as an arbitrary fer-instance.
I’m coming up blank, but maybe this post will help focus the question & lead to better answers. Or did I miss your goals entirely?
- Human height (at a given age or adult)
- Birth weight
- Average weight (like an apple, or people at a given age or adult)
- ACT/SAT scores (since they are students)…hell…your class tests are probably on a bell curve
- I think shoe sizes too but that is really a function of height (I think…as in tall people tend to have bigger feet…I think those two would track with each other pretty closely)
It’s more abstract than you’d like, but could they build or access a Galton’s Quincunx? I think the Smithsonian had or used to have a big one on display, but memory fails.
Better known to many of us as a Plinko machine from The Price is Right.
And if nothing else, I’m sure they’d enjoy saying “quincunx” while smirking.
What about plotting sunrise/sunset times (no DST)?
Careful on another front. I’d stay well away from anything involving human measurements of ANY kind. Otherwise you’re in danger of opening a can of worms or powder keg that could trigger political noise that has nothing to do with the math you are trying to teach.
That’s a sine wave, not a Gaussian distribution.
This article lsts some “naturally occurring” normally-distributed values. Some have already been mentioned (like rolling dice and flipping coins) and aren’t all that “natural”. But if you’re looking for statistics “in the wild”, you might try his suggestions of Blood Pressure or Birth Weights of babies, or whatever. Assuming you can find a table full of typical values that your students can use to compile a graph.
Or you could take my suggestion and weigh or measure coins, or something else that’s supposed to be standardized. et a bunch of boxes of something from the supermarket that are all supposec to weigh a pound, or something, and see what the distribution looks like
Hey – here’s a listing of such data – the lengths of housefly wings. Your students can use this data to make histograms that ought to have a normal distribution.
I know it’s not glamorous, but i gave it to you for free. If you want to do supermodel shoe sizes, you’ll have to do your own research.
Yes and no. Let me try to clarify
Let’s say students are looking for bell curves and they find women’s shoe sizes are a bell curve distribution. Great they can use it. It has a mean of 8 and a standard deviation of 1.5. Double great they can use it.
Now they measure their (or another woman’s) shoe size. She is a size 6. The student now calculates her z-score of -1.33 which give a left-tail area of 0.0918 that puts her in the 9th percentile. Lather Rinse. Repeat.
Exactly. I use the example of IQ scores but not gonna have students take an IQ test or administer a test to other students. Weight is iffy because of calculating percentile so ain’t touching that. And looking for something interesting. Like let’s say the growth of potato plants after 1 month were a bell curve (no clue if it is) then a students can
- Confirm it is a bell curve
- Locate the mean and standard deviation
- Grow 3 plants for a month
- Measure their height
- Calculate each plant’s z-score and percentile
Yeah, plants would be a good one - they could be grass seedlings sprouted on a wet paper towel; give them a set period of growing time then measure the length of the shoots