Settle this dispute: average v. median

If you pass over the semantics, there IS a difference...depending on the distribution away (more of an extreme) from the norm in an average class vs a median class-size scenario.

In reality, those classes in a scenario which is/are considerably above than average might be closer to what someone would be considered a burden.

For example, take 2 examples of class sizes with tow different distributions:

Example 1:
#1 18 students
#2 16
#3 20
#4 22
#5 24
#6 21

Example 2:
#1 15
#2 18
#3 20
#4 24
#5 26
#6 28

In example 1, you have 'reasonable 'class size around that 20 student average.

In example 2, you have 2 classes with 'burdensome' overcrowding

Average and Median are two different measures. At times they will be different. I don't think either of them are "meaningless" for determining the how overcrowded classes are since "overcrowded" is a subjective term. Mathematics can give you a value. It can't tell you if the value is "meaningful" or not. That is really a matter of your personal opinion.

Personally I would think that the maximum class size is also important as a statistical measure. If you tell me that some classes (or any class) had more than 30 students... that would be overcrowded. The percentage of classes that are more than 30 would be a more persuasive measure for me.

I'd go for the mode over the mean or the median. All three can be used when discussing "average" outcomes. They are all measures of central tendency, which is really what you're discussing when you use the word "average". The mean is the arithmetic mean (the one used in your example and is derived by dividing the total sum, by some measure (students divided by teachers). The median (middle score of ranked values) is useful when the data are skewed in one direction or the other. The mode (most prevalent outcome) is meaningful when there is a very common outcome along with a few scattered outliers. Note: all three values are the same when a distribution is normally distributed (classic bell curve). You'd have to look at the distribution of the scores to see which one is most appropriate. The median is always less influenced by outliers than the mean, but the mode (most common result) is usually telling.

If there are 20 classrooms and 400 students then you'd have a mean of 20 students per class. If 18 of those classrooms have 18 students (324 students total) and the other 76 students are in the remaining two classrooms then the median and mode would both be 18 (great news for everyone not in the two rooms). If there's all sorts of scatter, but the mode is 16 or 17, say, in 10 rooms the median could be higher or lower than that depending on how the rest of the rooms are distributed. Bottom line, unless all three numbers are given then you really can't judge whether "20" is a reasonable average.

Another factor is WHAT class has HOW MANY.

A gym class of 40 runs a lot different than a special eduation or advanced physics class of 12.

Another factor is age. A class of twenty 16 year-olds would need different teaching strategies than a class of twenty 5 year olds.

I'm thinking that there are probably a lot of kids that take a "study hall" for an elective and there is no teacher for that. Then there are the advanced/remedial/special education classes and independent studies that have a very low teacher to student ratio. Some advanced classes are even taken off campus at the local jr. colleges.

I imagine the general education classes are crammed. The newspaper photo accompanying the story showed a freshman English class -- I counted 41 students in the photo.

For example: one semester in college I took an independent study, a class with 20 people, a class with 12 people, and a class with 300 people.

If I just said my average class size was 83 people, that wouldn't be a very usable statistic.

Depending on how deeply you want to investigate the question, you are either both wrong or Mr. B is right.

Given that there is a hard lower limit on individual class sizes (zero) but no hard upper limit, the average class size is likely to be greater than the median class size. So if your question is, "is the typical class in Oregon overcrowded?", then the average is a more pessimistic measure than the median of what counts as "typical". Looking at the median instead of the average would not change a verdict of "not overcrowded". In this sense, Mr. B is right.

But if instead you are asking, "how much of a problem are overcrowded classrooms in Oregon?", you are right that the average by itself is meaningless. That's because not all classes are average. For all you know, classes in lucky school districts could have 10 students in them, whereas classes in unlucky ones could have 50. The unlucky school districts would still have a serious problem, and you would want to know the extent of it.

In that case, though, you're wrong about the alternative figure to look at. To estimate the extent of the crowded-classroom problem, you need a sense about not just typical class sizes, but also about untypical ones. There are several ways of getting that. For example, you could look at the worst-case class size, or the 90th-percentile class size, or the standard deviation, or the percentage of classes larger than X, where X is your threshold for "overcrowded". Either of these can be useful. An alternate figure for the typical class size won't do, however.

bowing out. G'day!

Neither - I think in general you need more information. For simplicity say you have 6 classrooms - 4 have 5 students and 2 have 50. Well the average would be 20 and the median would be 5. So looking at those stats in either case you would say not overcrowded, however, if you were the unlucky parent to have a student in a classroom of 50 then you would say yes overcrowded.

But that is extreme - I would say overall and realistically though in either case it would give you a good indication as usually classrooms tend to have about the same number of children. Schools tend to move kids so that most classrooms have a minimum and/or maximum amount of kids.

I would more likely ask -- what is the max amount of kids in a room -- that would give you a better indication of overcrowding.

As has been noted by posters, overcrowding is relative to a situation. I too have been in classes of 250 at my university, and the opposite, some classes of twelve or less students, which intensifies the experience one way or another. Most - I suppose - would agree now that a class of 54 first graders is a bit much when taught by one person. Unless that is a nun in 1947, with the teaching mores of the time -

my first grade class:


(I'm the shy girl behind the St. in the St. Monica's sign)

I thought that, by default, the husband is always wrong.

Now that is the most correct answer of all.

A+

If a man says something in the forest... and no woman is around to hear him, is he still wrong?

always...this trumps the tree noise thingy

Their was of calculating assumes all the teachers are teaching all the time, that's probably not the case. If nothing else, bet the headteacher does other things than just teach.

I believe one needs a histogram for each subject, showing the breakout of different class sizes, and the number of classes with each respective size.

Then one might be able to show whether for a specific subject, a specific class size was effective, if there was a correlation of the class size to the average grade within that class size. In other words, would one be able to prove that some class sizes have a lower, or higher, average grade, within a specific subject? Actually, I would not use "average grade," but the mode of the grades (the grade that reflected the most students). The median is just the grade in the middle; the average is just a calculated number that can be skewed by highs and lows. The mode, in my opinion, can show "effectiveness," or "ineffectiveness," since it shows the greatest number of a specific grade.

First one collects the data, the puts it into a form that one can arrive at conclusions.

P.S.: When "averages" are used, analysts might just throw out the high and the low, to get numbers that are not skewed by a high and a low.