52 votes

What is the point of teaching variance?

Actually, your definitions are backwards: the standard deviation is the square root of the variance. In other words, one defines variance first --- it has a simpler formula, and it has simpler ...
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25 votes

Probability Misconception: Two Bags with Black and White Marbles

Firstly, don't forget that your student has thought hard to come up with his answer and to be told it is wrong may be taken as invalidating his effort, or even insulting his intelligence. This might ...
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21 votes
Accepted

How do I sketch a good gaussian curve freehanded, or by using only common sketching tools?

I would put dots where I want 1 standard deviation to be, because I know that's where the inflection points are. (I just graphed $y=e^{-x^{2}/2}$ on desmos, and I see that the inflection points are at ...
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  • 17.5k
19 votes

What is the point of teaching variance?

An analogy: speed is to standard deviation, as kinetic energy is to variance. Energies can be added usefully; speeds can only be added in very limited circumstances. Similarly, variances can be ...
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  • 2,871
18 votes

How to explain that the sums of numerators over sums of denominators isn't the same as the mean of ratios?

One observation is that (sum of numerators) divided by (sum of denominators) is not well defined. For example, let's work with the two ratios $a=\frac01$ and $b=\frac11$. The ratio of the sum of ...
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  • 7,703
15 votes

Why do we teach estimation in Statistics and Mathematics?

Number Sense: At the elementary level, estimation helps students to develop number sense. As Daniel R. Collins notes, order of magnitude estimates can be quite important. Anecdotally, I once rented ...
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14 votes

How to explain that the sums of numerators over sums of denominators isn't the same as the mean of ratios?

It actually depends on exactly what you're asking. Or even what you SHOULD be asking. If you want the average profitability of all the 500+ operators in the Permian, you could just average all the ...
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  • 141
13 votes

Where can I find realistic data for college-level elementary statistics problems?

DASL (pronounced "dazzle" and short for Data And Story Library) is an online collection of stories with matching data sets to be used for educational purposes. They are real data from real research. ...
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13 votes
Accepted

Teaching new stats students confidence intervals, hypothesis testing, and other general techniques for inference

I've been teaching introductory statistics for the same amount of time at a large urban community college. I have never had this response from a class in toto. Last semester I did have one student say ...
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12 votes

How to explain that the sums of numerators over sums of denominators isn't the same as the mean of ratios?

I like guest's answer. To elaborate, here is a possible question to ask them. You take two trips in your car: Trip 1 is a 100 mile drive that takes you 2 hours. Trip 2 is a 200 mile drive that ...
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  • 19.1k
10 votes

Any tips in explaining the central limit theorem in statistics?

In my experience, there are a few key things that students misunderstand around the central limit theorem. Firstly, many students don't actually have a concept of distribution in the first place. ...
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10 votes
Accepted

Statistics Class Held in a Computer Lab

I have been an IT/maths teacher, so I have spent several years teaching in a computer lab, and watched others use the room, sometimes very effectively, sometimes not so much. I have recently seen ...
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  • 2,588
10 votes

Why teach absolute mean deviation?

The question we pose to students is: How far away, on average, are these values from their mean? The "natural" way to answer that question is to compute the deviations of the individual data points ...
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  • 16.4k
9 votes

Teaching the difference between standard deviation and interquartile range

A simple example for the IQR is to consider the following two data sets: A = {1,1,1,1,1,1,1} and B = {1,1,1,1,1,1,100000000}. IRQ for both is 0, but SD is very different. You can argue about which ...
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9 votes

Probability Misconception: Two Bags with Black and White Marbles

Ask whether they think putting the marbles in a bag into any particular arrangement would affect the outcome. If they're ok with this, have them consider the arrangement of Bag 2 where the marbles are ...
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  • 4,890
8 votes
Accepted

What are good survey questions for statistics students to ask each other in class?

If you already have the class roster, you can look at the students' names and see if you can find any outliers in measures associated with their names. Numbers of letters, longest run of consonants, ...
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  • 7,405
8 votes

Probability Misconception: Two Bags with Black and White Marbles

DavidButlerUofA's answer hits the spot on pedagogical methodology. However, the actual question is about establishing the correct intuition. With that said, a good way to falsify the wrong intuition ...
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8 votes

Statistics Class Held in a Computer Lab

I see you teach university level courses, however, I think that my experience in a high school classroom may offer some insight. I teach an introductory applied statistics class at my high school ...
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8 votes

What is the point of teaching variance?

The variance is calculated directly, while the SD is calculated in terms of the variance. The variance is additive for independent variables. The effect of sample size is a lot easier to explain using ...
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7 votes

What are good survey questions for statistics students to ask each other in class?

EDIT 4/8/15 I began teaching Statistics with the same difficulty that you had. I started with basic sorts of questions (e.g., age, height) but my students weren't really responding to these types of ...
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7 votes
Accepted

Passage from Descriptive to Inferential Statistics - analogies with other Math-fields?

On the (false) distinction between descriptive and inferential statistics In my view, it is rare that your only purpose is simply to describe the data you have. Even a simple graph is usually used to ...
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7 votes
Accepted

Who put the skew in my Skittles? Have there been studies as to which candy has a fairly uniform distribution of flavors?

(Sorry if my answer is as offensive as responding to a question about Coca-Cola with data about Pepsi!) There are certainly some lesson plans around looking at statistics for M&M colors. For ...
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7 votes

What is a logical way to introduce probability and statistics to students that don't know fractions or percentages yet?

I'm going to suggest what you're considering is very difficult. And also, I don't think it's something I'd want to do. (But we'll do it below anyway, for fun!) Fractions are an early concept that ...
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  • 7,405
7 votes

Probability Misconception: Two Bags with Black and White Marbles

One suggestion that might be worth considering is asking the students the same question but for a bag with no white balls. Suppose you have a bag with 1 black and no white balls ( probability of ...
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  • 262
7 votes

Probability Misconception: Two Bags with Black and White Marbles

I wrote a long answer to this, which then made me realise that I think this needs the rule. [Restart:] A few pointers first: Don't number the bags if you have numbers of marbles: big/small, black/...
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  • 71
7 votes
Accepted

Where can I find realistic data for college-level elementary statistics problems?

(I came to mention DASL, but since it's already been mentioned, I'll give some other resources.) opendata.stackexchange.com often has mentions of useful sources of data, some of which are small (and ...
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  • 503
7 votes

Moving from discrete probability distributions to continuous ones

This is an uncomfortable moment, mathematically, in a non-calculus-based statistics course; frankly, we simply need to steal the calculus concept and hope that students trust us about it, without ...
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7 votes

Why do we teach estimation in Statistics and Mathematics?

I'd say a good approximation is often better that an exact result. This may sound counterintuitive, but as the phrase is vague anyway, here is a longer explanation what I mean: An "exact result&...
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  • 2,932
7 votes

How to explain even higher moments

I must confess I'm not an educator, but I like this question and at the very least I can answer with the intuitive picture I use in my own head. The $n$-th central moment $\mu_n$ of a random variable ...
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