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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 ...
Lee Mosher's user avatar
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 ...
Sue VanHattum's user avatar
  • 20.8k
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 ...
Jasper's user avatar
  • 3,178
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 ...
user52817's user avatar
  • 11k
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 ...
Xander Henderson's user avatar
  • 8,225
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 ...
guest's user avatar
  • 141
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 ...
Daniel R. Collins's user avatar
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 ...
Chris Cunningham's user avatar
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 ...
mweiss's user avatar
  • 17.4k
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 ...
Acccumulation's user avatar
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 ...
Daniel R. Collins's user avatar
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&...
Dirk's user avatar
  • 2,991
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 ...
el duderino's user avatar
7 votes

Fun, impressive, or compelling examples of scaling of the standard deviation like $1/\sqrt{n}$?

If you have a bunch of identical dice, (I recommend non-standard dice; as of writing, mathsgear is a good source of interesting ones), you can just pass out dice to students -- then have them collect ...
Chris Cunningham's user avatar
7 votes

Are these assumptions in statistics correct or beneficial?

It is worth considering that, if the ages would have been recorded as integers, rather than intervals, the assumption would have still been wrong in a similar but less obvious way. That is, a 25 year ...
Adam's user avatar
  • 5,713
6 votes

Moving from discrete probability distributions to continuous ones

This is treason, but anyway: If your students can jump from "ratio of outcomes in $A$ over all possible outcomes" to "ratio of length of interval, over total feasible length", then the answer why ...
Alecos Papadopoulos's user avatar
6 votes

Impressive common misleading interpretations in statistics to make students aware of

This fallacy is probably less well-known than others: large samples always mean better confidence. This turns out to be false in the presence of even the slightest bias. Imagine an experiment to ...
Benoît Kloeckner's user avatar
6 votes

Looking for examples from the MCMC family of ideas

Perhaps the "Metropolis Ball-Walk" algorithm for computing the volume of a polyhedron might be a good example? I found two sets of lecture notes on the topic, neither of which may be ideal, but... ...
Joseph O'Rourke's user avatar
6 votes

Why teach absolute mean deviation?

The foundations of statistical inference are very hard to teach at any level, and almost certainly, at the 7th grade level, little or no serious motivation is given for the rules presentd. Probably at ...
Dan Fox's user avatar
  • 5,869
6 votes
Accepted

Favorite datasets to use when teaching statistics

19 public data sets, from Springborg blog, curated by T.J. DeGroat. Summaries and links for each in DeGroat's page. United States Census Data FBI Crime Data CDC Cause of Death Medicare Hospital ...
Joseph O'Rourke's user avatar
6 votes
Accepted

Are these assumptions in statistics correct or beneficial?

This is a real-life situation: Sometimes you receive data in groups (bins) like this; that's a pretty common result from using automatable multiple-choice survey forms. There is no way to retrieve the ...
Daniel R. Collins's user avatar
6 votes

Statistics, for the mathematically rigorous

I am not familiar with this book, but the title alone suggests it might be worth examining for your purposes. Statistics for Mathematicians: A Rigorous First Course. Victor M. Panaretos. Compact ...
Joseph O'Rourke's user avatar
5 votes
Accepted

Small data sets with integral sample standard deviations

Sure, try this data set: $-2, -2, -1, -1, -1, 0, 0, 0, 3, 4$. Unless I've fudged things up, it has $\overline{x} = 0$, $\sum\left(\overline{x}-x_i\right)^2=36$, $N-1=9$.
Jered Wasburn-Moses's user avatar
5 votes

Why do we teach estimation in Statistics and Mathematics?

Most real-world problems are only approximately described by nice mathematical formulas. Depending on the situation, it can be either silly or dangerous to assume that an "exact" result of a ...
Jasper's user avatar
  • 3,178
5 votes

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

I have been tutoring stats for a couple of years, and I find that there are a couple of things that students generally find difficult in stats (as compared to other courses): The symbols: Students ...
Jorge Medina's user avatar
5 votes

Why teach absolute mean deviation?

You're in the U.S. (according to your profile), and in the U.S. square roots are not generally introduced until the 8th grade (for example, 8.EE.A.2 in the Common Core). I believe the topic "absolute ...
Dave L Renfro's user avatar
5 votes
Accepted

What to include in an "elevator pitch" for an undergraduate statistics class

I suggest you tie the "undergraduate statistics class" to data science. (1) For example, Target’s pregnancy prediction algorithm: How do you explain data science to non computer science people? (2) ...
Joseph O'Rourke's user avatar

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