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 ...
- 759
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 ...
- 20.1k
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 ...
- 3,148
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 ...
- 10.3k
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 ...
- 7,520
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 ...
- 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 ...
- 24.4k
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 ...
- 21.2k
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 ...
- 17.3k
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 ...
- 1,440
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 ...
- 24.4k
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&...
- 2,992
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 ...
- 171
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 ...
- 21.2k
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 ...
- 5,192
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 ...
- 9,079
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...
...
- 29.5k
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 ...
- 1,512
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 ...
- 5,728
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 ...
- 29.5k
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 ...
- 24.4k
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 ...
- 29.5k
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 ...
- 533
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 $\overline{x} = 0$, $\sum\left(\overline{x}-x_i\right)^2=36$, $N-1=9$.
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 ...
- 3,148
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 ...
- 5,768
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) ...
- 29.5k
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