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Questions tagged [statistics]

For questions about the practice or science of collecting and analysing numerical data in large quantities, for instance for the purpose of inferring proportions in a whole from those in a representative sample.

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76 votes
20 answers
19k views

Impressive common misleading interpretations in statistics to make students aware of

Statistics are used everywhere; politicians, companies, etc. argue with the help of statistics. Since calculations are needed for the interpretation of statistics, such things should be taught in ...
Markus Klein's user avatar
  • 9,438
30 votes
4 answers
4k views

Open-Source Math Textbooks

It seems to me that an open-source model could work quite well for textbooks, with issues being raised by the users of the book and different forks of the project being created for different ...
Chris Cunningham's user avatar
23 votes
9 answers
2k views

Any tips in explaining the central limit theorem in statistics?

Many of my students don't have a mathematical background, and are not comfortable with concepts such as limits, random variables and distributions. Is there any intuitive way of explaining why the ...
Kenji's user avatar
  • 333
21 votes
2 answers
1k views

Adult Mathematical Literacy

In short, my question is: What percentage of American adults know what a prime number is? Since this question is very specific, and my interests are a bit broader, I'd also be happy with: Is ...
Daniel Litt's user avatar
20 votes
8 answers
4k views

What is the point of teaching variance?

I am a teaching assistant for a sophomore engineering laboratory. We use standard deviation a lot during the semester. It is an incredibly useful concept that can be used in a lot of engineering ...
BobTheAverage's user avatar
20 votes
14 answers
4k views

Probability Misconception: Two Bags with Black and White Marbles

I asked this question in a class of 13-year-old students: Bag 1 contains 2 black marbles and 1 white one. Bag 2 contains 20 black marbles and 10 white ones. Which bag is more likely to yield a black ...
Behzad's user avatar
  • 2,363
18 votes
4 answers
1k views

Emphasizing Statistics instead of Calculus

In a 3 minute talk on ted.com, mathematician Arthur Benjamin made the argument that it makes sense to give emphasis on statistics instead of on calculus in school, after students have been given a ...
user avatar
16 votes
7 answers
1k views

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

I'm creating a large number of practice problems for my statistics students. These problems are for an elementary stats course where students: measure central tendency measure dispersion use linear ...
futurebird's user avatar
16 votes
3 answers
92k views

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

I think this is a nontrivial question, because to avoid embarrassment or singling-out, I cannot ask students about: their age anything about their body (height, weight) anything involving money ...
Chris Cunningham's user avatar
15 votes
4 answers
2k views

Why is rounding half away from zero the only method taught?

Rounding to the nearest even digit is very practical in a lot of areas (e.g. statistics, accounting), but is never taught anywhere from elementary school to college. Even in R, the go-to statistics ...
jpd527's user avatar
  • 519
13 votes
3 answers
3k views

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

I'm a lousy artist. If I want my Gaussian curves to be accurately drawn when I use a whiteboard, or work with pen & paper, what are my options? Is there a way to use a straight edge, or compass, ...
Kiteration's user avatar
13 votes
2 answers
2k views

Looking for a creative way to teach ANOVA

Background I'm currently teaching a Statistics course (for the first time), one in which I been trying to teach with a hands-on approach. I have had my students (all traditional college age, non-STEM ...
Andrew Sanfratello's user avatar
12 votes
8 answers
2k views

Are these assumptions in statistics correct or beneficial?

(I hope the question in in scope, please see my question on Meta about that) My 15 yo son (2nde in France, this is the first year of the equivalent of a High School) is going through basic statistics....
WoJ's user avatar
  • 1,388
12 votes
4 answers
374 views

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

I have instructed for community colleges and adjuncted for major universities for just over fifteen years now. In all my time doing this job, I've found that the worst manifestation of so-called "...
Thomas Rasberry's user avatar
12 votes
5 answers
962 views

Moving from discrete probability distributions to continuous ones

I'm teaching an introductory statistics class at a community college, and we've just finished a unit on discrete probability. At the moment, the students' conception of the probability of an event A ...
Jared's user avatar
  • 2,223
11 votes
8 answers
6k views

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

I am a teaching assistant for an intro programming course. One assignment asked for the averages of a certain ratio, but most students, rather than returning $$\frac{\text{sum of all ratios}}{\text{...
JohnnyApplesauce's user avatar
11 votes
4 answers
5k views

Favorite datasets to use when teaching statistics

There are so many datasets available that it seems difficult to sort through them all and identify the best ones to use when teaching an introduction to statistics class. What are your favorite ...
eternalGoldenBraid's user avatar
11 votes
3 answers
421 views

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

I am a guest here, having responded to a general invitation extended to the Cross Validated community, to possibly contribute answers whenever some question related to Statistics comes up in this site....
Alecos Papadopoulos's user avatar
9 votes
6 answers
1k views

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

Students are exposed to sets very early in their education, so my first inclination is that this would be the best method to give children in the early primary grades an introduction to probability ...
jonsca's user avatar
  • 743
9 votes
6 answers
1k views

Statistics, for the mathematically rigorous

I don't know where I can find a rigorous statistics course or textbook. The closest thing I can think of is measure-theoretic probability theory, but I wouldn't really call that "statistics"....
John Clever's user avatar
8 votes
7 answers
555 views

Hypothesis Tests in Students' Lives

Consider, in a basic statistics class, the difference between the following two examples: A six-sided die is rolled twenty times. It comes up a "two" eight times, which seems unfair. The owner of ...
Chris Cunningham's user avatar
8 votes
5 answers
551 views

Why teach absolute mean deviation?

I was helping my niece (7th grade) with homework and one of the topics was the absolute mean deviation. It's basically the same thing as standard deviation except instead of squaring the difference ...
Dean MacGregor's user avatar
8 votes
4 answers
508 views

Statistics Class Held in a Computer Lab

I'm looking into holding my basic statistics class in a computer lab in the future to avoid a lot of the by-hand computing that happens in statistics classes. For example, very few students get ...
Chris Cunningham's user avatar
8 votes
3 answers
26k views

Teaching the difference between standard deviation and interquartile range

Are there any good examples for high school studends where: Interquartile range is "better" to describe "spread" in an (empirical) statistical distribution of data standard deviation is a "better" ...
Julia's user avatar
  • 1,265
8 votes
1 answer
355 views

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

Since the beginning of time, candy has been used to illustrate the principles of distributions in early lessons on statistics. A recent informal study seems to indicate that the flavors of Skittles ...
jonsca's user avatar
  • 743
8 votes
3 answers
3k views

Self-study Linear Algebra textbook for Machine Learning and Statistics

I am looking for a good linear/matrix algebra textbook, suitable for self-study, that covers topics relevant to statistics and machine learning. I have access to ...
neuron's user avatar
  • 221
8 votes
1 answer
121 views

How to teach steady state in queueing (if at all?)

I am teaching an undergraduate course in Operations Research to business students (they are not: maths students). I want to check, if and how teaching the steady state makes any sense. As in the ...
Statos's user avatar
  • 219
8 votes
2 answers
187 views

In introductory statistics hypothesis testing, why not always use P-values?

A test statistic is a measure of significance of a data set with respect to a claim. My statistics textbook is insistent that the students should be able to interpret the test statistic in two ...
Chris Cunningham's user avatar
8 votes
0 answers
143 views

Good Source for German Tank Problem

I would like to teach the German Tank Problem to bright students with little prerequisites. They are 16 year old high school students with a lot of maths competition experience, but no prior knowledge ...
J Fabian Meier's user avatar
7 votes
2 answers
190 views

Published papers for Intro Stat students to read

I am looking for studies and experiments in the literature that I can share with undergraduate students in an intro statistics course. I do not expect students to understand everything, and I plan to ...
Jordan's user avatar
  • 603
7 votes
3 answers
198 views

Does it make sense to speak of whether the standard deviation is a "good measure" of some particular distribution?

I came across this question (picture below, the question where the drop-down bar is highlighted) on edulastic.com. The answer, apparently, was that "The standard deviation is a good measure of the ...
user avatar
7 votes
3 answers
372 views

Standardized Exam for Statistics?

I have been trying to find a standardized exam for statistics, but have not had any luck. For example, there is an AP statistics exam for high schoolers to take, but I am looking for something that ...
Jeh's user avatar
  • 171
7 votes
0 answers
64 views

Statistics for Primary School: Informal Inferential Reasoning

Is there anyone that is experienced in teaching Informal Inferential Reasoning in primary school? Mind to share your experience?
Russasmita Sri Padmi's user avatar
6 votes
4 answers
391 views

Why do we teach estimation in Statistics and Mathematics?

Please forgive me if this is naive. I am only an aspiring educator after all. Why do we still teach estimation when there are easily accessible/teachable exact techniques? Why do statisticians teach $...
euclidiography's user avatar
6 votes
3 answers
317 views

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

I'm going to be giving a five minute "elevator pitch" presentation to undergraduate math majors in order to advertise an introduction to statistics class that I'll be teaching in the spring. It's an ...
eternalGoldenBraid's user avatar
6 votes
2 answers
2k views

Small data sets with integral sample standard deviations

I'm looking for small data sets ($N\approx10$) that have integral (or even rational) sample standard deviations. Given a list of observations $\{x_1,\ldots,x_N\}$ with mean $\bar{x}$, the sample ...
Jared's user avatar
  • 2,223
5 votes
2 answers
97 views

Looking for examples from the MCMC family of ideas

I am teaching a "computation" course, where we get students to explore mathematics and statistics via a high-level programming language. So the course is less about mathematics proper, and more ...
Ryan Budney's user avatar
5 votes
3 answers
176 views

Is there a case for ditching any of the paper tables in elementary statistics courses?

The textbook I'm using explains the it is "impractical" to have a normal distribution for all values of $\sigma$ and $\mu$, hence the standard normal distribution table. To me, this simply doesn't ...
futurebird's user avatar
5 votes
1 answer
229 views

How to explain even higher moments

In prob/stats, students mostly get the idea of mean/expected value, and variance/s.d. slowly sinks in. Even the third and fourth moments (about the mean) have "standard" interpretations - skewness ...
kcrisman's user avatar
  • 5,976
5 votes
2 answers
292 views

Where can I find a collection of bad/misleading data visualizations?

Are there any collections or blogs of bad data visualizations? I know I've seen such misleading graphics in the news or in print, made misleading either maliciously or thoughtlessly, but I usually see ...
Mike Pierce's user avatar
  • 4,845
5 votes
2 answers
198 views

What are some suggestions fo teaching statistics concepts to struggling college students?

I'm a private math tutor. I'm fairly new at this, and this semester is the first time I've been tutoring for a statistics class at a community college. I enjoy experimenting and learning about ways to ...
composerMike's user avatar
5 votes
2 answers
367 views

Trends in math education: Majors? Applied math? Statistics?

I would be quite interested in learning of trends (in the U.S. or internationally) of student interest at the undergraduate level in pure math vs. applied math, say, measured by majors at graduation. ...
Joseph O'Rourke's user avatar
5 votes
1 answer
281 views

What should I cover when teaching hypothesis testing in high school?

I'm currently teaching basic probability and after that I would like to do some simple hypothesis testing. Frankly, probability theory and statistics have never really interested me but I feel like my ...
Huy's user avatar
  • 699
5 votes
0 answers
124 views

After building the probability space, how to motivate for random variables? [closed]

Having put my audience through developing a probability space $(\Omega, \mathcal{F}, P)$, where $\Omega$ is the sample space of a random trial, $\mathcal{F}$ is a $\sigma$-field on it, and P is a ...
TonyK's user avatar
  • 51
4 votes
3 answers
286 views

Statistics students lack calculator skills, how to help them?

Many of my statistics students will calculate the standard deviation for a set of data using the formula when it is not required or appropriate. When faced with something like $\sqrt{56}$ they will ...
futurebird's user avatar
4 votes
2 answers
932 views

Hypothesis testing for children (grade 1-4)

What do you think, could hypothesis testing be taught, in some way (probably informal) to that age group of kindergarten to 4th grade? Ideas, some resources, published papers, and so on? This would ...
kjetil b halvorsen's user avatar
4 votes
1 answer
154 views

Is there any university program that offers an introductory statistical methods class that is bayesian -instead- of a frequentist one?

Is there any university program that offers an introductory statistical methods class that is bayesian -instead- of a frequentist one? Surely every intro to stats class in every program in the world, ...
Mitch's user avatar
  • 451
4 votes
2 answers
154 views

suggestion for probability and stats text to suit my learning style.

I am of a mature aged learner and want to learn probability and statistics at a senior high school (k12) and undergraduate level for my own general understanding. I have discovered in the past that I ...
hgtest35's user avatar
4 votes
1 answer
241 views

What are some very concrete examples of statistical models to present to students?

In order to teach students what "statistical modeling" is, it would be helpful to show them some very concrete, specific (and maybe classic) examples of statistical models. Something you can point to ...
eternalGoldenBraid's user avatar
4 votes
1 answer
194 views

What is a realistic situation that illustrates precisely what a p-value is?

Students in the basic statistics courses I teach often learn a little bit of probability and then learn hypothesis testing. The core concept that ties the course together is the p-value, but most ...
Chris Cunningham's user avatar