A simple R/Shiny app to illustrate two properties of means and medians

 Recently I saw two interesting discussions on Twitter that had to do with means and medians and the relationship between both. Both were in Dutch. The first one was between Casper Albers (@CaAl) and Zihni Özdil (@ZihniOzdil) about student loans (see here). The bottomline is dat Casper Albers reminded us that a positive stochastic variable can never have a median that is more than twice the mean.

The second discussion was between Joël De Ceulaer (@jdceulaer), Karel Anthonissen (@KAnthonissen),  Youssef Kobo (@Youssef_Kobo) and Koen Fillet (@filletk) about young people buying houses and the support they get from their parents (see here). That discussion also involved means and medians.  I mentioned that if a distribution has a finite variance, the absolute value of the difference between mean and median is at most equal to the standard deviation  (see here). 

These two properties are not well know and suprising to some. I will admit that I only learned about them many years after I had left university and even then rather by accident.

To illustrate this I made a small R/Shiny App that allows you to flexibelly specify a distribution. The app will then generate some data according to that distribution, calculate mean and median, and plot the results to show that the properties hold. 

To specify the distribution I use a mixture of two 5-parameter beta-distributions. The first component of the mixture distribution specifies the bulk of the distribution. Optionally one can use the second component to specify outliers that are much further away from the first component. 

You can access the R/Shiny here. Enjoy!


Comments

  1. AnonymousMarch 16, 2023 at 3:10 AM

    I am from Maction Consulting - www.maction.com - Please refer to our Reddit Page : https://www.reddit.com/user/maction_survey/

    We can do Statistical Analysis for you from your data. You can contact us for data gathering too, We are from Ahmedabad, India.

    ReplyDelete

Post a Comment

Popular posts from this blog

(small) samples versus alternative (big) data sources

Image
Those of you who already have attended a meetup of the Brussels Data Science Community know that, besides excellent talks, those meetups are fun because of the traditional drinks afterwards. So after the last meetup we were on our way to a bar on the campus of the University of Brussels and I had this chat with @KrisPeeters from Dataminded. Now if you are expecting wild stories about beer and loose women (or loose men for that matter), I'm afraid I'll have to disappoint you. Instead we discussed ... sampling. Kris was questioning whether typical sample sizes market research companies work with (say in the hundreds or a few thousand at the max) still matter these days, given that we have other sources that give us much larger quantities of data. I told him everything depends on the (business) question the client has. To start with we can look at history to answer this question. In 1936 the Literary Digest poll had a sample size in the millions. But, obviously, that sample wa
Read more

Market Research and Big Data: A difficult relationship

Image
This is a write up of the talk I gave on the ' Insight Innovation eXchange Europe 2015 ' conference on 18-02-2015 in Amsterdam. IIeX is a conference that is focused around Innovation in Market Research. My talk was a rather general one in which I tried to sketch the relationship between market research and big data. After a brief introduction, I started by explaining how computing played an important role in Market Reseach right after the second world war. Then I gave an overview of the current state, and finally I looked at what the future might bring us when it comes to Big Data applications in Market Research. When I talk to people in market research and I tell them that I work in Big Data I have the impression that I'm greeted with less enthusiasm than was the case a few years a go.  Indeed, it appears that the initial enthusiasm for Big Data in the Market Research community has dwindled down a bit. I like to describe the relationship between market rese
Read more

Why The Nielsen Company is an #mrx Big Data company avant la lettre

Recently there was an interesting discussion on the Next Gen Market Research (NGMR) Linkedin group. The original discussion was started by Emma Kingham, Marketing Manager at Warc. She asked to "Make a prediction about the future of market research that you believe is GUARANTEED to happen". Pretty soon there was a subthread on market research and Big Data. Most of us agreed that the analytical capabilities you will find in the market research world can be valuable for Big Data, especially given the strong IT-leaning it seems to have. What we didn't agree on was, suprise suprise, the definition of Big Data itself.  Basically there were two schools of thought. One group saw Big Data as a relative concept: what is small for one community might be big for another. This school basically saw no difference between Big Data and Normal Data: It's just more of it. The other group, that included me, stressed the technical challenges (Hadoop, Mahout, and so on). In my view a lo
Read more