Mode: eye colours
About this app
The eye colours of 100 people sort themselves into four bars, brown 41, blue 33, grey 14, green 12: the tallest bar is the mode. Two counter-checks show why mean and median fail for nominal variables: averaging all colours gives a murky blob, and who stands at places 50 and 51 of the line-up depends on the arbitrary order of the categories.
With explain mode: an AI tutor walks you through the app, points out what matters in the scene and answers your questions.
The idea
The mode is the value that occurs most often. It is the only measure of location you can compute for nominal variables, that is categories without an order and without distances: eye colour, means of transport, favourite drink. You can average body heights, and for salaries the median is popular. For eye colours neither works, because there is nothing to add up and no natural order. If several categories are equally frequent and the most frequent, the distribution has several modes.
What the app shows
100 eyes first lie in random order and then sort themselves into four bars: brown 41, blue 33, grey 14, green 12. The tallest bar is the mode, brown with 41 percent. Two counter-checks show why mean and median make no sense here. Averaging all colours gives a murky blob that matches no eye colour. If everyone lines up by category, places 50 and 51 hold blue eyes with the order brown, blue, green, grey, and brown eyes with the order green, grey, brown, blue.
What you can try
Switch between shuffled, bars and line-up and let the mixed colour appear. Drag a bar or a block sideways to change the order of the categories and watch who ends up in the middle. The sliders change the frequencies, for example so that two categories are equally large: then the app shows two modes. Besides eye colours there are the examples commute and drink. The values panel shows the table, the mode, the middle of the line-up and the mixed colour.
Frequently asked questions
- What is the mode in statistics?
- The mode is the value with the highest frequency. For 100 people with 41 brown, 33 blue, 14 grey and 12 green eyes, the mode is brown. It can be determined for every level of measurement, including nominal variables.
- Why is there no mean and no median for nominal data?
- The mean requires adding values, the median requires ordering them by size. Categories such as eye colours have neither distances nor a natural order. If you still put them in a line, the middle depends on the arbitrarily chosen order.
- Can there be several modes?
- Yes. If two categories are equally frequent and more frequent than all others, the distribution is bimodal and has two modes. With more than two it is called multimodal.
- What can I change in the app?
- The view (shuffled, bars, line-up), the order of the categories by dragging or with a button, the four frequencies from 0 to 50, the mixed-colour test and the example: eye colour, commute or drink.
Subject: Statistics
More from Statistics
- Anscombe's quartet
- Bias-variance / overfitting
- Box plot workshop
- Geometric mean
- Law of large numbers
- Histogram workshop
- Hypothesis test & p-value
- Confidence interval
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