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Dotplots

Introduction to Dotplots

The dotplot notes on this page, suitable for copying and pasting.

3 out of 4 Australians make up 75% of the population.

Al Coon's Website

Al Coons' website is a rich source of material for introductory statistics.

Why do statisticians consider themselves lucky? Because they only have a 5% chance of being rejected!

Datasets
Visit the Datasets page for more datasets and stories to support this topic.

Or, get some ideas on how students can gather their own data

If there is a 50% chance that something will go wrong, then 9 times out of 10 it will.

There are three kinds of statisticans, those that can count and those that can't.

   A traditional dotplot resembles a stemplot lying on its back, with dots replacing the values on the leaves. It does a good job of displaying the shape, location and spread of the distribution, as well as showing evidence of clusters, granularity and outliers. For smallish datasets a dotplot is easy to construct, so the dotplot is a particularly valuable tool for the statistics student who is working without technology.

Here is an assessment item from a test by Al Coons' website to illustrate these features. His website supports AP (Advanced Placement) Statistics, a course designed to give successful high school students university credit for introductory statistics.

Two machines, C1 and C2, are making pins which must have a diameter of 8 cm ± .01 cm or they are rejected. Dotplots of 50 pins from each machine are displayed below. They are both on the same scale.

  1. By simply looking at the dotplots, i.e. without doing any calculations or counting, compare C1 and C2 in light of "the six features that are often of interest when analyzing a distribution of data. - centre, variation, symmetry, outliers, clustering and granularity.
  2. In what sense is machine C1 ‘better’ at producing pins? Justify your argument.
  3. In what sense is machine C2 ‘better’ at producing pins? Justify your argument.

An Alternative Method of Constructing a Dotplot

Here is a dotplot from NCSS 97 of the time between eruptions from the Old Faithful dataset. As there are over two hundred data values it would not have been feasible to use a more traditional dotplot.

This plot displays the scale along a vertical axis. The value of each dot is given by its vertical component. The horizontal component is randomised so that not all points are plotted at exactly the same location. The darker points represent two or more values plotted at the same location

Which charactistics of the dataset does this dotplot highlight? This dotplot shows that the data is bimodal, and gives a good feel for the spread of the data. There is some granularity evident, and there are no outliers. This type of dotplot doesn’t give a good feel for the shape of the distribution of the data or allow the student to accurately estimate the location of the centre.

For many real datasets a single type of display doesn’t suffice, but each display adds to the overall picture that we are trying to form. Access to statistics software is vital if the student is to generate these displays without getting bogged down in this stage of the analysis.

| Read Me First! | Introduction | Acknowledgements |
| Looking for Patterns |Stemplots | Dotplots | Histograms |
| Measures of Location | Measures of Spread |
| Boxplots | Normal Plots | Scatterplots |

| Assessment | Datasets | Resources |
| VISITOR'S BOOK | SEARCH | HOME |

| Linear Regression | Normal Distribution |
| Probability | Sampling | Confidence Intervals |
| Hypothesis Testing | Non Linear Regression |