Displays show the distribution of values in the data
Even when a data set has no outliers or clusters, dot plots and stem and leaf plots show clearly the variability in the data — the distribution of values. They highlight which ranges of values are most common in the data and which ranges are less common. Several alternative phrases are used to describe this aspect of the data.
- The density of values in the data
- The distribution of the data
- The shape of the data's distribution
Of particular interest are the centre of the distribution and the spread of values around this. We will examine the concepts of centre and spread in Chapter 3: Numerical Summaries.
Example
The stacked dot plot below shows the distribution of marks for 41 students in a test that has been marked out of 50.

There are no outliers or noteworthy clusters in the data.
However the display shows clearly the student-to-student variability in these measurements. If similar data were collected from other students, we would expect about three quarters to be able to get a mark of 30 or more, with perhaps one in ten being under 20 and hardly anyone scoring below 10.
Symmetry and skewness
If the density tails off in a similar way at both ends of the distribution, we call the distribution symmetric. If one side of the distribution tails off more slowly, we say that the distribution is skew.
The centre of the distribution of the mark data above describes a 'typical' mark — say around 35. Although no students have marks 15 higher than this, a few have marks up to 30 lower than this 'centre'. The distribution is therefore skew with a long tail towards the lower marks.
The test therefore spreads out the weakest students, but does not distinguish well between the best students.