Displays show the distribution of values in the data

Even when a data set has no outliers or clusters, graphical displays such as dot plots, stem and leaf plots or histograms show clearly the distribution of values in the data — what kind of values are most common in the data and what values are less common. Three important features of the distribution are:

We will examine the concepts of centre and spread in more detail later.

Isometric Strength Data

The stacked dot plot below shows the distribution of strengths of 41 male Hong Kong students when lifting a horizontal bar 400 mm away from their feet.

There are no outliers or noteworthy clusters in the data.

However the display shows clearly the student-to-student variability in strengths. If similar data were collected from other students, we would expect about three quarters to be able to exert a force of between 10kg and 30kg, with perhaps one in ten being over 40kg and hardly anyone being below 10kg.

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 Isometric Strength distribution describes a 'typical' value — say just over 20 kg. Although no individuals have strength 15 kg below this, a few have strengths up to 30 kg above this 'centre'. The distribution is therefore slightly skew with a long tail towards the higher strengths.