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.

Holiday Home Rental data

The stacked dot plot below shows the distribution of the monthly rent asked for 41 houses in a holiday resort.

There are no outliers or noteworthy clusters in the data.

However the display shows clearly the house-to-house variability in rentals. If similar data were collected from other houses, we would explect about three quarters to charge between $1000 and $3000 per month, with perhaps one in ten being over $4000 per month and hardly any houses being below $1000.

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 Holiday Home Rental distribution describes a 'typical' value — say just over $2000 per month. Although no houses are $1500 below this, a few have strengths up to $3000 above this 'centre'. The distribution is therefore skew with a long tail towards the higher prices.