1.1.7 Describing Numerical Distributions – Shape

Shape

• The shape of a numerical distribution relies on two factors: symmetry and outliers.
• If you can draw a vertical line through some point in the distribution whereby the distribution to the left of the line looks similar to a mirror image of the distribution to the right of it, it is an approximately symmetrical distribution. If this is not the case, the distribution is asymmetric.

Note: in some cases, you may find situations where the distribution has perfect symmetry. In these situations, you can drop the “approximately” term and refer to it simply as symmetrical.

• Asymmetric distributions can be described as either positively skewed if most of the data points are grouped to the left of the distribution with the “tail” pointing in the positive x-direction, or negatively skewed if most of the data points are grouped to the right of the distribution with the “tail” pointing in the negative x-direction.
• When collecting numerical data, sometimes due to random error or sampling error, some data points don’t match the overall trend. These data points are called outliers and can be found using the upper and lower fences of the distribution. Any data points which don’t fit between the fences of the distribution are outliers.
• When describing the shape of a distribution, mention if it has outliers or not.

Note: there are also some specific distribution shapes, such as the normal distribution, which you will encounter in future notes. These particular names should be used to describe such distributions where relevant.

Example