Question

Draw any dotplot to show a dataset that is Approximately symmetric but not bell-shaped.

Short answer

A symmetric, non-bell-shaped dotplot can be drawn by having a dataset with repetitive values in the middle and unique values at the ends, leading to a symmetric, multi-modal dotplot. Example: a dataset with values from 1 to 10, with values 4, 5, 6, and 7 appearing twice, and all other values appearing once.

Step-by-step solution

Understanding symmetry and bell-shape in dotplots

A symmetric dataset means that the left and right sides of the plot mirror each other. A bell-shaped dataset, on the other hand, is a unique type of symmetrical dataset that follows the pattern of the Gaussian distribution, it's unimodal, having a single peak. Thus, for our dotplot to be symmetric but not bell-shaped, it has to be multi-modal (having multiple peaks) but still maintain symmetry.

Sketching a symmetric, non-bell-shaped dotplot

Imagine a dataset with values from 1 to 10, with values 4, 5, 6, and 7 appearing twice, and all other values appearing once. A dotplot of this dataset would be symmetric, because the left and right sides mirror each other. However, it's not bell-shaped since it's bimodal, having two peaks at 4 and 7. The result is a symmetric dotplot that is not bell-shaped, satisfying the exercise condition.

Finalising the Dotplot

Lastly, the dotplot should be properly labeled and clearly drawn to accurately represent the data points. This will present the viewer with a clear vision of the number of modes and the symmetry of the set, effectively demonstrating the concept required by the exercise.