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Line graphs, frequency polygons and stem and leaf diagrams

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As well as providing valuable evidence to support your finding, statistics can be misleading. They are often used to prove a point, and can easily be twisted in favour of that point.

Here are some examples of misleading graphs.

Question

What is wrong with this bar chart? How should the information be represented?

From this graph, it looks as though house prices have trebled in one year! It is misleading because the vertical axis does not start at 0. Look at the 'improved' version of the same graph. This gives a much more accurate picture of what has happened.

Question

What is wrong with this graph?

Although the vertical scale starts at 0, it does not go up in even steps. This distorts the graph, and makes it look as though the biggest jump is between 1 and 2, rather than 3 and 4.

Also, there are no labels on the axes, so we have no idea what this graph represents!

Question

What is wrong with this 3D bar chart?

This 3D bar chart might look very attractive, but it is also very misleading. There is no scale on the vertical axis and, because of the perspective, it looks as though sales for 1995 were far greater than those for any other year. In fact, they were identical to those in 1997.

The data would be better represented on a 2D-bar chart, with appropriate labelling on each axis:

Question

What is wrong with this pictogram showing the number of people who own different types of pets?

On this pictogram, there is no category for people who do not own a pet. The pictures are different sizes, and it appears that more people own a horse than any other animal.

An improvement would be to redraw the pictogram, with each of the animals the same size and aligned with one another like this:

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