Bar chart

In bar charts, the lengths of the bars are proportional to the frequency of the values. They are used for distributions of discrete quantitative variables. This is the reason why bars are thin and appear above the individual values of the variable. They are also used to represent qualitative variables.

Frequency histogram

Histograms are used for distributions of continuous variables. They consist of rectangles with bases that are the length of the intervals. If all the intervals are all the same length, the heights are proportional to the frequencies of the values, like in a bar graph.

It makes sense to use a histogram instead of a bar chart when we have a continuous variable (8 laps means fewer than 9), even if the data are not given in intervals (like the laps around an athletics track).

The number of audience members is a discrete quantitative variable, but because there are many different values it’s best to use intervals, and therefore, histograms.

Frequency polygon

Frequency polygons are used in the same situations as histograms. They are made by drawing a line connecting the midpoints of the tops of the rectangles and extending the line to the axis at the beginning and end.

They smooth out the ‘steps’ of the histogram.

Pie chart

In pie charts, the angle of each segment is proportional to the corresponding frequency of the value.

They can be used for all kinds of variables, but are most often used for qualitative variables. For example, the pie chart below shows the favourite types of films of a certain population in Spain by percentages:

A progression of pie charts can be particularly useful to represent data that changes over time. For example, we can look at how the education level of the population of a certain region changed over time, from 1950 to 2010. We see that the number of illiterate people and people with basic education decreases over time, and that the number of people with middle and higher education increases considerably.