Topic 3: Statistical Representation

Histogram 

The most appropriate method of illustrating a grouped frequency distribution is by means of a histogram.

Unlike bar charts, there are no gaps between the bars of a histogram. The bars are drawn between the class boundaries, and the area of the bar is proportional to the frequency.

It is constructed by first making off class boundaries on the x-axis and then drawing rectangles whose heights equal the class frequencies if classes are of equal width.

HISTOGRAM WITH EQUAL CLASS WIDTH

Example 1,

The diameters of 30 pipelines were measured and the information grouped as shown. Draw a histogram to illustrate the data.

Solution:

HISTOGRAM WITH UNEQUAL CLASS WIDTH

If the classes are of unequal width, then we may use Frequency Density.

   

Example 2, 

The diameters of 34 pipelines were measured and the information grouped as shown. Draw a histogram to illustrate the data.

Pie Chart

A pie chart is a circular diagram split into sections

The angle of each sector of the pie hart is in proportion to the amount of information it represents

The angles of the sectors in a pie chart add up to 360°

To draw a pie chart:

1. Draw a circle

2. Use a protractor to measure the angle for each sector

3. Either label the sectors or use a key.

Example 1, 

A travel brochure contains 24 picture from different countries. The table shows how many pictures there are from each country.

Bar Chart

A Bar Graph (also called Bar Chart) is a graphical display of data using bars of different height.

Bar Graph are good when your data is in categories such as "Comedy", "Drama" and etc. But when you have continuous data such as a person's height then use a histogram.

It is best to leave gaps between the bars of a Bar Graph, so it doesn't look like a Histogram.

Example 1, 

The colours of 30 cars in a park are shown in the frequency table.

a) Complete the bar chart to represent this information.