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Presenting numerical data

It is likely that you will need to use numerical information in your writing eg facts, figures, statistics or data that you have collected or analysed. This information can be used to illustrate an argument or present detailed information in a manner that is easy to read and understand.

There are three main ways you can do this:

  • Incorporate the data into the main body of your writing.
  • Use a table.
  • Use a graph or chart.

The method that you use depends on the amount of data, its complexity and who your reader is. Always discuss what this data reveals about the topic you are researching.

 

Using Numbers in your writing

Numbers are most effective in the main body of your writing if there are only two values to compare. For example: 86% of male students said they regularly ate breakfast compared to 63% of female students.

If you need to discuss three or more numbers your writing may be difficult for the reader to understand. Below are two ways to say the same thing. Example 2 is clearer than Example 1.

 

Example 1:

52% of male students said they always ate breakfast, 33% said they usually did, and 14% said they never at breakfast.

 

Example 2:

Male students said they ate breakfast:

  • Always 53%
  • Usually 33%
  • Never 14%

Tips:

  • It is always a good idea to list numbers from large to small, or small to large.
  • In general, numbers are not spelt out in the text. For example you would write 400 rather than four hundred. Some teachers prefer students to write out whole numbers between 1 and 10 and then use the numbers for values for all other numbers.

Tables

Tables are an effective way of presenting data:

  1. To show how a single category of information varies when measured at different points eg to show how the unemployment rate varies between different countries.
  2. When the dataset contains few numbers. Large tables can be hard to understand. Avoid using complex tables in talks and presentations when the audience will have a short time to take in the information.
  3. When the precise value is crucial to your argument and a graph is not useful. For example, it may be important that the reader knows that the result was 2.48 and not 2.45.
  4. When you don't want one or two very high or low numbers to detract from the message contained in the rest of your data.

 

Heading

Heading

Heading

Heading

Heading

Data

Data

Data

Heading

Data

Data

Data

 

Rows go from left to right across the page. Columns go up and down the page. Most people find it easier to read down a column than across the row. Tables are easier to read if the data is arranged in order of largest to smallest or vice versa, but this may not always be possible.

Tips:

  • Make sure your table is clear and easy to understand by planning how you will divide your data in rows and columns.
  • Numbers should be written in a simple format eg 4.6 million rather than 4,600,000.
  • Include a title that gives the reader a clear understanding of the content.
  • Give the source of the table if you found it in a book, journal or website.
  • If you include more than one table give them a unique reference number eg Table 1, Table 2.
  • Design your table so each box isn’t surrounded by a line.
  • Avoid large gaps between columns.
  • Make sure the boxes are even sizes.

Maths Vid 2

Khan Academy

Maths Vid 3

Graphs

Graphs

Graphs are a visual way to simplify complex information and highlight patterns and trends in data. They can present both large and small amounts of data. Type of graphs include:

  • Bar charts
  • Histograms
  • Pie charts
  • Line graphs
  • Scatter plots

 

Bar charts: These are the most commonly used types of graphs and are used to display and compare the number, frequency or other measure for different categories or groups. Graphs are constructed so the heights or lengths of the different bars reflect the size of the category they represent.

 
  Description: num2.gif

 

 

 

 

 

 

 

In the example above:

  • The X axis is the horizontal line at the bottom of the graph. The X axis has 7 categories running along it. It doesn’t contain any measurements.
  • The Y axis is the vertical line running up and down the left side of the graph. It has a scale of measurements that run from 0 to 60.

 

It is possible to switch the X and Y axis so the bars run across the page instead of up and down. Don’t forget to add a title and acknowledge the source if you didn’t build a graph. You also need to add a heading to describe the X Axis and also add one for the Y axis. If you include more than one graph in your work, give them unique numbers.

 

Below is an example of a horizontal line bar graph:

 
   

 

Below is an example of a grouped bar graph, where sub groups appear together on the X axis:

 

 
   

Below is an example of a horizontal stacked bar graph.

 
   

Stacked bar graphs are similar to grouped bar charts because they display information about sub-groups that make up different categories. In the example above the sub-groups are placed on top of each other to make a single column. The overall length of the bar shows the total size of the category whilst different shadings are used to indicate the relative contribution of the different sub-groups.

 

Histograms: They are a special type of bar chart where the data represents continuous rather than separate categories. To highlight the continuity gaps aren’t placed between the columns.

You will see that categories on the X axis above run in a continuous grouping. A histogram is also different because both the X and the Y axis has a scale. This means that the area of the bars are proportional to the size of the category represented, some bars will be wider than other bars. The total area of a bar is more important than their actual height.

 

Pie Charts: They are a visual way of showing how data is distributed between different categories. The circular graph is divided into wedges that represent a category’s contribution to the total value of the pie.

 

 
 

 

 

 

 

 

Pie charts are generally used for showing information grouped into a small number of categories. They are an alternative to a simple table, especially if the data isn’t numbers but objects/people/categories. As a general rule it is best to have about 6 categories so you allow the reader to easily distinguish the different wedges.

Two pie charts can be used side by side to compare sets of data where the categories are the same or similar but there is a change in another variable such as time or age.

Don’t forget to add a title and acknowledge the source if you didn’t build it. If you include more than one graph in your work, give them unique numbers.

 

 

Line graphs: They usually show time series data or how one or more variables change over a continuous time period eg monthly rainfall or annual unemployment rate. These graphs are useful for identifying patterns and trend eg seasonal effects, turning points and large changes.

 
 

 

 

The data you use for these graphs needs to be collected at regular intervals so the reader can make accurate estimates about points that lay half-way along the line between two measurements.

 

 

Scatter plots: These graphs show the relationship between pairs of measurements that are made for the same object/individual eg the age and height difference for one person as they age.

 

 
 

 

 

By analysing the dots in the graph above you can identify the relationship between the two measurements and explain why a change occurs eg the child above has grown taller as they aged until they were 17.

Graph design:

Horizontal Grid lines can provide clarity to your bar graphs but make sure that that the design elements you use provide clarity rather than make it more difficult to read the graph. Colours and shades can be used but make sure they are easy to distinguish. Many computer programs will allow you make a 3D graph but quite often they make it harder for readers to judge measurements.

[The text above is based on that provided by the University of Leicester]