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Skills for Learning

Maths & Stats - Handling Data

Learning Outcomes

If you work through this section you should be able to:

  • Recognise a variety of types of chart and why they are useful.
  • Understand the benefits and weaknesses of different types of chart for representing and comparing series of data in different ways.
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You may also find the Interpreting charts and the Processing and representing data using charts sections useful.

A chart, sometimes called a graph, is used to display data from a table of rows and columns, in a graphical format that makes it easy to read the data at a glance.

The various styles of chart

The following are words that will come up frequently in this section.

Diagram of chart terminology.

Axis

Reference lines on a chart used to measure the position of points. Most charts have a grid with a horizontal axis (X axis) at the bottom and a vertical axis (Y axis) at the left, meeting at a right angle.

Data

Factual or numeric, often statistical, information collated for reference or analysis. Often gathered and used to inform an argument or to aid decision-making. Also used to refer to information gathered in an electronic format.

Data series

A sequence of related data. For example, the profits of a company over 12 months: each of the 12 values put together make a data series. These are illustrated by the bars, pie wedges, lines, or other elements that represent plotted values in a chart (often corresponds to rows of data in a table).

Graph

This is a chart that demonstrates the relation between sets of data (usually two sets). 'Graph' can be used to refer to a line chart specifically. Here quantities are measured along a vertical and a horizontal axis and points are plotted. Lines joining these points demonstrate the relation between the data sets.

Grid lines

These are evenly spaced horizontal and vertical lines that run across the chart in parallel with the X- and Y-axis. These are useful when plotting charts as they make it clearer where different values are on the X and Y-axis. They are also useful for interpreting charts as it is clearer what value each point, column, or bar is demonstrating.

Key

A guide for those interpreting a chart, this shows what each column/line/segment represents.

Table

Data organised into columns and rows.

Data can be presented in columns and rows but for greater visual impact a chart can be used. To demonstrate the way charts can be used we will use the following table of data throughout this section. You will see it at the top of each of the subsequent sections on charts.

Profits by region - 1st Quarter
  January February

March

North 45 69 85
South 27 81 36
East 78 47 58
West 52 29 45

As you can see, this is not very easy to interpret by simply glancing at it. Where tables simply present raw data, charts highlight the trends and changes in data series and the relationships between different sets of data. Using a chart can make relationships between data clearer. They are often used to illustrate arguments about the meaning behind figures and statistics, as they can highlight data relationships more dramatically.

Profits by region - 1st Quarter
  January February

March

North 45 69 85
South 27 81 36
East 78 47 58
West 52 29 45

This is one of the most commonly used styles of chart. It is effective at illustrating changes in data over a period of time. It is also useful for highlighting comparisons between items.

This chart plots just one series of values from the table above - that of the profits earned by the North region.

Each column in the chart is a visual representation of a data value in the table. Each column is called a data point or data marker.

When the chart includes the data from all regions, i.e. more than one series of data, a colour or pattern is applied to identify each series.

Example of a column chart

An axis title is also added for clarification - in this case to the vertical axis to indicate the values are thousands of pounds.

An axis is a reference line for your chart data. A column chart is plotted along a vertical and a horizontal axis. In column charts, the vertical axis, called the value or Y axis, holds numeric values. The categories are plotted along the horizontal axis, called the category or X axis. (The categories on the X axis of column charts are often time, e.g. months or years). This enables us to demonstrate variation in data over time.

As you can see, this chart allows you not only to compare the different amounts across the different areas in one month like the previous column chart, but also the different amounts over all the months for a particular area, through the use of colour. It is better to use colours that are easily distinguishable from each other so that you can pick out the columns you are looking at more easily. The emphasis is on the months and the change over time rather than the regions though, as it is the months that are represented on the X axis.

Profits by region - 1st Quarter
  January February

March

North 45 69 85
South 27 81 36
East 78 47 58
West 52 29 45

Example of a bar chart.

Bar charts look and act similarly to column charts but the categories are on the vertical axis and the numerical values are on the horizontal axis. This places the emphasis on the values of each bar. This makes bar charts very useful for comparisons among individual items. If the emphasis is on the non-numerical categories, such as months or years where change over time is the focus, column charts are more appropriate. If you have large numbers of data values to compare, bar charts are ideal.

In this example, the regions are on the vertical axis and the values are on the horizontal axis so that the focus is on the values. The time periods have less emphasis in this chart (they are only represented by colour rather than on the axis) so comparing the values between regions is the primary demonstration here.

Profits by region - 1st Quarter
  January February

March

North 45 69 85
South 27 81 36
East 78 47 58
West 52 29 45

An example of a line chart

Example of a line chart.

In line charts, points are plotted using an X and a Y axis. The horizontal axis is used for categories, such as time, and the vertical axis is used for numerical data. Points are plotted at equal intervals along the horizontal axis and these points are then joined up by a line, which is read from left to right.

Line charts are ideal for demonstrating changes in data series over time. The emphasis is firmly on trends, which are highlighted by upwards and downwards movements in the line.
In this example, the focus is on the profits rising and falling.

 

Profits by region - 1st Quarter
  January February

March

North 45 69 85
South 27 81 36
East 78 47 58
West 52 29 45

An example of a pie chart

Example of a pie chart.

A pie chart highlights the proportion of the items that make up a data series in relation to the whole (sum of the items). The data adds up to 100% and each portion is shown as a percentage.

Pie charts are only suitable for illustrating one data series at a time. In this example the 'South region' data series is shown.

Avoid using pie charts if the data includes negative values, missing values, or very small values as these cannot be charted satisfactorily.

 

Profits by region - 1st Quarter
  January February

March

North 45 69 85
South 27 81 36
East 78 47 58
West 52 29 45

An example of an area chart

An example of an area chart.

Area charts are plotted in the same way as line charts and, similarly, are useful for showing shifts over a period of time, but to place the emphasis on the magnitude of change the area between the X axis and the line is coloured or shaded in some way.

The relationship of parts to the whole is also demonstrated effectively in area charts.

Multiple series of data can be represented on the same chart.

An example of a box and whisker chart.

A box and whisker chart divides a data set into four equal parts, so each part represents a quarter of the data set. The box and whisker chart shows: the greatest value, third quartile, median, first quartile, and the smallest value of a data set.

The upper quartile represents the highest 25% of the data values.

The lower quartile represents the lowest 25% of the data values.

The range is the difference between the greatest value and the smallest value.

The interquartile range is the difference between the third quartile and the first quartile, which represents the middle 50% of the data values.

Multiple sets of data can be represented on the same chart.

An example of an X-Y scatter chart

Example of an X-Y scatter chart.

An X-Y scatter chart is similar to a line chart in that points are plotted using an X and a Y axis. However, the horizontal axis is used for numerical rather than categorical data. The data has to be in value pairs and the aim is to compare these by plotting them as X and Y data points and seeing how these plotted points compare. Each point is plotted above the appropriate value on the X axis and along from the appropriate value on the Y axis. You don't always need to draw a line to connect the points. Sometimes this is not appropriate and it is patterns in the scattered points plotted that you are looking for.

These charts can be very complex to interpret. They are used, in particular, for the display of scientific data.

There are various spreadsheet programs that can convert your data into charts. Microsoft Excel is probably the most popular one. Statistical programs such as Minitab and SPSS also do this.

You will also find reference books and self-teach books on using these programs available for loan in Leeds Beckett Library.

There is a section on using Excel in the IT section of this site.

Skills for Learning also run IT classes as part of the Skills for Learning Workshops series, one of which is for using Excel (see the link to the Workshops information on MyHub).

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