Contents:
- Pictograms
- Pie charts
- Bar chart
- Component bar charts
- Percentage component bar charts
- Compound bar chart
- Histograms
- Frequency Polygons
- Ogives
Pictograms
The following pictogram was constructed from the TimeWeb sample data on population. The data show the total UK workforce jobs measured in thousands in 1990 and 2000. Notice that you have to be careful over the dimensions of the picture that you use to reflect the increase/decrease in the indicator.
There is more available on the use of scale in pictograms and how it can be mis-used.
[Top]
Pie charts
In order to calculate the size of each segment of a pie chart, you need the following:
- The number value of each component part of the whole.
- The total of all the component parts.
The calculation is as follows:
Number value of the component part / total of all the component parts
Then multiply by 360.
The result is measured in degrees, so all you have to do is to use a compass and protractor to measure the size of each segment.
Check your calculations by adding up the degree total. This should be equal to 360.
Now all that remains it to draw the circle, mark off all the segments and divide the whole into its component parts.
If you have the skills in Excel you can carry out this operation very quickly. It is essential though that you know how to calculate the degrees of each part of the pie chart. How would you work it out if you didn't have a computer, after all?
Here's an example of pie charts being used to show the change in employment patterns in the UK economy over the period 1960 to 1990. Notice how clearly the chart indicates the structural changes that have occurred over this period.
In the reference section is the TimeWeb guide to Excel which gives some help on how to use Excel to create charts and graphs.
[Top]
Bar chart
The TimeWeb sample data provides numbers for the UK total resident population. Look for the annual data type DYAYAU. The figures for total population at decade intervals since 1959 are given below:
Year | Total UK Resident Population |
1959 | 51 956 000 |
1969 | 55 461 000 |
1979 | 56 240 000 |
1989 | 57 365 000 |
1999 | 59 501 000 |
We can chart this simply using Excel. There are still pitfalls to beware of and your Excel skills need to be well-practiced. Notice that the chart below is a very basic one, with no use of 3-dimensional effects. It is very often the case that the simpler the chart, the more effective is the impression given of the data involved. Notice too that the scale on the y-axis begins at zero. Try to see the different impression given if you allow Excel's chart wizard to set this scale automatically.
[Top]
Component bar charts
Let's continue with the example data drawn from the TimeWeb sample data, to demonstrate this chart. Male and female population figures are given in the annual data types BBABAU and BBACAU respectively. The table below contains enhanced data on the UK's population 1959 - 99.
UK Resident Population:
Year | Total | Male | Female |
1959 | 51 956 000 | 25 043 000 | 26 913 000 |
1969 | 55 461 000 | 26 908 000 | 28 553 000 |
1979 | 56 240 000 | 27 373 000 | 28 867 000 |
1989 | 57 365 000 | 27 988 000 | 29 377 000 |
1999 | 59 501 000 | 29 299 000 | 30 202 000 |
Notice that once again although Excel is a useful tool, you have to think about what information you provide by way of instructions. In particular, here, you don't need to input the total population figure - the male and female data is sufficient. If you try to include the total population data, Excel will add this to the male and female data. This would mean that the UK's population would be twice its actual level!
[Top]
Percentage component bar charts
You should make sure that you know how to convert the data from nominal into percentage form. You may not always be able to rely on Excel to calculate it for you!
There is more on Percentages in the 'digging' section if you are not sure how to calculate or interpret them.
[Top]
Compound bar chart
[Top]
Histograms
Here's a very simple example of how histograms are used to handle data.
Imagine that a medium-sized retailer, thinking of expanding into a new region, identifies a comparable business, that it considers as being ripe for takeover. It finds the following annual profit figures (in tens of thousands of pounds) for the target retailer's last ten years trading:
9 9 7 7 7 6 5 4 3 3
The predator company wants to convert this number series into a histogram.
To do this we can begin by drawing a horizontal line across the page to represent the range of values of all the numbers; then we can mark a 'x' above the appropriate value along the line as follows:
Every value in the original distribution is shown by an 'x' above the appropriate number. So there is one x for values 4, 5 and 6, because these values occur once in the distribution; two x's for 3 and 9, and three x's for 7.
This means that the frequency of any particular value is reflected in the height of the column of x's above that value.
We can see at a glance that 7 is the most frequent value in the distribution; this tells the company some vital information instantly, without having to scour lists of numbers.
Now imagine how much easier this would make it for a business to get a clear picture of hundreds of values in a data set, not just ten as in this case.
In practice, the frequency of the values in a distribution is represented with vertical blocks, not columns of x's. So the above data set would normally be illustrated as follows:
This diagram is the same as the x column chart earlier. But notice the extra touches: the horizontal line is still there showing the values in the data set, but now it has become the x axis of a traditional graph; there is now a vertical line, which is of course the y axis; as a result, you can tell from the height of the blocks the frequency of each value. The higher the block, the more frequent the value.
To summarise, we have looked at the basic principles of recording the frequency of values occurring in a distribution. The most common method of graphically representing a frequency distribution is by using a histogram.
The highest block in a histogram indicates the most frequent values. The lowest blocks show the least frequent values. Where there are no blocks, there are no results that correspond to those values. Blocks of equal height indicate that the values they represent occur in the same frequency.
Two standard characteristics of a histogram are also very important to understand and remember: the further to the right on the x axis that a block appears, the higher the value represented; the higher a column stands, the more frequent that value in the distribution.
The shape of the histogram is always determined by the data set that it represents. Now you should go to the worksheet section for activities on the basic reading of a histogram. If you practice this skill, you should soon be able to describe some important features of a distribution from just a quick inspection of its histogram.
There is a worksheet available on Translating a Histogram.
[Top]
Frequency Polygons
The histogram used for the predator company is shown below, with a frequency polygon for the same data superimposed.
[Top]
Ogives
Income Level (£ per month) |
No of People (frequency) |
Cumulative frequency |
>499 but <600 | 1 | 1 |
>599 but <700 | 3 | 4 |
>699 but <800 | 14 | 18 |
>799 but <900 | 26 | 44 |
>899 but <1000 | 9 | 53 |
>999 but <1100 | 5 | 58 |
Total = 58 |
Now, the ogive can be used to read-off 'less-than' figures. For instance, to find the number of people earning under £750, you just look up 750 on the x-axis and read off the corresponding value on the y-axis. This process is shown on the following chart.
In this case, approximately 28 people in our sample earn below £750 per month.
Ogives also prove useful when you want to find the median of a data set. For example, in our data on people's monthly incomes, there is a total of 58 observations. To be completely accurate you ought to calculate this using the formula: 1/2 (n + 1)th observation
This would mean the 1/2 * 59th = 29 1/2 th observation. The median for this series of data is clearly going to be approximately £760.
There is also a worksheet available on Ogives.
[Top]