Contents:

• Pictograms
• Pie charts
• Simple bar charts
• Component bar charts
• Percentage component bar charts
• Compound bar charts
• Other charts
• Frequency Polygons
• Frequency Curves

Pictograms:

Pictograms are simple diagrams that use pictures to convey number data.

The choice of picture depends on the type of variable being described.

For instance, if you were dealing with house sales data you might choose to use simple pictures of houses to represent the quantity of house selling at different times.

• Each house could represent 10 000 sales.
• The total number of sales, to the nearest 1000, in each region of the country, could be shown by whole or partial houses.
• The reader of the report would be able to see quickly how much activity there was in the housing market in different parts of the country.

You should always show the scale used in your pictogram.

As you can probably tell fractions or parts of whole numbers are difficult to show in a pictogram. But if you are trying accurately to show precise figures, then pictograms are unlikely to fit the bill. They are really good for giving a quick and rough idea of relative size.

There is more on Pictograms in the illustration section.

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Pie charts:

A pie chart is a good way of showing the constituent parts of a variable. It consists of a circle split into segments. The segments represent individual parts which, taken together, make up the total.

The 360^o circle is divided in proportion to the parts that make up the total.

There is more on Pie charts in the illustration section.

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Simple bar charts:

In a simple bar chart the figures used to make comparisons are represented by bars. These are either drawn vertically or horizontally. The height or length of the bar is drawn in proportion to the size of the figure being illustrated.

You can identify the figure that each bar represents within the bar itself, at the base of the bar, or you can use a key to show that a colour or shade indicates a particular item.

One of the most important points to remember when drawing even simple bar charts is that you must start the scale from zero. Making the scale suit your argument is one of the most common ways of using data to create an illusion.

There is more on Bar charts in the illustration section.

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Component bar charts:

When you want to draw a bar chart to illustrate your data, it is often the case that the totals of the figures can be broken down into parts or components.

You start by drawing a simple bar chart with the total figures as shown above. The columns or bars (depending on whether you draw the chart vertically or horizontally) are then divided into the component parts. Remember to put a key on the diagram.

There is more on Component bar charts in the illustration section.

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Percentage component bar charts:

If you want to know what proportion of a total each component represents, you could use a percentage component bar chart rather than a pie chart.

The method for this is the same as for a component bar chart, except that all the columns or rows of the chart are the same height or length, representing 100%. These are then divided up into the appropriate proportions.

There is more on Percentage component bar charts in the illustration section.

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Compound bar charts:

You may find that your data allows you to make comparisons of the component figures themselves. If so, you will want to create a compound bar chart.

This type of chart enables you to trace the trends of each individual component, as well as making comparisons between the components.

There is more on Compound bar charts in the illustration section.

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Other charts

With some types of dataset, knowing how to use pictograms, pie charts, bar charts, component and compound bar charts will be sufficient. But if the data to be illustrated are contained in a frequency distribution, then these earlier types of chart will be of limited use.

Frequency tables are constructed so that the reader can see what the spread of the data is. Sometimes this will be achieved, but for many people the table will only appear to be a jumble of numbers. In these cases we should use a simpler method of presentation. The three main commonly used ways to represent frequency tables pictorially are listed below:

• Histograms
• Frequency polygons and frequency curves
• Ogives or cumulative frequency curves

Histograms:

Explanation:

We have seen elsewhere in TimeWeb that when we are dealing with a list of numerical data, we can get an idea of central tendency from the data's mean, median and mode.

But, to understand a set of statistical data more clearly, we really need to know how the measured values are spread out from the central tendency.

This means that we should try to find out if the measured values in our data set are all clustered around the middle value, or if there are any very low and very high values.

So, the range and the various averages that we can calculate, tell us something, but they don't accurately describe the distribution of the values.

How the values are distributed is important; what we want to know about the distribution of a set of numbers is the frequency of the various results. The frequency means how many high values there are, how many values that equate to the average, how many low values are in the data set, and so on.

This concept of the distribution of a data set is very important. It's worth spending time to make sure you understand fully what it means:

Distribution refers to the way in which a set of numbers are scattered across a particular range. It may help you to think of the distribution as the pattern of values in your data set.

One of the most helpful ways to view this pattern is with a simple diagram which is known as a histogram. A histogram enables you immediately to see a distribution's particular shape or pattern. Histograms consist of a series of blocks or bars, each with an area proportional to the frequency. In a histogram the horizontal scale is used for the variable and the vertical scale to show the frequency.

There is more on Histograms in the illustration section.

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Frequency Polygons

As an alternative to using a histogram, you may be required to draw a frequency polygon. What this does is try to emphasise the 'shape' of the data. The simplest way to create a frequency polygon is to have drawn the histogram of the data already.To obtain the frequency polygon of the data, merely mark the mid-point of the top of each histogram column, and then join up the marks.

There is more on Frequency Polygons in the illustration section.

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Frequency Curves

The frequency polygon created in the above section displays very jagged lines. If you were using data for a histogram that had very small class intervals, and therefore many columns, (one for each class interval), then the marked points of the frequency polygon would be very much closer together. This would have a smoothing effect on the appearance of the polygon, one that if you continued to narrow the class intervals, would eventually produce a smooth curve.

Cumulative Frequency Curves (Ogives)

Often in your studies, or working in a business organisation, you may need to answer questions such as: 'How many fewer people pay tax on their incomes today than twenty years ago?' or 'How much of our factory's machine downtime lasts longer than 30 minutes?' If you are using a frequency distribution or a histogram, you would have to do some calculations to get to the answer. But if you were able to draw an ogive or cumulative frequency curve for your data, you could read off the answers straight away.

An ogive is drawn with the cumulative frequency total plotted against the upper limit of the relevant interval. This kind of diagram allows you to read off numbers below (or less than) a specified value. It's no surprise then that it is sometimes called a 'less-than ogive'.

There is more on Frequency Curves in the illustration section.

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