Pie Charts and Pictograms


Introduction

Required Prior Knowledge : Percentages

Pie Charts are circles, sliced into sectors whose areas represent the proportion of a quantity to the whole.

Of the 130 000 people who graduated between 1973 and 1993, about one-third had less than the minimum entry requirements for a traditional University. This pie chart shows that in 1995 nearly half of new OU undergraduates had either no educational qualifcations ("low") or 1 A-Level or less ('lowish')

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Drawing up a Pie Chart

The areas of a pie chart are not calculated directly. We actually need to calculate the sector (or wedge) angles, remembering that a full circle encompasses 360 degrees.

Work out the proportions as follows:

  1. For each category, state this category as a fraction of the whole

  2. Multiply this fraction by by 360 to calculate the required angle of the sector (or wedge)

  3. Decide on the size of the circle to use and where to start with the first category.

  4. Draw in the sectors using a protractor to measure the angles between the sectors.


Example

If the category represents 1/5

1/5 of 360

= 1/5 × 360

= 72 degrees


Background Knowledge If percentages are required, then you multiply each fraction by 100. If you need some revision in this topic, click here

A full circle will consist of 360 degrees. Therefore 1% on a pie chart will be represented by 3.6 degrees.

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General Guidelines

Guidelines

  • Use a small number of categories. If you have more than six, try to combine categories, and if this can't be done efficiently, consider another way of presenting your data. Here is an example of a bar chart with many categories - do you think the information could have been presented in a better way ?

    Women who have climbed Everest, by nationality

  • Label categories directly and add percentages, if required. Avoid using a key if possible.

  • For comparison pie charts: where the totals of the pie charts differ, draw them so that their areas give some indication of these differences. Keep equivalent segments in a similar place (in other words, work consistently around each pie either clockwise or counter-clockwise, starting with the same category in the same place). If there are more than three pie charts to compare, think about using stacked bar charts instead.

    Composition of Atmospheres

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Words of Caution

Some opinions from Illinois University. For example :-

Two chart types that should always be avoided.

Two common charts easily produced by spreadsheet programs that should almost always be avoided are the stacked bar chart and the pie chart.

Pie charts are fun to look at, but generally involve using a great deal of ink to display very little data. In addition, the charts often make it difficult to discern the exact magnitude of the size of the pie slices. Using multiple pie charts to display more than one variable is also a bad idea. All this is made even worse by exploiting the power of the spreadsheet technology to produce 3-D pie charts and "exploding" 3-D pie charts. If you think that you really must use a pie chart, make sure it is for data that does indeed at up to a total (i.e., the percentages for the slices add up to 100) and stay away from the fancy stuff.

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Pictograms

Pictograms are fairly straightforward - go to this site from Exeter University for details.

There is a slight rider about pictorial representations being used wrongly and distorting the data - go to this site for further details.

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Past Exam Questions


Which pie chart shows the results in this table?


(The images below haven't reproduced very well)


A survey was carried out as part of a catering course, to find out what 40 people ate in the canteen on 2 days of one week.


1. Which 2 items were more popular on Tuesday than on Thursday?

  • A    Chicken and Chips
  • B    Pizza and Chilli
  • C    Pizza and Sausage
  • D    Chicken and Chilli

2. The sector that represents Chips on Thursday is 90. How many people does this represent?

  • A    90
  • B    40
  • C    36
  • D    10


This chart shows the ages of the voters in a local election

1. The pie chart shows that

  • A    most of the voters are in the 21-40 age group
  • B    the smallest group of voters is the 65+ age group
  • C    most of the voters are in the under-21 age group
  • D    about half the voters are in the 41-64 age group

2. The pie chart shows that the percentage of voters in the 21-40 age group is approximately

  • A    20%
  • B    50%
  • C    70%
  • D    90%

3.     54 000 people voted in the local election. 4 500 of these were under-21. What is the angle of the pie chart for this group ?

  • A    30 degrees
  • B    35 degrees
  • C    40 degrees
  • D    45 degrees

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