Pareto charts - overview

The following issues are discussed below:

1. The problem being addressed.

2. The parts of a Pareto Chart.

3. Example.

5. Drawing using Excel.

6. The Pareto Principle.

The problem:

When analysing situations, it is often important to analyse the most important factors in a particular sutuation. For example:

which parts of a business return the greatest revenue?
what are the most common problems identified by consumers in relation to a particular type of produce (eg computers, kitchen scales, accessing information on a website, etc)
what model car or TV or maths topic is the most favoured?
what is the most common health condition?
what are the most significant items on which a person spends money?

A Pareto chart was developed to assist in quality control. It is a technique used to display data measured on a nominal scale (so categories).

The purpose of the Pareto chart is to highlight the most important among a reasonaby large set of characteristics.

The parts of a Pareto Chart?

The Pareto Chart uses a combination of bars and line graphs.

The bars indicate the frequency for each characteristic and they are arranged from left to right in descending order of frequency.
The higher the bar, the more of the characteristic that bar accounts for.
The names of each characteristic are written at the base of each bar.
The left (vertical) axis has a scale indicating the frequency for each bar. The values could be some other relevant characteristic such as time or cost.
The lines extending from left to right across the chart trace the increasing values of the cumulative frequency across the bars.
The right (vertical) axis has a scale indicating the increasing percentage of the total number of observations as more bars (i.e. characteristics) are included in the total.

The following chart shows these characteristics:

Drawing a Pareto chart by hand.

Action by step:

1. Collect the data by category and frequency or value, etc. into a table with three columns.

2. List the categories down Column 1.

3. Record the corresponding frequencies for each category down column 2.

4. Reorder Columns 1 and 2 so that the highest frequency is in the top row and the lowest frequency is in the bottom row.

5. In the third column, record the cumulative frequencies by adding successive frequencies using the re-ordered values in Column 2.

6. Draw a normal histogram of the frequencies for each of the ordered categories using an axis at the left of the graph.

7. Draw a line graph of the cumulative frequencies of the ordered categories using an axis at the right of the graph whose scale finishes at the total number of observations across all categories.
As with the usual ogive for cumulative frequency graphs, the point marked is in line with the right side of each column.

Drawing a Pareto chart using Excel.

The Pareto Principle.

Pareto Charts are often used in business situations especially for quality control. That use has led to the commonly cited observation that "80% of a situation can be attributed to 20% of the group". Pareto himself, for example, concluded that 80% of the land in Italy was owned by 20% of the population.

There are many similar conclusions in various contexts. For example:

many natural phenomena have been shown to exhibit such a distribution;
there are also many examples in Physics and Chemistry;
in sport, many trainers believe that 20% of exercises and habits produce 80% of the required impact. Hence these trainers recommend their athletes should reduce the variety of training exercises and just focus on the basic 20% effective exercises;
in health care, many areas and indeed countries accept the principle that about 20% of patients account for 80% of the health care resources;
in computing, programmers and systems analysts use the rule that 80% of the bugs in a network are contained in 20% of the programmable modules. Using that as a guide, testing times and attention can be made more efficient and effective.

With another view, the Pareto Principle can be viewed as the degree of inequality in a system. For example 80% of the decisions by a Government might be made through consultation with 20% of parliamentary members.

Income distribution is commonly measured by a Gini Coefficient. The closer to 100% in its value, the more inequity in a population.