If you ask me which tool, out of the seven basic tools of quality, appears most difficult to understand, my answer would be the scatter diagram.

Did you notice that I asked, “Which tool appears most difficult”?

I did not ask which tool is difficult to understand, difficult to draw, or difficult to interpret.

Other charts use lines or bars to show findings, while a scatter diagram uses only dots. This is why this graph looks a bit different. However, this chart is just as easy to understand as line and bar charts.

I hope, after reading this blog post, you will not face any problems in understanding the scatter diagram.

Okay, let’s get started.

### Scatter Diagram

The scatter diagram is known by many names, such as scatter plot, scatter graph, and correlation chart. This diagram is drawn with two variables, usually the first variable is independent and the second variable is dependent on the first variable.

The scatter diagram is used to find the correlation between these two variables. This diagram helps you determine how closely the two variables are related. After determining the correlation between the variables, you can then predict the behavior of the dependent variable based on the measure of the independent variable. This chart is very useful when one variable is easy to measure and the other is not.

**Example**

You are analyzing the pattern of accidents on a highway. You select the two variables: motor speed and number of accidents, and draw the diagram.

Once the diagram is completed, you notice that as the speed of vehicle increases, the number of accidents also goes up. This shows that there is a relationship between the speed of vehicles and accidents happening on the highway.

According to the PMBOK Guide 5th edition, the scatter diagram is, “A correlation chart that uses a regression line to explain or to predict how the change in an independent variable will change a dependent variable.”

The PMBOK Guide states that scatter diagram helps you see the changes in the dependent variable if you make any change to the independent variable. Since this diagram shows you the correlation between the variables, it is also known as a correlation chart.

Usually the independent variable is plotted along the horizontal axis (x-axis) and the dependent variable is plotted on the vertical axis (y-axis). The independent variable is also known as the control parameter because it influences the behavior of the dependent variable.

It is not necessary for one parameter to be a controlling parameter. You can draw the scatter diagram with both variables independent to each other. In this case you can draw any variable on any axis.

Please note that the scatter diagram is different than the Ishikawa or fishbone diagram. With the Ishikawa diagram you see the effect of a cause, and in the scatter diagram you analyze the relationship between the two variables.

### Type of Scatter Diagram

The scatter diagram can be categorized into several types; however, I will discuss the two types that will cover most scatter diagrams used in project management. The first type is based on the type of correlation, and the second type is based on the slope of trend.

I am giving you two types because it will show you the same chart with two different perspectives, this will help you build a solid understanding regarding the scatter diagram.

According to the type of correlation, scatter diagrams can be divided into following categories:

- Scatter Diagram with No Correlation
- Scatter Diagram with Moderate Correlation
- Scatter Diagram with Strong Correlation

#### Scatter Diagram with No Correlation

This type of diagram is also known as “Scatter Diagram with Zero Degree of Correlation”.

In this type of scatter diagram, data points are spread so randomly that you cannot draw any line through them.

In this case you can say that there is no relation between these two variables.

#### Scatter Diagram with Moderate Correlation

This type of diagram is also known as “Scatter Diagram with Low Degree of Correlation”.

Here, the data points are little closer together and you can feel that some kind of relation exists between these two variables.

#### Scatter Diagram with Strong Correlation

This type of diagram is also known as “Scatter Diagram with High Degree of Correlation”.

In this diagram, data points are grouped very close to each other such that you can draw a line by following their pattern.

In this case you will say that the variables are closely related to each other.

As discussed earlier, you can also divide the scatter diagram according to the slope, or trend, of the data points:

- Scatter Diagram with Strong Positive Correlation
- Scatter Diagram with Weak Positive Correlation
- Scatter Diagram with Strong Negative Correlation
- Scatter Diagram with Weak Negative Correlation
- Scatter Diagram with Weakest (or no) Correlation

Strong positive correlation means there is a clearly visible upward trend from left to right; a strong negative correlation means there is a clearly visible downward trend from left to right. A weak correlation means the trend, up of down, is less clear. A flat line from left to right is the weakest correlation, as it is neither positive nor negative and indicates the independent variable does not affect the dependent variable.

#### Scatter Diagram with Strong Positive Correlation

This type of diagram is also known as Scatter Diagram with Positive Slant.

In positive slant, the correlation will be positive, i.e. as the value of x increases, the value of y will also increase. You can say that the slope of straight line drawn along the data points will go up. The pattern will resemble the straight line.

For example, if the temperature goes up, cold drink sales will also go up.

#### Scatter Diagram with Weak Positive Correlation

Here as the value of x increases the value of y will also tend to increase, but the pattern will not closely resemble a straight line.

#### Scatter Diagram with Strong Negative Correlation

This type of diagram is also known as Scatter Diagram with Negative Slant.

In negative slant, the correlation will be negative, i.e. as the value of x increases, the value of y will decrease. The slope of a straight line drawn along the data points will go down.

For example, if the temperature goes up, sales of winter coats goes down.

#### Scatter Diagram with Weak Negative Correlation

Here as the value of x increases the value of y will tend to decrease, but the pattern will not be as well defined.

#### Scatter Diagram with no Correlation

In this type of chart, you are not able to see any kind of relationship between the two variables. It might just be a series of points with no visible trend, or it might simply be a straight, flat row of points. In either case, the independent variable has no effect on the second variable (it is not dependent).

### Limitations of a Scatter Diagram

The following are a few limitations of a scatter diagram:

- Scatter diagrams are unable to give you the exact extent of correlation.
- Scatter diagram does not show you the quantitative measure of the relationship between the variable. It only shows the quantitative expression of the quantitative change.
- This chart does not show you the relationship for more than two variables.

### Benefits of a Scatter Diagram

The following are a few advantages of a scatter diagram:

- It shows the relationship between two variables.
- It is the best method to show you a non-linear pattern.
- The range of data flow, i.e. maximum and minimum value, can be easily determined.
- Observation and reading is straightforward.
- Plotting the diagram is relatively simple.

### Summary

Scatter diagrams are very useful to determine the relation between two variables. Usually the first variable is independent and the second is dependent on the first variable. To analyze the pattern of the relationship, you make changes to the independent variable and monitor the changes in the dependent variable.

Please keep in mind that the scatter diagram is different than the Ishikawa diagram. The Ishikawa diagram shows you only the variables; it does not show you the relationship between these variables. However, the Ishikawa diagram can help you draw the scatter diagram; for example, you can find the two variables (cause and effect), and then draw the scatter diagram to analyze the relationship between them.

Here is where this blog post on the scatter diagram ends. If you have something to share or any questoins, you can do so through the comments section.

Vijay says

Thanks for the good article.

pls note that there’s one typo, it should be “dependent” variable is plotted on the vertical axis (y-axis).

“Usually independent variable is plotted along the horizontal axis (x-axis) and independent variable is plotted on the vertical axis (y-axis) “

Fahad Usmani says

Thanks for your comment Vijay.

Error is corrected.

Bijoy Ghosh says

Good article. Thanks a lot.

Fahad Usmani says

You are welcome Bijoy.

muhsin al-kazy says

thank you.. Really i am understood very well .Mnay thanks for you.

Fahad Usmani says

You are welcome Muhsin.

Mark says

The first variable is independent and the second is dependent in the first variable

Fahad Usmani says

Correct.

Sp says

Asalaam-o-alaikum !

The way you explain every topic is marvelous. Thank you.

Could you please explain Resource optimization techniques and Influence diagram.

Fahad Usmani says

Okay.

I have noted it, and soon you will see a post on this topic.

Raj says

Very good article and very clear explanation. Really appreciate the effort.

Fahad Usmani says

Thanks Raj.

Trapti says

I didnt understand the exact diff b/w two types of scatter diagrams: type of correlation ans slope of trend coz both the types are showing the same thing. Pls throw some light on my confusion.

Fahad Usmani says

Notice the spread of dots. It shows how closely they are related.

Bilshan says

I’ve really enjoyed the explanation you made above. Thank you

Fahad Usmani says

You are welcome Bilshan.

Ritika says

Thanks Fahad. I have been going through all your posts and they are indeed very helpful.

Please keep helping PMP Aspirants like me with your blogs.

Thanks once again!!!

Fahad Usmani says

You are welcome Ritika.

mike says

thank you very much. so usefull

Fahad Usmani says

You are welcome Mike.

muhsin al-kazy says

Hi

please could you explain what are diffrents between risk audit and risk assessment in control risk .

Thank you

Fahad Usmani says

Risk Assessment: Here you assess the current risks if they are still valid or can be closed if outdated.

Risk Audit: It deals with effectiveness of risk responses as well as the effectiveness of the risk management process.

Zafar Iqbal says

Thanks really good explanation.

May you please explain “Decision tree”?

Thanks again

Fahad Usmani says

Sure, soon I will write a blog post on it.

Arshley Mun Van says

Thank you’re the best ?

Fahad Usmani says

Thanks Arshley for your comment.

Hermenegildo Lemos says

Thank you it was usefull for me .

Fahad Usmani says

You are welcome Hermenegildo.