7.05 Stacked area graphs, Radar graphs and Pareto charts

Radar graphs

A radar chart is a graphical method of displaying multivariate data (e.g. different features of an item, time periods etc). These graphs look a bit like spider webs, with each variable represented by spokes (called radii) starting from the same point and spread out in a circle. 

A line is drawn connecting the data values for each radii so it looks like a star. This helps us identify the frequency of each observations and whether there are any outliers.

 

Worked example 

Example 1

The annual sales per $1000$1000 units of two products are shown in the following radar chart.

a) How many units of Product B were sold in November?

Think: Where is the Product B's red dot for November on the graph?

Do: The red dot for November is on the $6$6, which means $6000$6000 units of Product B were sold in November

 

b) How many more units of Product A were sold in June than Product B?

Think: This time we're going to look at the difference between the blue dot and red dot for the June spoke.

Do: The blue dot is on the $10$10 and the red dot is on the $3$3, this is a difference of $7$7, so $7000$7000 more units of Product A were sold in June than Product B.

 

Practice question

Question 1

 

 

Pareto charts

A Pareto chart is used to identify the most significant factors in a set of categorical data. The chart combines a column graph and a line graph, and has two vertical axes, one for each graph type.

• The columns represent the frequency for each category, or factor in a process, but could also represent cost, or some other unit of measurement. The columns are arranged in descending order, from tallest on the left to shortest on the right (i.e. most significant to least significant). The value for each column is read from the left vertical axis.
   
• The line graph or polygon represents the cumulative percentage of the values for each column. It always curves upwards, but decreases in steepness, from left to right. The value of any point on the line graph is read from the right vertical axis.

Below is a Pareto chart showing some of the common reasons for failing a driving test. 

We can see from the chart above that the most common reasons for failing a driving test are:

• Observations at intersections (not checking for traffic carefully in all directions)
• Use of mirrors (not using the cars mirrors to check the position of other vehicles)

If we draw a line from the $80%$80% mark on the right vertical axis to the line graph, and then continue that line down to the horizontal axis, the most important factors appear on the left of the line. In this case, it is the first two factors (represented by the first two points on line graph) that contribute to the majority of driving test failures. One could argue that the third factor, 'inappropriate speed' is also significant, due its closeness to the $80%$80% mark. 

Pareto charts are based on something called the Pareto principle, which says that around $80%$80% of problems in a process tend to come from only $20%$20% of factors. While these percentages are only a guide, they are common enough to be called the $80$80/$20$20 rule.

Process improvement teams often use Pareto charts to determine which factors in a process are causing the most problems, so they can focus their efforts on those. This is an important part of quality control, often used to improve customer service or reduce the number of defects in a product.
 

Practice question

Question 2

Stacked area graphs

Stacked area graphs are similar to line graphs in that they both display data that changes over time. However, while a line graph shows how one variable changes over time (e.g. a product's sales figures from a particular shop), a stacked area graph is used to show changes in several variables that make up the total in the data being graphed (e.g. total sales figures across several stores in a chain). A stacked area chart shows how much each part contributes to the whole amount. 

The area between axes and lines are commonly emphasised with different colours or patterns.  

For example, the area chart below displays the total revenue made by a business across three products. The difference between the lines indicates the amount of revenue made by each product. For example, in the fourth month, Product B made $\$3000$$3000 ($\$9000-\$6000$$9000−$6000 ).

 

Worked example

Example 2

The revenues generated in thousands for a company from their four major products are shown in the area chart above.

a) What was the monthly revenue generated by Product A in April?

Think: For the product at the bottom of the graph we need to just read the value of the line in April.

Do: In April, the line for Product A sits at $100$100. Hence, Product A produced $\$100000$$100000 revenue in April.

 

b) What was the monthly revenue generated by Product C in May?

Think: We need to find the difference between the upper and lower lines for Product C in May.

Do: The top line for Product C sits at $450$450 and the bottom line sits on $300$300. As the difference is $150$150, Product C generated $\$150000$$150000 revenue in May.

c) What percentage of the revenue in May was made by product C?

Think: We need to calculate the fraction of the revenue that Product C generated out of the total revenue in May and write this as a percentage.

Do: From part b) we have that Product C generated $\$150000$$150000 in revenue. Reading the top of the graph will give us the total revenue across the $4$4 products, hence, the total revenue in May is $\$550000$$550000.

$\text{Percentage revenue Product C in May}$Percentage revenue Product C in May	$=$=	$\frac{\text{Revenue for Product C}}{\text{Total revenue}}\times100%$Revenue for Product CTotal revenue​×100%
	$=$=	$\frac{150000}{550000}\times100%$150000550000​×100%
	$\approx$≈	$27.3%$27.3%

Practice question

Question 3