B. Global Inequalities: Economic Development and Quality of Life · Global Inequalities: Economic Development and Quality of Life

Scatter Graphs: Finding Relationships in Development Data

B3.3 B2.4About 50 minutes

Learning goals

I can construct a scatter graph on paper and with a graphing program.
I can describe a relationship as positive, negative or no relationship, and spot outliers.
I can draw a line of best fit and use it to make an estimate.
I can explain why a relationship between two indicators does not prove that one causes the other.

Words to know

scatter graph
A graph of points that shows whether two sets of numbers are related. Each point is one case, such as one country.

independent variable
The variable we think might influence the other one. It usually goes on the horizontal (x) axis.

dependent variable
The variable that might be affected. It usually goes on the vertical (y) axis.

positive relationship
As one variable increases, the other tends to increase. The points rise from left to right.

negative relationship
As one variable increases, the other tends to decrease. The points fall from left to right.

outlier
A point that is far away from the pattern of the others.

line of best fit
A straight line drawn through the middle of the points to show the general trend.

correlation
A relationship between two variables. Correlation does not prove causation.

Hook: do richer countries live longer?

If you lined up every country by income and by life expectancy, would you see a pattern? A scatter graph lets you see the answer at a glance. Geographers use scatter graphs to explore links between indicators, such as income and health, or clean water and infant deaths.

How to construct a scatter graph

Decide which variable is independent (x-axis) and which is dependent (y-axis). If you think income affects life expectancy, put income on the x-axis.
Choose a scale for each axis that fits the smallest and largest values. Mark equal spaces. You do not have to start the y-axis at 0, but if you don't, say so.
Label both axes with the variable and the unit. Give the graph a title and a source.
Plot one point for each case. Do not join the dots.
Look for the pattern and draw a line of best fit if the points form a line-like trend: about half the points above and half below.

Country (fictional)	GDP per capita (thousands of US$)	Life expectancy (years)
A	1	58
B	2	64
C	4	68
D	8	72
E	15	76
F	30	80
G	45	82
H	60	83

A practice data set. The countries are fictional, but the shape of the pattern is similar to what real world data show.

Scatter graph of the practice data. Each dot is one fictional country. Life expectancy rises quickly as income grows from very low levels, then levels off.

Reading the pattern

Positive relationship: points go up from left to right (income and life expectancy).
Negative relationship: points go down from left to right (access to safe water and infant mortality: more water access, fewer infant deaths).
No relationship: points are scattered with no trend.
Strong if points are close to a line; weak if they are spread out.
Some patterns are curved. In the graph above, life expectancy rises fast at low incomes and then levels off. A little more income helps a lot when people cannot afford food or medicine, but adds less once basic needs are met.

The three kinds of relationship. The dashed line of best fit shows the trend; with no relationship, there is no sensible line to draw.

Correlation is not causation

Two indicators can move together without one causing the other. Richer countries have longer lives partly because money pays for hospitals, food and clean water. But both might also be linked to a third factor, such as education or a stable government. A scatter graph shows a relationship. You need more evidence to explain why.

Just for fun

A real 2012 article in the New England Journal of Medicine showed that countries that eat more chocolate per person also tend to have more Nobel Prize winners per person. Sadly, eating a chocolate bar before your test will not win you a Nobel Prize. Correlation is not causation!

Worked example

Let's read a scatter graph

Use the graph above. Describe the relationship and estimate the life expectancy of a fictional country with a GDP per capita of $20 000.

Direction: the points go up from left to right, so the relationship is positive.
Shape: the rise is steep from A to D and flattens after F, so the pattern is curved.
Estimate: $20 000 is between E ($15 000, 76 years) and F ($30 000, 80 years), closer to E. Reading along the trend gives about 77 years.
Caution: this is an estimate from the trend; a real country could be above or below it.

A positive, curved relationship. A country at $20 000 would be expected to have a life expectancy of about 77 years.

Worked example

Let's make one with a graphing program

How do you build the same graph in a spreadsheet such as Google Sheets or Microsoft Excel?

Type the data into two columns: GDP per capita in column A, life expectancy in column B. Put headings in row 1.
Select both columns, then choose Insert → Chart and pick Scatter.
Add a chart title, axis titles with units, and the source.
In the chart options, add a trendline (line of best fit). Many programs can also fit a curved trendline.

A digital scatter graph is quick to change and easy to update when new data come out.

Hands-on activity

Height and arm span scatter graph

You need: a tape measure, paper or graph paper, a pencil, and 6 to 10 family members, friends or neighbours (ask permission to measure them).

Measure each person's height and arm span (fingertip to fingertip with arms stretched out) in centimetres.
Put height on the x-axis and arm span on the y-axis. Choose scales that fit your numbers.
Plot one point per person and draw a line of best fit.
Describe the relationship (positive, negative or none; strong or weak). Are there outliers?
Bonus: make the same graph in a spreadsheet and compare.

What to look for: most people's arm span is close to their height, so you should see a strong positive relationship. Then think: what development indicators might show a similar pattern?

Your turn

Which variable usually goes on the x-axis?

Describe the relationship you would expect between access to safe drinking water and infant mortality.

In the practice graph, which country is the poorest, and what is its life expectancy?

What is an outlier?

Why should you not join the dots on a scatter graph?

Two indicators show a strong positive relationship. Does that prove one causes the other? Explain.

Using the practice graph, estimate life expectancy for a country with GDP per capita of $6 000.

More practice: warm-up

Points that fall from left to right show a ___ relationship.

What does each dot represent in a scatter graph of countries?

What must every axis have?

What is a line of best fit?

Points scattered everywhere with no trend show ___ relationship.

More practice: on your own

Fictional data: % with safe water and infant mortality (per 1 000): P 40%, 85; Q 55%, 70; R 60%, 60; S 75%, 45; T 85%, 30; U 90%, 20; V 98%, 8; W 100%, 4. Which axis gets which variable, and what relationship do you see?

Using the same data, estimate infant mortality for a country with 80% safe water access.

A country with 90% safe water access has an infant mortality of 70. Is it an outlier? What might explain it?

Explain why the income and life expectancy pattern levels off at high incomes.

Name two advantages of using a graphing program instead of paper.

Challenge

Suggest a third factor that might explain why both literacy and life expectancy are higher in some countries.

You plot 150 countries: x = number of mobile phones per 100 people, y = life expectancy. You find a positive relationship. Write a careful conclusion.

Why might a geographer use a curved trendline instead of a straight line for income and life expectancy? What would a straight line get wrong?

Check your understanding

Quiz

In a scatter graph, what does a negative relationship look like?

Which variable should go on the y-axis if you think water access affects infant mortality?

What is a line of best fit?

A strong positive relationship between two indicators shows that…

A point far from all the others is called…

In the practice graph, which is the best estimate of life expectancy at $20 000 GDP per capita?

For parents and teachers

What this lesson is about: scatter graphs (Ontario curriculum B3.3) to explore relationships between development indicators, plus interpreting data (B2.4).

How to help at home:

The arm span activity is a fun way to make a real scatter graph. Help measure carefully.
If you have a spreadsheet program, let your child build the chart and add a trendline.
Ask "Does that prove one causes the other?" whenever you see a statistic in the news.

Common difficulties:

Joining the dots like a line graph.
Uneven axis scales.
Saying one variable causes the other just because they are related.