Mini Lesson 4 (Instruction)

Identify meaningful relationships using a scatter plot

Data Literacy Project

Do light cars go farther on a gallon of gas than heavy cars do?

Background: Miles per gallon (mpg) is one way of measuring the fuel-efficiency of a car or truck.

A car with high mpg goes more miles on one gallon of gas than a car with low mpg does. It costs less to run and releases less CO2 into the atmosphere.

The US Environmental Protection Agency (EPA) rates the fuel efficiency (mpg) of every car model sold in the US.

An interesting question: Do lighter cars go farther on a gallon of gas than heavier cars do?

In other words:

Is fuel efficiency (mpg) correlated with vehicle weight?

Here are some data about 15 different 2011car models.

To see if mileage rating is correlated with vehicle weight, you can plot the two values for each car on a graph with two axes.

Draw two axes.

Each of the two variables gets an axis.

For now, lets give Vehicle weight the X axis and EPA mileage rating the Y axis

Vehicle weight (lbs)

EP

A m

ileag

e ra

ting

(mpg

)

Put a scale on each axis using the range of points for each variable in the data set.

(The scale doesn’t have to start at 0)

Put a point for each car in the space on the graph where the two values intersect.

5527

18

All of the points are plotted

Chevy suburban

Corvette

Each car is represented by one dot

Do heavier cars generally have lower mileage?OR

Do heavier cars tend to have higher mileage?OR

Is there no correlation between mileage and weight?

Does there seem to be a correlation between mileage rating and vehicle weight?

Draw a line that goes near most of the points.(This is called the “Line of best fit”)

For practice: 1. Is lung cancer rate correlated with smoking rate? 2. Is melanoma (skin cancer) rate correlated with smoking rate?

Strong positive correlation No correlation

The higher the smoking rate, the higher incidence of lung cancer

The points don’t fall close to a line. Skin cancer seems unrelated to smoking rates.

The arrangement of the points shows • How strong the correlation is • Whether the correlation is positive or negative

________________

Positive correlation: one variable is HIGH and the other is also HIGH

“The water temperatures at high and low tides are positively correlated”

Wat

er t

empe

ratu

re a

t lo

w t

ide

Water temperature at high tide

Negative correlation: one variable is HIGH and the other is LOW

The maximum wind speed of a hurricane is negatively correlated with its minimum barometric pressure.

Minimum barometric pressure

Max

imum

win

d sp

eed

Hurricanes

No correlation: Data points are scattered and don’t form an obvious line.

The rate of skin cancer (melanoma) is not correlated with smoking rate.