DESCRIBING THE CORRELATION OF A SCATTER GRAPH

Correlation is a statistical measure that indicated the extent to which two or more variables fluctuate in relation to each other.

Positive correlation : 

A positive correlation would be 1. This means the two variables moved either up or down in the same direction together.

Negative correlation:

A negative correlation is -1. This means the two variables moved in opposite directions.

Zero or no correlation :

A correlation of zero means there is no relationship between the two variables. In other words, as one variable moves one way, the other moved in another unrelated direction.

Problem 1 :

Ms. Thomas wanted to know if the amount of class time that he gave students to study affected their test scores. The scatter plot below shows the result.

What kind of relationship between class study time and test scores is shown in the scatterplot?

a) no correlation                b)  Positive correlation

c)  negative correlation

d)  positive than negative correlation 

Solution :

By drawing the line of best fit, we will get a raising line. So it is positive correlation.

Problem 2 :

The following scatterplot shows the weight and lengths of some dinosaurs.

Which statement accurately describes the information in the scatter plot ?

a)  The information shows a positive correlation. The weight f a dinosaur tends to increase according to its length.

b)  The information shows a negative correlation. The weight of a dinosaur tends to decrease according to its length.

c)  The information shows no correlation. The weight and length vary according to the type of dinosaur.

d)  The information shows no correlation. The relationship between the weight and length of a dinosaur is uncertain.

Solution :

x-coordinate ==> Length of dinosaur in feet

y-coordinate ==> Weight of dinosaur in tons

As length of dinosaur is increasing weight is also increasing. So, option a is correct.

Problem 3 :

The scatterplot shows the number of absences in a week for classes of different sizes. Trevor concluded that there is a positive correlation between class size and the number of absences.

Which statement best describes why Trevor's conclusion was incorrect ?

a)  The largest class does not have the most absences.

b)  The smallest class does not have the least number of absences.

c)  The data show no relationship between class size and the number of absences.

d) The data show a negative relationship between class size and number of absences.

Solution :

Option b:

When the class size is 15, the number of absences is 2 or 10. 

Option c :

There is a relationship.

Option d :

There is a positive relationship.

Option a : 

The largest class (40) has 10 absences. So, option a is correct.

Problem 4 :

Which data will most likely to show a negative correlation when graphed on a scatterplot

a) the outside temperature and the number of people wearing gloves.

b) the distance a student lives from school and the amount of time it takes to get to school.

c) the number of visitors at an amusement park and the length of the lines for the rides.

d)  a student's height and grade point average.

Solution :

Negative correlation means changes should happen in opposite direction.

Option a :

If temperature decrease outside, then number of people wearing gloves will increase, because of cold.

So, option a is correct.

Problem 5 :

This scatterplot could show the relationship between which two variables ?

a) speed of an airplane (x) vs distance traveled in one hour (y)

b)  outside air temperature (x) vs air conditioning cost (y)

c)  age of an adult (x) vs height of an adult (y)

d)  distance traveled (x) vs gas remaining in the tank (y)

Solution :

The given scatterplot represents the negative correlation. While covering the long distance, fuel expenses will be more. So, option d is correct.