State whether the following graphs show a positive correlation, a negative correlation, or neither:
State whether the following graphs show a linear or non-linear correlation:
Identify the type of correlation in the following scatter plots, as either:
Strong negative correlation
Weak negative correlation
No correlation
Weak positive correlation
Strong positive correlation
Identify the type of relationship represented by the following scatter plots, as either:
Positive linear
Negative linear
No relationship
Identify the type of relationship in the following scatter plots as either:
Strong positive linear
No relationship
Weak positive linear
Weak negative linear
Strong negative linear
For each pair of variables, state whether their relationship would have a positive or negative correlation:
Time spent studying and exam performance.
Rainfall and traffic accidents.
Height and weight.
Temperature and ice cream sales.
Describe the relationship between the variables in the following scatter plots:
Yvonne has a high income but does not like her job. Which dot in the graph would represent her?
Scientists conducted a study where each person was asked to read a paragraph and then recount as much information as they can remember. They found that the longer the paragraph, the less information each person could retain.
Is the correlation between the length of the paragraph and the information retained, positive or negative?
A database compare the income per capita of a country and the child mortality rate of that country. A sample of the data is shown in the table.
If a scatter plot was created from the entire database, describe the relationship you would expect it to have in terms of strength, direction and shape.
| Income per capita | Child Mortality rate |
|---|---|
| 1465 | 67 |
| 11\,428 | 16 |
| 2621 | 35 |
| 32\,468 | 9 |
After a mathematics exam, Lachlan commented that he left out Question 10 because it was not relevant to the topics that were assessed, but that the other questions were fine. The teacher felt that Question 10 and Question 7 were assessing the same skills, so she decided to look at the results of students across all 8 classes. She plotted the percentage who had gotten Question 10 correct against the percentage who had gotten Question 7 correct as shown below:
According to the graph, who is correct: Lachlan or the teacher?
Let's assume that Lachlan performed exceptionally well in every other question. If a whole class of students had the same result as Lachlan, in which region would this class’s results appear on the scatter plot?
The following table shows the number of traffic accidents associated with a sample of drivers in different age groups:
| Age | 20 | 25 | 30 | 35 | 40 | 45 | 50 | 55 | 60 | 65 |
|---|---|---|---|---|---|---|---|---|---|---|
| Accidents | 41 | 44 | 39 | 34 | 30 | 25 | 22 | 18 | 19 | 17 |
Graph this data on a scatter plot.
Describe the correlation between a person's age and the number of accidents they are involved in, as positive or negative.
Describe the correlation between a person's age and the number of accidents they are involved in, as strong or weak.
Is there an outlier in this data set?
The following table shows the average IQ of a random group of people against their height:
| Height (cm) | 140 | 145 | 150 | 155 | 160 | 165 | 170 | 175 | 180 | 185 |
|---|---|---|---|---|---|---|---|---|---|---|
| IQ | 103 | 95 | 98 | 111 | 85 | 89 | 108 | 145 | 110 | 93 |
Use the graphing facility of your CAS calculator to graph this data on a scatter plot.
Is there a correlation between IQ and height?
Which point on the scatter plot represents an outlier?
The marks of twelve students in Maths and Art were recorded in the following table:
Use the graphing facility of your CAS calculator to graph this data on a scatter plot.
Describe the correlation between students' marks in Maths and Art as positive or negative.
Describe the correlation between students' marks in Maths and Art as strong or weak.
Which student's marks represent an outlier on the scatter plot?
| Student | Maths Mark | Art Mark |
|---|---|---|
| 1 | 63 | 44 |
| 2 | 92 | 74 |
| 3 | 60 | 52 |
| 4 | 79 | 70 |
| 5 | 88 | 67 |
| 6 | 81 | 60 |
| 7 | 61 | 73 |
| 8 | 91 | 86 |
| 9 | 72 | 84 |
| 10 | 42 | 93 |
| 11 | 66 | 57 |
| 12 | 92 | 92 |
A study was conducted to compare running times in various outdoor temperatures. The table below lists the time taken to sprint 400 metres by runners in different temperatures:
| \text{Temperature }(C) | 5 | 2 | 10 | 8 | 1 | 7 | 6 | 4 | 3 | 9 |
|---|---|---|---|---|---|---|---|---|---|---|
| \text{Sprint time }(s) | 60 | 67 | 48 | 69 | 65 | 49 | 57 | 53 | 59 | 52 |
Use the graphing facility of your CAS calculator to graph this data on a scatter plot.
How many runners were tested in the study?
Describe the correlation between temperature and sprint time as positive or negative.
Describe the correlation between temperature and sprint time as strong or weak.
Which pair of temperature and sprint time represents an outlier?
A researcher is studying the relationship between the number of passers-by near an emergency situation and the time taken until help is offered. The results are shown in the table below:
Use the graphing facility of your CAS calculator to graph this data on a scatter plot.
Describe the relationship between the number of passers-by and the time until help is offered.
Is the relationship strong or weak?
Are there any outliers?
| \text{Passers-by } (p) | \text{Time until help}\\ \text{is offered }(t) |
|---|---|
| 1 | 8 |
| 2 | 19 |
| 3 | 26 |
| 4 | 37 |
| 5 | 51 |
| 6 | 65 |
Scientists were looking for a relationship between the number of hours of sleep we receive and the effect it has on our motor and processing skills. Some people were asked to sleep for different amounts of time, and were all asked to undergo the same driving test in which their reaction time was measured. The results are shown in the table:
Use the graphing facility of your CAS calculator to graph this data on a scatter plot.
Describe the relationship between the amount of sleep and reaction time.
| Hours of sleep | Reaction time in seconds |
|---|---|
| 9 | 3 |
| 6 | 3.3 |
| 4 | 3.5 |
| 10 | 3 |
| 3 | 3.7 |
| 7 | 3.2 |
| 2 | 3.85 |
| 5 | 3.55 |
To determine whether the presence of sharks in a coastal region is influenced by cage diving, the number of nearby cage diving operations and the number of nearby shark sightings was recorded each month over several months. The results are shown in the table:
Use the graphing facility of your CAS calculator to graph this data on a scatter plot.
According to the data, is it possible to determine whether cage diving operations encourage more sharks to come near the shoreline?
Describe the relationship between the number of shark sightings and the number of cage diving operations.
| Operations | Sightings |
|---|---|
| 10 | 4 |
| 2 | 3 |
| 4 | 5 |
| 7 | 4 |
| 8 | 1 |
| 5 | 4 |
| 1 | 5 |
| 9 | 7 |
| 6 | 10 |
| 3 | 8 |
The market price of bananas varies throughout the year. Each month, a consumer group compared the average quantity of bananas supplied by each producer to the average market price (per unit). The results are shown in the table:
Use the graphing facility of your CAS calculator to graph this data on a scatter plot.
Describe the relationship between the supply quantity and the market price of bananas.
What needs to happen for a supplier to receive a high price per banana?
| Supply (kg) | Price ($) |
|---|---|
| 550 | 15.25 |
| 600 | 14.75 |
| 650 | 14.75 |
| 700 | 14.75 |
| 750 | 14.25 |
| 800 | 14.00 |
| 850 | 13.75 |
| 900 | 13.25 |
| 950 | 13.50 |
| 1000 | 13.25 |
The following table has data results from an experiment:
| x | 1 | 4 | 5 | 8 | 9 | 11 | 13 | 15 | 18 | 19 |
|---|---|---|---|---|---|---|---|---|---|---|
| y | 2 | 4 | 6 | 8 | 12 | 24 | 30 | 46 | 52 | 64 |
Use the graphing facility of your CAS calculator to graph this data on a scatter plot.
Describe the shape of the correlation between the data points as linear or non-linear.
A study was conducted to find the relationship between the age at which a child first speaks and their their aptitude test results when they are teenagers. The data is shown in the table below:
| \text{Age when first spoke }(x \text{ months}) | 9 | 9 | 16 | 21 | 17 | 10 | 7 | 19 | 18 | 22 |
|---|---|---|---|---|---|---|---|---|---|---|
| \text{Aptitude test results }(y) | 96 | 69 | 84 | 90 | 101 | 87 | 92 | 99 | 104 | 93 |
Use the graphing facility of your CAS calculator to graph this data on a scatter plot.
Describe the correlation between the variables in terms of strength, direction and shape.
A student was performing an experiment to study the relationship between the current and voltage through a resistor. He noted his results in the following table:
| \text{Current }(x) | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
|---|---|---|---|---|---|---|---|---|---|---|
| \text{Voltage }(y) | 1 | 6 | 3 | 10 | 13 | 10 | 16 | 15 | 21 | 17 |
Create a scatter plot for this data.
Describe the correlation between the variables in terms of shape and direction.
The following table shows the time taken to finish a lap on a race track for several average speeds:
| \text{Speed }(x) | 20 | 25 | 30 | 35 | 40 | 45 | 50 | 55 | 60 | 65 |
|---|---|---|---|---|---|---|---|---|---|---|
| \text{Time }(y) | 85 | 87 | 75 | 82 | 69 | 73 | 60 | 57 | 45 | 49 |
Create a scattor plot to display this data.
Describe the type of correlation between the variables in terms of direction and shape.