8. Two Variable Data Analysis

Worksheet

1

For each of the following scatter plots, describe the correlation as positive or negative:

a

b

c

d

2

For each of the following scatter plots, describe the correlation in terms of strength and direction:

a

b

c

d

e

3

For each of the following scatter plots, describe the data as linear or nonlinear:

a

b

c

d

e

f

4

Consider the following graph:

a

Describe the correlation as linear or non-linear.

b

What is the term for the three points located away from the main graph?

5

Considering the scatter plot shown, describe the relationship between someone’s vision and their height.

6

The scatter plot shows the relationship between air and sea temperature:

a

Describe the relationship between air and sea temperature.

b

Describe the correlation between air and sea temperature in terms of strength, direction and form.

7

Yvonne has a high income but does not like her job.

Which dot is most likely to represent Yvonne?

8

The market price of bananas varies throughout the year. Each month, a consumer group recorded the average quantity of bananas supplied by each producer and the average market price (per unit).

Findings are displayed in the table and scatter plot below:

\text{Supply (kg)} | \text{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 |

a

Describe the correlation between the supply quantity and the market price of bananas.

b

According to this data, when will a supplier of bananas receive a higher price per banana?

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:

a

According to the graph, who is correct: Lachlan or the teacher?

b

Let's assume that Lachlan performed exceptionally well in every other question. If a whole class of students had the same result as Lachlan, where could this class’s results appear on the scatter plot, region 1, 2, 3 or 4?

10

The land size of a sample of properties and their selling price were graphed on the scatter plot below:

a

State the size range that contains the most properties.

b

Another property that is not represented in the scatter plot sold for \$704\,000 and measured 3600 square feet in size. Is this consistent with the relationship shown in the graph?

11

The following scatter plot shows the relationship between sea temperatures and the amount of healthy coral:

a

Describe the correlation between sea temperature the amount of healthy coral.

b

Which variable is the dependent variable?

c

Which variable is the independent variable?

12

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.

If the length of the paragraph were plotted (on the horizontal axis) against the amount of information retained (on the vertical axis), would the correlation be negative or positive?

13

A study was conducted to find the relationship between the age at which a child first speaks and their level of intelligence as teenagers. The following table shows the ages of some teenagers when they first spoke, and their results in an aptitude test:

a

Construct a scatter plot from the data in the table.

b

Describe the correlation between the data points in terms of strength, direction and form.

Age when first spoke | Aptitude test result |
---|---|

14 | 96 |

27 | 69 |

9 | 84 |

9 | 90 |

16 | 101 |

21 | 87 |

17 | 92 |

10 | 99 |

7 | 104 |

19 | 93 |

14

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:

a

Construct a scatter plot for the data in the table.

b

Describe the correlation between the data points.

Current | Voltage |
---|---|

1 | 1 |

2 | 6 |

3 | 3 |

4 | 10 |

5 | 13 |

6 | 10 |

7 | 16 |

8 | 15 |

9 | 21 |

10 | 17 |

15

The following table shows the time taken to finish a lap on a race track for various average speeds:

Speed | 20 | 25 | 30 | 35 | 40 | 45 | 50 | 55 | 60 | 65 |
---|---|---|---|---|---|---|---|---|---|---|

Time | 85 | 87 | 75 | 82 | 69 | 73 | 60 | 57 | 45 | 49 |

a

Construct a scatter plot for the data.

b

Describe the correlation between speed and time for this data.

16

The following table displays 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 |

a

Construct a scatter plot for this data.

b

Describe the correlation between X and Y.

17

The following table shows the number of traffic accidents associated with a sample of drivers of 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 |

a

Construct a scatter plot for this data.

b

Describe the correlation between a person's age and the number of accidents.

c

Does this data set contain any outliers?

18

The marks of 12 students in Math and Sports were recorded in the following table:

a

Construct a scatter plot for the students' marks in Math vs their marks in Sports.

b

Describe the correlation between students' marks in maths and marks in sport.

c

Which student's scores appear to represent an outlier?

Student | Mark in Maths | Mark in Sports |
---|---|---|

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 |

19

The following table shows the average IQ of a random group of people against their height:

\text{Height (cm)} | 140 | 145 | 150 | 155 | 160 | 165 | 170 | 175 | 180 | 185 |
---|---|---|---|---|---|---|---|---|---|---|

\text{IQ} | 103 | 95 | 98 | 111 | 85 | 89 | 108 | 145 | 110 | 93 |

a

Construct a scatter plot to represent this data:

b

Describe the relationship between IQ and height.

c

How tall is the person who appears to be an outlier?

20

A researcher is studying the relationship between the number of passers-by present in a situation and the time taken, in seconds, until a stranger in an emergency receives help from a passer-by. The data is recorded in the table below:

a

Construct a scatter plot to represent the data in the table.

b

Comment on the relationship between the number of passers-by and the time until assistance is offered by a passer-by to a person in an emergency.

c

Describe the correlation between the number of passers-by and the time until assistance is offered by a passer-by to a person in an emergency.

\text{Passers-by} | \text{Time until} \\ \text{offered help} |
---|---|

1 | 8 |

2 | 19 |

3 | 26 |

4 | 37 |

5 | 51 |

6 | 65 |

21

The following table shows the marks of 12 students in English and French:

a

Construct a scatter plot for English mark vs French mark.

b

Describe the correlation between students' English and French marks.

c

Which student's scores appear to represent an outlier?

Student | English | French |
---|---|---|

1 | 85 | 89 |

2 | 71 | 71 |

3 | 57 | 56 |

4 | 60 | 62 |

5 | 79 | 86 |

6 | 76 | 75 |

7 | 71 | 77 |

8 | 91 | 86 |

9 | 50 | 90 |

10 | 49 | 47 |

11 | 66 | 67 |

12 | 92 | 92 |

22

The table lists the time taken to sprint 400 metres by runners who all ran in different temperatures as part of a study:

a

Construct a scatter plot to represent the data in the table.

b

How many runners were tested in the study?

c

Describe the correlation between temperature and sprint time for the data.

d

Which data point represents an outlier?

\text{Temperature }\\( \degree\text{C}) | \text{Time (sec)} |
---|---|

5 | 60 |

2 | 67 |

10 | 48 |

8 | 69 |

1 | 65 |

7 | 49 |

6 | 57 |

4 | 53 |

3 | 59 |

9 | 52 |

23

Scientists were looking for a relationship between the number of hours of sleep and the effect it has on motor and process skills. Subjects slept for different amounts of time, and then did the same driving challenge in which their reaction time was measured. The table shows the results:

a

Construct a scatter plot for this data.

b

Describe the relationship between amount of sleep and reaction time.

Amount of sleep (hours) | Reaction time (seconds) |
---|---|

9 | 3 |

6 | 3.3 |

4 | 3.5 |

10 | 3 |

3 | 3.7 |

7 | 3.2 |

2 | 3.85 |

5 | 3.55 |

24

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 below:

a

Construct a scatter plot for the observations in the table.

b

According to the data, is it possible to determine whether cage diving operations encourage more sharks to come near the shoreline?

c

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 |

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Create a scatter plot to represent the relationship between two variables, determine the correlation between these variables by testing different regression models using technology, and use a model to make predictions when appropriate.