11.06 Bivariate data
State whether the following are examples of univariate data or bivariate data:
A school collects data on the height of each student in two classes in order to compare the classes.
A scientist collects data on iron levels in soil and growth of a type of weed in order to investigate the relationship between them.
A school collects data on the shoe size of each student in the school.
A hockey club collects data on time travelled to get to training from members of three teams in order to compare them.
A political group collects data on the taxable income and the addresses of the local electoral constituents in order to investigate if there is an association.
A psychologist collects data on the number of days in daycare and NAPLAN results in grade three in order to investigate the relationship between them.
John wishes to investigate whether there is an association between the amount of natural sunlight in a classroom and student’s exam results.
Emma wishes to investigate whether players in the A hockey team have higher average mathematics test results than players in the B hockey team.
State whether there is likely to be a relationship between the following pairs of variables:
Study time and test score.
Length of hair and number of pets.
Typing speed and dancing ability.
Driving time and petrol used.
For each pair of variables, state whether one variable has a direct effect on the other. If yes, state which variable affects the other.
Temperature (\degree \text{C}), Distance from the equator (\text{km})
Weekly income, Number of friends
Time of travel (minutes), Distance covered (\text{m})
Age (years), Time spent watching television
Time spent working, Wages earned
Time spent to finish a novel, Number of pages
Height (\text{cm}), Number of children
Number of pets, Time spent caring for pets
Time spent training, Athletic performance
For each of the following pairs of variables:
State the independent variable.
State the dependent variable.
Number of ice cream cones sold and temperature outside
Size of a pizza and cost of a pizza
Time spent studying and exam mark
Consider the following variables:
Ticket sales
Revenue from a show
Which variable affects the other?
State the dependent and independent variables.
A kite can rise to a height of 161 \text{ m} when the wind is blowing at 6 kilometres per hour and to a height of 322 \text{ m} when the wind is blowing at 12 kilometres per hour.
State the two variables in the above scenario.
From the two variables, state the dependent and independent variables.
A study was performed to find the relationship between the number of soft drinks consumed per week and the waist circumference of students.
Which variable is the independent variable?
Which variable is the dependent variable?
Which variable should be put on the x-axis?
Which variable should be put on the y-axis?
The graph shows the height of a ball after it is dropped off the side of a building:
Which variable is the dependent variable?
Which variable is the independent variable?
The scatter plot shows the relationship between sea temperature and the amount of healthy coral:
Which variable is the dependent variable?
Which variable is the independent variable?
Create a scatter plot for the set of data in the following tables:
| x | 1 | 3 | \, 5 | \, 7 | \, 9 |
| y | 2 | 7 | 11 | 15 | 17 |
| x | 1 | 3 | \, 5 | \, 7 | \, 9 |
| y | 3 | 7 | 11 | 13 | 17 |
| x | 1 | 2 | \, 4 | \, 7 | \, 8 |
| y | 20 | 18 | 17 | 15 | 11 |
| x | 1 | 3 | \, 5 | \, 9 | \, 12 |
| y | 7 | 3 | 11 | 15 | 19 |
Georgia has a high income but does not like her job. Which dot would represent her?
The following table shows the number of apples eaten per week and the number of visits to the doctor per year by six students:
| \text{Number of apples eaten per week} | \, 0 | \, 3 | \, 6 | 7 | 9 | 11 |
| \text{Number of visits to the doctor per year} | 17 | 14 | 11 | 6 | 3 | \, 0 |
Create a scatter plot for the set of data.
Vanessa wants to visit the doctor as few times as possible each year. According to the plot, should she eat 0 or 11 apples per week?
The table shows the number of books read per year by six students and the mark they received in their yearly maths exam:
| \text{Number of books read per year} | \, 5 | 15 | 20 | 30 | 40 | \,50 |
| \text{Mark in yearly maths exam} | 50 | 65 | 70 | 80 | 90 | 100 |
Create a scatter plot for the set of data.
In this group of students, Valentina achieved the highest mark in the yearly maths exam. Use the plot from part (a) to find out how many books she read throughout the year.
The teacher told the class: "The more books you read, the higher your yearly maths exam mark will be." According to the plot in part (a), is the teacher correct?
The table shows the age and height of six children in a family:
| \text{Age (years)} | \, 3 | \enspace 4 | \enspace 9 | \, 11 | \, 13 | \, 16 |
| \text{Height (cm)} | 90 | 105 | 130 | 145 | 160 | 165 |
Create a scatter plot for the set of data.
Bob is the second youngest child in the family. Use the plot from part (a) to find out how tall he is.
The following table shows the number of carrots eaten per day by six rabbits, and their hop length:
| \text{Number of carrots eaten per day} | \, 2 | \, 3 | \, 6 | 10 | 14 | 16 |
| \text{Hop length (cm)} | 43 | 70 | 46 | 54 | 51 | 59 |
Create a scatter plot for the set of data.
What is the difference in hop length between the rabbit who eats the most carrots and the rabbit who eats the least carrots per day?
The table shows the head circumference of six students, and the time it takes them to travel to school each day:
| \text{Head circumference (cm)} | 42.2 | 43.6 | 44.6 | 45.2 | 46.6 | 47.4 |
| \text{Time taken to travel to school (min)} | \enspace 12 | \enspace 52 | \enspace 45 | \enspace 21 | \enspace 37 | \enspace 18 |
Create a scatter plot for the set of data.
Vincent has the longest trip to school each day. According to the plot, what is the circumference of Vincent's head?
The number of customers that visit a new clothing store is recorded on the days that Iain is working. The results are shown in the table:
| \text{Number of days since store opened} | \, 1 | \, 2 | \, 3 | \, 5 | \, 7 | \, 9 |
| \text{Number of customers} | 10 | 15 | 25 | 35 | 35 | 60 |
Create a scatter plot for the set of data.
What is the average number of customers that went to the store on the6 days that Iain was recording?
The height of the tide at a beach is recorded at ten different hours in one day:
| Time (hours) | 13 | 24 | 7 | 2 | 4 | 15 | 6 | 11 | 21 |
|---|---|---|---|---|---|---|---|---|---|
| Height (m) | -0.21 | -0.05 | 0.92 | 0.55 | 0.84 | -0.76 | 1.01 | 0.31 | -0.68 |
State the dependent and independent variables.
Construct a scatter plot for this data.