36 students were asked whether or not they were allergic to nuts and dairy. The two-way table is provided below.
| Allergic to nuts | Not allergic to nuts | |
|---|---|---|
| Allergic to dairy | 10 | 6 |
| Not allergic to dairy | 6 | 14 |
State the number of students that are allergic to nuts.
State the number of students that are allergic to nuts or dairy, or both.
State the number of students that are allergic to at most one of the two things.
150 tennis players were asked whether they would support equal prize money for the women’s and men’s draw.
Complete the given table.
How many more players are there in support of equal prize money than against it?
Find the percentage of the male tennis players that support equal prize money. Round your answer to one decimal place if necessary.
| Support | Do not support | |
|---|---|---|
| Males | 35 | |
| Females | 66 | 12 |
This table describes the departures of flights out of an airport for the months of May and June.
Calculate the percentage of flights in June that were delayed, correct to one decimal place.
| Departed on time | Delayed | |
|---|---|---|
| May | 144 | 21 |
| June | 116 | 40 |
Calculate the fraction of the total number of flights during the two months that departed on time in May.
Calculate the percentage of flights in June that were on time, correct to one decimal place.
Two motels promoted packages for 1 night and 2 night stays. Results on the number of packages sold are recorded in the table:
Find the percentage of the stays that are 2 night stays, correct to two decimal places.
Find the fraction of the two night stays that were in Motel X.
Find the percentage of the total accommodation that was in Motel X, correct to two decimal places.
| One night stay | Two night stays | |
|---|---|---|
| \text{Motel }X | 463 | 266 |
| \text{Motel }Y | 804 | 817 |
A vet has a total of 28 pets visit their practice in a day.
The pets are categorised based on whether they have been vaccinated and whether they have been microchipped as shown in the Venn diagram:
Complete the following table:
| Microchipped | Not Microchipped | |
|---|---|---|
| Vaccinated | ||
| Not vaccinated |
Sophia asked some people in her community whether they were vegetarian or not.
29 responders said they were vegetarian, of which 8 were children. 14 children said they were not vegetarian, and 11 adults said they are not vegetarians.
Complete the given two-way table based on the results of Sophia's survey:
What proportion of responders are vegetarian?
What proportion of adults are vegetarian?
| Not vegetarian | Vegetarian | |
|---|---|---|
| Children | ||
| Adults |
Glen surveyed all of the students in Year 12 at his school and summarised the results in the following table:
| Play netball | Do not play netball | |
|---|---|---|
| \text{Height} \geq 170 \text{ cm} | 62 | 138 |
| \text{Height} < 170 \text{ cm} | 60 | 140 |
Which variable is the explanatory variable?
Create a row percentage frequency table for this data. Round the values to the nearest percentage.
Members of a gym were asked what kind of training they do. Each of them only did one kind of training. The table shows the results:
| Cardio | Weight | |
|---|---|---|
| Male | 15 | 35 |
| Female | 22 | 8 |
Which variable is the explanatory variable?
Create a row percentage frequency table for this data. Round the values to the nearest percentage.
Does there appear to be an association between the type of training and the gender of gym members? Explain your answer.
Does a person’s gender cause them to choose a certain type of training? Explain your answer.
An online streaming service was interested in the viewing habits of high school students and whether there was any association between year group and preferred genre. 25 students were chosen at random from each year group at a particular school and asked the following questions:
Question 1: What is your favourite genre? Cartoons, Reality TV, Movies or Documentaries
Question 2: Which year group are you in?
Which variable, genre or year group, represents the explanatory variable in this problem?
The results of the survey are recorded in the table below.
| Cartoons | Reality TV | Movies | Documentaries | Total | |
|---|---|---|---|---|---|
| Year 7 | 15 | 5 | 3 | A | 25 |
| Year 8 | 13 | 5 | 4 | 3 | 25 |
| Year 9 | 11 | 4 | 5 | 5 | 25 |
| Year 10 | 9 | B | 6 | 7 | 25 |
| Year 11 | 6 | 4 | 6 | 9 | 25 |
| Year 12 | 1 | 3 | 11 | 10 | 25 |
| Total | C | 24 | 35 | 36 | D |
Find the values of:
Calculate the percentage of:
Year 7 students who watch cartoons.
Year 12 students who watch cartoons.
Comment on the percentage of Year 7 and Year 12 students who watch cartoons.
170 people were surveyed about their music preference. The results have been recorded in the table below:
| Music Preference | Male | Female | Total |
|---|---|---|---|
| \text{Rock and Roll} | 24 | 19 | 43 |
| \text{Classical} | 8 | 15 | 23 |
| \text{Pop} | 17 | 17 | 34 |
| \text{Rap} | 6 | 2 | 8 |
| \text{Country and Western} | 17 | 24 | 41 |
| \text{R and B} | 6 | 9 | 15 |
| \text{Punk} | 4 | 2 | 6 |
| \text{Total} | 82 | 88 | 170 |
State the explanatory variable for this data set.
Which of the following 100\% stacked column charts should be used to look for an association between the variables?
Does the stacked column chart suggest that there is an association between music preference and gender? Explain your answer.
A group of year 12 students surveyed their class and recorded the hair colour and eye colour for each student. The results are displayed in the 100\% stacked column chart shown:
State the explanatory variable for this chart.
Does the chart suggest an association between eye colour and hair colour? Explain your answer.
Can we say that having blue eyes causes a high chance of having blonde hair? Explain your answer.
The local library constructed divided bar graphs showing the last six months of book loans by category:
Assume that the total number of loans was exactly the same for each month.
In which month did subscribers borrow the most business books?
Which month was the best month for children's books?
State the response variable for this data.
Does the divided bar graph suggest that there is an association between the variables? Explain your answer.
This stacked column chart shows the fitness levels for various categories of smokers:
State the response variable for this chart.
Does there appear to be an association between fitness level and category of smoker?
Describe this association.
25 students were chosen at random from each year group at a particular school and asked the following questions:
Question 1: What is your favourite genre? Cartoons, Reality TV, Movies or Documentaries
Question 2: Which year group are you in?
The results are displayed in the divided column graph below:
Using the graph above or another method, describe the association between:
Cartoons and Year Group.
Documentaries and Year Group.
Genre and Year Group
Weekend workers at a fast food store were surveyed as to which pathway they followed at school (ATAR or Non-ATAR) and the type of phone (IPhone, Samsung or Other). The results are displayed in the column graph below.
Complete the frequency table, for the above data:
| iPhone | Samsung | Other | Total | |
|---|---|---|---|---|
| ATAR | 25 | |||
| non-ATAR | 27 |
A 100\% stacked column graph is to be created that can be used to help determine if there is a relationship between the variables. Which variable (School Pathway or Type of Phone) should be plotted on the horizontal x axis?
Choose the statement that best describes the association between School Pathway and Type of Phone.
It appears that there is an association. Students following an non-ATAR pathway are more likely to have an iPhone.
There appears to be no association between the variables. The numbers in each category of phone are similar.
It appears that there is an association. Students following an ATAR pathway are more likely to have an iPhone.
It appears that there is an association. Students following an ATAR pathway are more likely to have a Samsung phone.