Aussie Maths & Science Teachers: Save your time with SmarterEd
The school canteen wishes to conduct a survey to find out the preferred sandwich fillings of students so they can ensure they are catering to the likes of the students.
Which of the following survey options would provide the most useful information.
\(D\)
\(\text{Considering each option:}\)
| A. | \(\text{Not representative of the whole school population.}\) |
| B. | \(\text{Not necessary to survey students who do not use the canteen.}\) |
| C. | \(\text{Not representative of the whole school population.}\) |
| D. | \(\text{Students from each year who use the canteen are surveyed,}\) |
| \(\text{so representative of the whole population of canteen users. }\checkmark \) |
\(\Rightarrow D\)
Which of the following would be best conducted as a sample?
\(D\)
\(\text{Considering each option:}\)
\(\text{A. You could measure the all players }\longrightarrow\ \text{Census}\)
\(\text{B. This information would be available from ticket sales }\longrightarrow\ \text{Census}\)
\(\text{C. Could be determined exactly with a stocktake of remaining bottles }\longrightarrow\ \text{Census}\)
\(\text{D. It would not be possible to interview every household to determine popularity }\longrightarrow\ \text{Sample}\)
\(\Rightarrow D\)
Explain the difference between a census and a sample. (2 marks)
--- 2 WORK AREA LINES (style=lined) ---
\(\text{A census surveys the whole population.}\)
\(\text{A sample surveys a section of the population.}\)
\(\text{A census surveys the whole population.}\)
\(\text{A sample surveys a section of the population.}\)
Explain why a door-to-door survey conducted between the hours of 9 am and 3 pm on a Tuesday may not give results representative of the population. (2 marks)
--- 2 WORK AREA LINES (style=lined) ---
\(\text{It would not be representative of the whole community.}\)
\(\text{For example day workers and school children would not be included.}\)
\(\text{It would not be representative of the whole community.}\)
\(\text{For example day workers and school children would not be included.}\)
The local council is researching possible uses for a large area of land close to an established housing development.
One of the options for the land is a football stadium with a crowd capacity of \(30\ 000\) people.
The council is considering surveying people as they exit an existing football stadium in a neighbouring town.
Give a reason why this survey may not provide reliable data. (2 marks)
--- 2 WORK AREA LINES (style=lined) ---
Min is writing a report regarding the capacity of dams in NSW during 2023 projecting in to 2024. He wishes to include rainfall data for the previous 12 months in each of the catchment areas.
Should Min use primary or secondary sources to obtain this informaiton? Give a reason for your answer. (2 marks)
--- 2 WORK AREA LINES (style=lined) ---
\(\text{Secondary Source data}\)
\(\text{Reason: See worked example}\)
\(\text{Secondary source data.}\)
\(\text{It would not be possible for Min to collect this information}\)
\(\text{himself so he would therefore need to rely on already existing}\)
\(\text{secondary source data.}\)
Michael is conducting a survey to determine whether his clients are happy with the customer service they receive at his restaurant.
Should Michael use primary or secondary source data for his survey? Give a reason for your answer. (2 marks)
--- 2 WORK AREA LINES (style=lined) ---
\(\text{Primary Source data}\)
\(\text{Reason: See worked example}\)
\(\text{Primary source data.}\)
\(\text{Michael would survey his actual customers}\)
\(\text{to obtain their opinions and is therefore using}\)
\(\text{primary source data.}\)
Explain the difference between continuous and discrete data, giving an example of each. (3 marks)
--- 4 WORK AREA LINES (style=lined) ---
\(\text{See worked example}\)
\(\text{Discrete can be assigned a numerical value and can}\)
\(\text{usually be counted.}\)
\(\text{Examples could include:} \)
\(\text{Continuous data can be assigned any value in a range}\)
\(\text{and usually involves a measurements.}\)
\(\text{Examples could include:} \)
The following question was asked in a survey.
'What month were you born?'
How would the responses be classified?
\(A\)
\(\text{Months are names and so categorical data and}\)
\(\text{they are ordered}\)
\(\longrightarrow\ \text{Categorical, ordinal.}\)
\(\Rightarrow A\)
Organisers were choosing relay teams for the regional athletics carnival.
They asked the following question.
'What were the times for the 15 Years boys relay teams at zone athletics carnivals?'
How would the responses be classified?
\(D\)
\(\text{The times recorded are measurements}\)
\(\text{so all numbers on the scale are possible}\)
\(\longrightarrow\ \text{Numerical, continuous.}\)
\(\Rightarrow D\)
Which of the following is an example of categorical nominal data?
\(C\)
\(\text{French Bulldog, Poodle and Cavoodle are types of dogs (order not important) }\)
\(\longrightarrow\ \text{categorical nominal}\)
\(\Rightarrow C\)
Which of the following is an example of categorical ordinal data?
\(B\)
\(\text{Small, Medium, Large are categories with an order }\longrightarrow\ \text{categorical ordinal}\)
\(\Rightarrow B\)
Which of the following is an example of numerical continuous data?
\(A\)
\(\text{Weights are measurements (quantitative) }\longrightarrow\ \text{numerical continuous}\)
\(\Rightarrow A\)
Which of the following is an example of numerical discrete data?
\(B\)
\(\text{The number of competitors in a triathlon can be counted }\longrightarrow\ \text{numerical discrete}\)
\(\Rightarrow B\)
State whether the following categorical data is nominal or ordinal.
--- 1 WORK AREA LINES (style=lined) ---
--- 1 WORK AREA LINES (style=lined) ---
--- 1 WORK AREA LINES (style=lined) ---
--- 1 WORK AREA LINES (style=lined) ---
a. \(\text{Ordinal}\)
b. \(\text{Nominal}\)
c. \(\text{Nominal}\)
d. \(\text{Ordinal}\)
a. \(\text{The data is ranked}\ \longrightarrow\ \text{Ordinal}\)
b. \(\text{Colours are the names assigned}\ \longrightarrow\ \text{Nominal}\)
c. \(\text{Preferences are the names assigned}\ \longrightarrow\ \text{Nominal}\)
d. \(\text{Grades rank the data}\ \longrightarrow\ \text{Ordinal}\)
State whether the following data is categorical or numerical. If numerical, state whether discrete or continuous.
--- 1 WORK AREA LINES (style=lined) ---
--- 1 WORK AREA LINES (style=lined) ---
--- 1 WORK AREA LINES (style=lined) ---
a. \(\text{Numerical continuous}\)
b. \(\text{Categorical}\)
c. \(\text{Numerical discrete}\)
a. \(\text{Data is a measurement}\ \longrightarrow\ \text{Numerical continuous}\)
b. \(\text{Fruit is grouped into categories or types}\ \longrightarrow\ \text{Categorical}\)
c. \(\text{Students can be counted}\ \longrightarrow\ \text{Numerical discrete}\)
Match each variable with its classification on the right. (2 marks)
\begin{array} {ll} \text{A. Hair colour of students in Year 7} &\text{1. Numerical discrete} \\\text{B. Heights of players in the Boomers basketball team} & \text{2. Categorical ordinal} \\\text{C. The number of people living in each household in NSW}\ & \text{3. Numerical continous}\\\text{D. A, B, C, D, E grades on a report card} & \text{4. Categorical nominal}\end{array}
\(\text{A}\longrightarrow 4,\ \text{B}\longrightarrow 3,\ \text{C}\longrightarrow 1,\ \text{D}\longrightarrow 2\)
\(\text{A. Hair colour is data grouped in categories with no order}\)
\(\therefore\ \text{4. Categorical nominal}\)
\(\text{B. Heights are measurements which are numerical and continuous}\)
\(\therefore\ \text{3. Numerical continous}\)
\(\text{C. The people living in each household are counted}\)
\(\therefore\ \text{1. Numerical discrete}\)
\(\text{D. Grades on a report card are categorical but the order is important}\)
\(\therefore\ \text{2. Categorical ordinal}\)
Classify the following as either categorical or numerical data.
--- 1 WORK AREA LINES (style=lined) ---
--- 1 WORK AREA LINES (style=lined) ---
a. \(\text{categorical}\)
b. \(\text{numerical}\)
a. \(\text{Colours of cars are words therefore categorical.}\)
b. \(\text{Temperatures are measurements therefore numerical.}\)
Which of the following is not an example of categorical data?
\(D\)
\(\text{Heights are quantitative (measurements) and therefore not categorical.}\)
\(\Rightarrow D\)
What is the term used to describe data that is grouped in categories such as gold, silver and copper? (1 mark)
--- 1 WORK AREA LINES (style=lined) ---
\(\text{Categorical}\)
\(\text{The term for data that is not numerical is categorical.}\)
The variables age (under 55 years, 55 years and over) and preferred travel destination (domestic, international) are
\(A\)
\(\text{Age is a categorical ordinal variable}\)
\(\text{because it is categorical data that can}\)
\(\text{have an order.}\)
\(\text{Preferred travel destination is a categorical}\)
\(\text{nominal value because the data has a name.}\)
\(\Rightarrow A\)
The variables blood pressure (low, normal, high) and age (under 50 years, 50 years or over) are
\(B\)
\(\text{Blood pressure is an ordinal variable}\)
\(\text{because it is categorical data that can}\)
\(\text{have an order.}\)
\(\text{Under 50 and over 50, likewise, is an}\)
\(\text{ordinal variable.}\)
\(\Rightarrow B\)
The variables recovery time after exercise (in minutes) and fitness level (below average, average, above average) are
\(D\)
\(\text{Recovery time in minutes → numerical variable}\)
\(\text{Fitness level → ordinal (categories that can be ordered)}\)
\(\Rightarrow D\)
The variables
region (city, urban, rural)
population density (number of people per square kilometre)
\(C\)
\(\text{Region is a categorical variable and population}\)
\(\text{density is a numerical variable (i.e. it can be}\)
\(\text{represented by countable numbers).}\)
\(\Rightarrow C\)
A survey of which of the following would provide data that are both categorical and
nominal?
`A`
`text(By elimination:)`
`text{Qualitative (not quantitative)}`
`text{→ Eliminate B and C}`
`text(Nominal data is not ordered)`
`text{→ Eliminate D}`
`=> A`
A survey asked the following question for students born in Australia:
"Which State or Territory were you born in?"
How would the responses be classified?
`B`
`text{The data is categorical (not numerical) since}`
`text(the name of a State is required.)`
`text(This data cannot be ordered.)`
`=> B`
A survey asked the following question.
'How many brothers do you have?'
How would the responses be classified?
`text(C)`
`text(The number of brothers a person has is)`
`text(an exact whole number.)`
`:.\ text(Classification is numerical, discrete.)`
`=>\ text(C)`
Which set of data is classified as categorical and nominal?
`A`
`text(Categorical and nominal data is)`
`text(qualitative and not ordered.)`
`=> A`
On a school report, a student’s record of completing homework is graded using the following codes.
C = consistently
U = usually
S = sometimes
R = rarely
N = never
What type of data is this?
`A`
`text(The data has been grouped into categories and)`
`text(because each category can be ranked, it is ordinal.)`
`⇒ A`
The eye colours of a sample of children were recorded.
When analysing this data, which of the following could be found?
`C`
`text(Eye colour is categorical data)`
`:.\ text(Only the mode can be found)`
`=> C`
A high school has 100 students in each year group, Year 7 to Year 12. A survey is to be conducted to determine the average number of text messages sent per month by students at the school.
Which of the following would provide the most representative sample for this survey?
`C`
`text(The best sample would have an equal amount)`
`text(of people in each year randomly selected.)`
`=>\ C`