aExample Question: Does your family have any pets? If yes, what kind(s)?
Quantitative or Qualitative:qualitative
B
bPopulation: Students attending the school
Sampling method: See solution.
C
c See solution.
Practice makes perfect
a We want to conduct a survey to find out what kinds of pets the families of students from our school have. To do so, we must first come up with an unbiased question. A survey question is biased when it contains assumptions. This means that we should start by asking if the student even has a pet at home.
Survey Question
Does your family have any pets? If yes, what kind(s)?
This question does not contain any assumptions and therefore is unbiased. We also want to determine whether the collected data will be quantitative or qualitative. In this case, the collected data — which are yes or no answers and kinds of pets — can be neither measured nor numerically compared. Therefore, the data will be qualitative.
b We want to describe a population and a sampling method for our survey. Let's start by choosing the population.
Because we want to find out what kinds of pets the families of students from our school have, the population will be all students attending our school. Next, we need to choose an unbiased sampling method for our survey. To do so, let's recall the methods that we know.
Since we want to survey students from all grade levels, we will separate our high school into the four grades. Then we will survey a random sample of students from each grade. For example, we can number the students and choose them using a random number generator. To choose the sample size, let's use the applet.
Let's assume that there are 100 students in each grade. In this case, we will randomly select 25 students from each grade and survey them. This sample is called a stratified sample.
Alternative Solution
Another Sampling Method
Please note that we could have also chosen to do a random sample of the entire school and it would have been valid. However, since we wanted to have equal representation between the grades, this was not our choice.
c Using the survey that we created in Part A and Part B, we will now collect data and present the results in a graph. Because the sample size is 25 for each grade level, we will have 100 responses in total. Let's collect the data in the form of a frequency table.
Pet
Frequency
Dog
64
Cat
43
Freshwater fish
12
Reptile
11
Bird
10
Rodent
8
Horse
3
Saltwater fish
2
Other
5
Remember that this is only one example of a data set that we could collect. Also, it happened that only 86 of the 100 respondents had a pet in their household. Finally, we can display the data collected in the table in a graph. Because the data is qualitative, we will use a bar graph.
