Surveys and Sampling
You want to find out how many Grade 7 students at your school play a team sport. What’s one sampling method you could use to collect this information fairly?
Use a systematic random sampling method, such as selecting every 5th student on the class list to ask whether they play a team sport.
After collecting school-wide data on students’ favourite school event (e.g., talent show, sports day, spirit day), you calculate the percentage each event received.
Would a circle graph or bar graph be more effective in showing these results? Why?
A circle graph would be better because it visually shows how each category makes up a portion of the whole.
Is the answer to this question qualitative or quantitative: “What is your favourite school subject?” Explain your reasoning.
It’s qualitative data because “favourite subject” is not a number and cannot be measured with a scale.
In a survey of 20 students, 8 say they like action movies best. What is the relative frequency (in percent) of students who chose action movies?
40%
Find the mean of these values: 12, 15, 10, 13, 20.
14
Explain how selecting only students from your class to represent the whole grade could result in biased data.
Only selecting students from your own class could lead to biased results because it doesn’t represent all Grade 7 students fairly. For example, your class might have more athletes than others.
You survey 200 students about their lunch choices. You want to show that most students picked pizza, while some picked sandwiches, salad, or other.
Which graph would give the clearest visual impression of how popular pizza is? Why?
A circle graph would clearly show how large the pizza portion is compared to the whole, which makes it great for emphasizing dominance.
You ask students, “How much screen time do you have each day?” Is this quantitative discrete or continuous data? Explain
This is quantitative continuous data because screen time can be measured in fractions and has a range.
You surveyed 25 students and 5 of them said their favourite lunch is pizza. What percentage of students is that?
20%
Find the median of these numbers: 45, 30, 60, 35, 50.
Put numbers in order: 30, 35, 45, 50, 60
Median = 45 (middle number)
You want to know how often students in your grade buy lunch from the cafeteria. Describe one way to collect a random sample to get accurate results.
You could use a simple random sample by assigning numbers to every student in Grade 7, then using a random number generator to choose a sample.
You want to compare the favourite ice cream flavours of two different classes.
Would a bar graph or a circle graph be better? Why?
A bar graph is better because it allows you to directly compare data between two groups. Circle graphs only show data for one group at a time
Describe a question that would result in qualitative data. Then, describe one that would result in quantitative continuous data.
Qualitative example: "What’s your favourite movie genre?"
Quantitative continuous: "How tall are you in cm?"
Two classes (each with 25 students) were surveyed about their favourite sport. 14 students in Class A and 10 students in Class B said they liked soccer. What is the total percentage of students who preferred soccer?
48%
Here are the number of texts sent by students in a week:
120, 130, 110, 115, 400
Identify the outlier and explain why it stands out.
Outlier = 120
It’s much higher than the other numbers, which are all around 50.
A school sends out a survey through their website and asks for feedback on cafeteria food. Why might this sampling method lead to inaccurate or biased results?
Surveying only students who visit the school website could lead to bias because students who don’t use the website won’t be included, and their opinions might differ.
You track your math quiz scores for the last 8 weeks. Which graph would best show how your performance changed over time? Explain your choice.
A line graph is appropriate because quiz scores over time represent continuous data and show trends clearly.
You collect data on the number of pets each student has. Is this quantitative discrete or continuous data? Explain.
The number of pets is quantitative discrete because you can count pets in whole numbers, and there are no fractional pets.
You tally the results of a survey on favourite fruit: 10 like apples, 6 like bananas, 4 like grapes, 5 like oranges.
Create a table showing the number of students and relative frequency (%) for each fruit.
Bananas 20%
Grapes 13%
Oranges 17%
Here are the monthly profits from a lemonade stand:
$100, $120, $115, $110, $500
Remove the outlier and calculate the new mean. Then explain how the outlier affected the original mean.
Original Mean =189
New Mean (without 500) = 111.254445=111.25
The outlier raised the average significantly.
You're conducting a survey to find out how often students in Grades 7 and 8 use public transportation.
You choose 10 students from each class, but later realize many of them live within walking distance.
Explain how stratified sampling could help reduce this kind of bias in future surveys.
Stratified random sampling would divide students into groups based on distance from school (e.g., near, far) and then randomly select students from each group. This ensures that the sample includes perspectives from students who are both likely and unlikely to use public transit, reducing bias.
You surveyed students in three grades about their favourite school event (e.g., sports day, talent show, field trip) and recorded the number of votes.
You decide to display this data in a double bar graph.
Explain why a double bar graph is appropriate, and describe what you should consider to ensure it is accurate and not misleading.
A double bar graph is appropriate because you’re comparing two sets of data (grades) for each category (event). To avoid misleading results, you must use the same scale for both bars, label axes clearly, and use consistent bar widths.
You're organizing data from a survey. The questions include:How tall are you? Rate your interest in science from 1-10.What is your favourite subject?
Classify each question by both type (qualitative/quantitative) and subtype (discrete/continuous if applicable), and explain your choices.
Height= quantitative continuous
Interest rating 1–10 = quantitative discrete (since the scale uses whole numbers)
Favourite subject = qualitative
These classifications help you choose the correct graph and analysis method for each question.
You surveyed 60 students about their favourite type of book. Fantasy is 18 students favourite genre.
If you were to display this data as a pie chart of this data, what is the angle for a preference for Fantasy books?
108∘
Here are the scores from two different classes on a math test:
Class A: 65, 70, 75, 80, 85, 90, 95
Class B: 60, 65, 70, 70, 95, 100, 100
Compare the mean, median, and mode for both classes. Then, explain which measure of central tendency gives the most accurate representation of student performance in each class and why.
Class A:
Mean = 80 Median = 80 No mode
Class B:
Mean =80 Median = 70 Mode = 70 and 100
Although the means are equal, Class A scores are more evenly spread, so the mean is a good representation. In Class B, the scores are skewed due to a cluster at 100 and a low at 60, so the median or mode may give a better picture of student performance.