A survey about school lunches asks only students in the chess club. What is the main problem?
Ontario MPT: Data and probability
Reading and choosing graphs, mean, median, mode and range, sampling and bias, and the probability of simple and compound events.
- No sign-up
- Every answer explained
- Independent · not a government site
- 14 questions
- Topic drill
Study reference: The Ontario Curriculum, Grades 1–8: Mathematics (2020) and Grade 9: Mathematics MTH1W (2021), Ch. 3 Data strand — Grades 3–8 strand D, Grade 9 strand D
All 14 questions in this test
Every question and its answer choices. The correct answers and explanations appear when you take the test above.
A survey about school lunches asks only students in the chess club. What is the main problem?
- Chess club members cannot answer surveys
- The sample is not representative of all students
- The survey has too many questions
- Lunch is not a suitable survey topic
A bar graph's vertical axis starts at 90 instead of 0. What effect can this have?
- Small differences look much larger
- The graph becomes more accurate
- The bars show percentages instead
- The data values change
A spinner lands on blue 18 times in 60 spins. What is the experimental probability of blue?
- 0.3
- 0.18
- 0.42
- 0.6
Find the mean of 4, 8, 6, 5 and 7.
- 7
- 5
- 6
- 30
Which graph is best for showing how a class's heights are distributed across intervals such as 140–149 cm and 150–159 cm?
- A circle graph
- A pictograph of pets
- A line graph
- A histogram
Shoe sizes in a class are 6, 7, 7, 8, 8, 8, 9. What is the mode?
- 7
- 8
- 7.6
- 9
A fair six-sided die is rolled once. What is the probability of rolling a number less than 3?
- 1/6
- 1/2
- 2/3
- 1/3
A fair die is rolled and a coin is tossed. How many outcomes are in the sample space?
- 12
- 2
- 6
- 8
On a scatter plot, as hours of practice increase, the number of errors decreases. What relationship is shown?
- A causal proof
- A negative correlation
- A positive correlation
- No correlation
A bag holds 4 red, 6 yellow and 10 green counters. What is the probability of drawing a yellow counter?
- 3/5
- 1/6
- 6/14
- 3/10
A data set is 12, 14, 13, 15, 61. Which measure is most affected by the 61?
- The mode
- The mean
- The number of values
- The median
Which is an example of qualitative data?
- Favourite season of each student
- Number of siblings each student has
- Time to run 100 m in seconds
- Height of each student in cm
Two fair coins are tossed. What is the probability of getting exactly one head?
- 3/4
- 1/3
- 1/2
- 1/4
Find the median of the even-sized set 3, 9, 4, 12, 7, 10.
- 8
- 7.5
- 9
- 7
Data and probability: key rules to remember
Our summary of what the official handbook says on this topic, in our own words. Read it before or after the practice questions above, then check the original chapter. Read the official chapter ↗
Ontario Curriculum, Data strand (Grades 3–8 D; Grade 9 D)
- Qualitative vs quantitative data; sampling and bias; representative samples.
- Graph choice: histogram (intervals), circle graph (parts of a whole), line graph (change over time), scatter plot (relationship).
- Mean, median (average of the two middle values for an even count), mode; outliers affect the mean most.
- Misleading graphs: axis not starting at zero exaggerates differences.
- Correlation (positive/negative) does not prove cause.
- Probability: theoretical = favourable ÷ total; experimental = observed ÷ trials; sample space by tree or table (die and coin = 12).
Other topics
- MPT requirement, format and scoringWho must pass the Mathematics Proficiency Test for Ontario certification, the two components, the 70% standard on each in the same attempt, cost, retakes, booking and test windows.
- Number: fractions, decimals, percents and ratiosPlace value, operations with fractions, decimals and integers, percents, rates and ratios, exponents and square roots, and proportional reasoning from the Grades 3–9 Number strand.
- Algebra, patterns and codingPatterns, variables and expressions, solving equations and inequalities, linear relations and their graphs, and reading simple code that uses loops and conditions.
- Spatial sense: geometry and measurementAngles and polygons, the Pythagorean relationship, transformations, area, surface area and volume, metric unit conversions and circles.
- Financial literacyBudgets, unit prices and best buys, simple and compound interest, sales tax and discounts, and exchange rates as taught in the Financial Literacy strand.
- Pedagogy: the mathematics curriculumHow the Ontario math curriculum is organized: strands, overall and specific expectations, the seven mathematical processes, social-emotional learning skills, coding and culturally responsive teaching.
- Pedagogy: assessment and evaluationGrowing Success: assessment for, as and of learning, the achievement chart's four categories and four levels, learning goals and success criteria, descriptive feedback and how grades are determined.
- Pedagogy: learning for all studentsLearning for All: universal design for learning, differentiated instruction, the tiered approach to prevention and intervention, and planning from each student's strengths and needs.