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MTH1W Data Literacy
Grade 9 Unit 6 — practice questions with full solutions

Measures of central tendency, the effect of outliers, sampling methods, recognising bias, scatter plots and lines of best fit. An 18-hour examinable unit that is easy to under-prepare for.

MTH1W · Grade 9 Strand D — Data 10 core 1 challenge
1Core
Find the mean, median and mode of: 12, 15, 11, 15, 18, 20, 15
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  1. Sort the data first: 11, 12, 15, 15, 15, 18, 20.
  2. Mean: add all values (11+12+15+15+15+18+20 = 106) and divide by 7 → 106 ÷ 7 ≈ 15.14.
  3. Median: with 7 values, the middle is the 4th → 15.
  4. Mode: the most frequent value is 15 (appears three times).
Final answermean ≈ 15.14, median = 15, mode = 15
2Core
An extra value of 60 is added to the data set above. Recalculate the mean and median, and state which measure is more resistant to outliers.
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  1. New sum: 106 + 60 = 166, with 8 values → mean = 166 ÷ 8 = 20.75.
  2. Sorted data is now 11, 12, 15, 15, 15, 18, 20, 60 — with 8 values the median is the average of the 4th and 5th.
  3. Median = (15 + 15) ÷ 2 = 15, unchanged.
  4. The mean jumped by more than 5 while the median did not move at all.
Final answermean = 20.75, median = 15; the median is far more resistant to outliers
3Core
Find the range of: 11, 12, 15, 15, 15, 18, 20
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  1. Range = largest value − smallest value.
  2. Largest = 20, smallest = 11.
  3. Subtract.
Final answer9
4Core
123456789024681012Hours spent studyingTest score improvementline of best fit
Study the scatter plot and its line of best fit. (a) Describe the correlation. (b) Use the line to estimate the score improvement for 4.5 hours of study. (c) A student claims the line proves that studying causes higher scores. Is that a fair claim?
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  1. (a) The points rise from left to right in a fairly tight band, so there is a strong positive correlation.
  2. (b) Read up from 4.5 on the horizontal axis to the dashed line, then across. The line is approximately y = 1.1x + 2.
  3. So at x = 4.5: y ≈ 1.1(4.5) + 2 ≈ 7. Any estimate near 7 is acceptable when reading from a graph.
  4. (c) No. Correlation shows the two variables move together, but it cannot establish cause.
  5. Another factor could explain both — for example, more motivated students may both study more and attend class more.
Final answer(a) Strong positive correlation   (b) ≈ 7   (c) No — correlation does not prove causation
5Core
Name the sampling method in each case: (a) surveying every 10th student on an alphabetical list; (b) splitting students by grade, then randomly selecting from each grade; (c) surveying whoever happens to walk past the cafeteria.
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  1. (a) Choosing at a fixed regular interval from an ordered list is systematic sampling.
  2. (b) Dividing the population into groups and sampling randomly within each is stratified sampling.
  3. (c) Sampling whoever is easiest to reach is convenience sampling — the least reliable of the three.
Final answer(a) systematic   (b) stratified   (c) convenience
6Core
Identify the bias in this survey question and rewrite it fairly: “Don't you agree that our excellent cafeteria should stay open longer?”
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  1. The phrase “Don't you agree” pressures the respondent toward saying yes.
  2. The word “excellent” is a loaded adjective that pre-judges the cafeteria's quality.
  3. This is a leading question — the wording steers the answer.
  4. A fair version removes both the pressure and the loaded language.
Final answerLeading/loaded wording. Fair version: “Should the cafeteria's opening hours be extended?”
7Core
A scatter plot compares hours spent studying with test scores, and the points rise steadily from left to right in a fairly tight band. Describe the correlation in terms of direction and strength.
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  1. Direction is given by the trend: points rising left to right means as one variable increases, so does the other.
  2. That is a positive correlation.
  3. Strength is given by how tightly points cluster around a line — a tight band means a strong relationship.
  4. Important caution: correlation does not prove that studying caused the higher scores.
Final answerA strong positive correlation (but correlation alone does not establish causation)
8Core
024681012350–60760–701270–80980–90490–100Test score (%)Number of students
Use the histogram of test scores to find: (a) the total number of students, (b) the modal interval, (c) how many students scored 80 or above, and (d) that group as a percent of the class, to one decimal place.
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  1. (a) Add every bar: 3 + 7 + 12 + 9 + 4 = 35 students.
  2. (b) The modal interval is the tallest bar — the 70–80 interval, with 12 students.
  3. (c) Scores of 80 or above come from the last two bars: 9 + 4 = 13 students.
  4. (d) As a percent: 13 ÷ 35 = 0.3714… × 100 ≈ 37.1%.
Final answer(a) 35   (b) 70–80   (c) 13   (d) ≈ 37.1%
9Core
Explain the difference between interpolation and extrapolation, and state which is generally more reliable.
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  1. Interpolation means estimating a value inside the range of the data you actually collected.
  2. Extrapolation means estimating beyond the range of the collected data.
  3. Interpolation is more reliable because the trend is supported by real observations in that region.
  4. Extrapolation assumes the pattern continues unchanged, which may simply not be true.
Final answerInterpolation estimates within the data range and is more reliable; extrapolation goes beyond it and is riskier
10Core
Distinguish between primary and secondary data, and give one example of each in a study of student sleep habits.
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  1. Primary data is collected first-hand by the person doing the study.
  2. Secondary data is collected by someone else and reused.
  3. Primary example: handing out your own sleep survey to classmates.
  4. Secondary example: using published Statistics Canada figures on teenage sleep.
Final answerPrimary = collected yourself (own survey); Secondary = collected by others (published statistics)
11Challenge
A line of best fit for a scatter plot of study hours (x) versus test score (y) is y = 6x + 52, based on data from 0 to 8 hours. (a) Predict the score for 5 hours. (b) Predict the score for 20 hours and comment on the reliability of that prediction.
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  1. (a) Substitute x = 5: y = 6(5) + 52 = 30 + 52 = 82.
  2. Since 5 is inside the 0–8 range, this is interpolation and is reasonably trustworthy.
  3. (b) Substitute x = 20: y = 6(20) + 52 = 120 + 52 = 172.
  4. A test score of 172 is impossible — and 20 hours lies far outside the data range.
  5. This is extrapolation, and it shows exactly why extrapolating far beyond the data can produce nonsense.
Final answer(a) 82   (b) 172, which is unreliable — it is extrapolation well beyond the data and gives an impossible score

MTH1W Data Literacy — common questions

Short answers to the things students ask most about this unit.

Why is the median better than the mean when there is an outlier?

The mean uses every value, so one extreme number drags it far off. The median only depends on the middle position, so it barely moves.

What is the difference between interpolation and extrapolation?

Interpolation estimates inside the range of your data and is fairly reliable. Extrapolation goes beyond the data and assumes the trend continues, which often fails.

More MTH1W practice — grade 9 math

MTH1W Number SenseMTH1W Algebraic Expressions & Exponent LawsMTH1W Solving Linear EquationsMTH1W Linear Relations & GraphingAll MTH1W units
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