WAEC / WASSCE
WAEC Statistics Practice Questions, Solved Step by Step
WAEC statistics theory questions ask for the mean, median and mode from raw data or frequency tables, means of grouped data using midpoints, medians and quartiles from cumulative frequency, and pie chart calculations. This page works through five original questions in WASSCE style with every table and formula shown in full.
Statistics is the closest thing the WASSCE theory paper has to guaranteed marks, because the methods are procedures: build the table, apply the formula, state the answer with units. Almost every year Section B carries a statistics question worth around 12 marks, often with a cumulative frequency curve or a grouped frequency table. The five questions below are original, written to match that style and difficulty rather than copied from any WAEC paper. I have laid out every table in words so you can rebuild it on paper, which is honestly how you should practise, since the table itself carries marks.
What WAEC statistics questions look like
The progression is predictable. Easiest: a list of raw numbers, find the mean, median and mode. Next: an ungrouped frequency table, where the mean is the sum of fx divided by the sum of f, and the median needs cumulative counting. Then grouped data: you take class midpoints, multiply by frequencies and divide, and the median or quartiles come from an interpolation formula or from reading a cumulative frequency curve drawn at upper class boundaries. Pie charts appear regularly too, converting sector angles to amounts and back. A full Section B question often chains these: complete a table, calculate the mean, draw the ogive, then read off the median and interquartile range.
Table marks and boundary traps
In a WAEC statistics question the table is not scratch work, it is marked. Columns for midpoint, fx and cumulative frequency each attract B marks, so draw them neatly and total them visibly. The classic trap is class boundaries: for classes like 21 to 30, the true boundaries are 20.5 and 30.5, and both the interpolation formula and the ogive must use them. Plotting an ogive against upper class limits instead of upper boundaries loses marks even when the shape looks right. Give means to the accuracy demanded, usually one or two decimal places, keep units like marks or kg on final answers, and remember the median position for grouped work is n over 2, not n plus 1 over 2.
Worked questions, step by step
The marks of ten students in a test are 4, 6, 5, 8, 6, 7, 6, 9, 5 and 4. Find (a) the mean, (b) the median, (c) the mode.
- Sum the marks: 4 plus 6 plus 5 plus 8 plus 6 plus 7 plus 6 plus 9 plus 5 plus 4 equals 60.
- Mean equals 60 divided by 10 equals 6.
- Arrange in order: 4, 4, 5, 5, 6, 6, 6, 7, 8, 9. With ten values the median is the average of the 5th and 6th: (6 plus 6) divided by 2 equals 6.
- The mode is the most frequent value: 6 appears three times.
Answer: (a) mean = 6 (b) median = 6 (c) mode = 6
Where marks slip: M1 A1 for the mean, B1 for ordering before finding the median, A1 for the median, B1 for the mode. Forgetting to reorder the data before taking the middle is the classic dropped mark.
Try one yourself: Find the mean, median and mode of 2, 3, 7, 3, 5, 3, 7, 2, 8, 5. [Answer: mean 4.5, median 4, mode 3]
The table shows the scores of 20 students: score 1 with frequency 3, score 2 with frequency 5, score 3 with frequency 6, score 4 with frequency 4, score 5 with frequency 2. Calculate (a) the mean score, (b) the median, (c) the mode.
- Compute fx for each row: 3, 10, 18, 16 and 10. The sum of fx is 57 and the sum of f is 20.
- Mean equals 57 divided by 20 equals 2.85.
- Cumulative frequencies are 3, 8, 14, 18, 20. The median is the average of the 10th and 11th values, and both fall where the cumulative frequency first reaches 14, at score 3.
- So the median is 3, and the mode is the score with the largest frequency, which is 3.
Answer: (a) mean = 2.85 (b) median = 3 (c) mode = 3
Where marks slip: B1 for a correct fx column, M1 A1 for the mean, M1 A1 for locating the median by cumulative frequency. Dividing 57 by 5, the number of rows, instead of 20 is the error the question is designed to catch.
Try one yourself: Scores 0 to 4 have frequencies 2, 4, 7, 5 and 2. Find the mean. [Answer: 2.05]
The masses, in kg, of 30 students are grouped as: 40 to 44 with frequency 4, 45 to 49 with frequency 8, 50 to 54 with frequency 10, 55 to 59 with frequency 6, 60 to 64 with frequency 2. Calculate the mean mass.
- Take class midpoints: 42, 47, 52, 57 and 62.
- Multiply by frequencies to get fx: 168, 376, 520, 342 and 124.
- Sum of fx equals 1,530 and sum of f equals 30.
- Mean equals 1,530 divided by 30 equals 51 kg.
Answer: 51 kg
Where marks slip: B1 for correct midpoints, B1 for the fx column, M1 for sum fx over sum f, A1 for 51 kg with units. A wrong midpoint like 42.5 shifts every product, so check midpoints before multiplying anything.
Try one yourself: Classes 10 to 14, 15 to 19, 20 to 24 and 25 to 29 have frequencies 3, 7, 8 and 2. Find the mean. [Answer: 19.25]
The marks of 40 students are grouped as: 1 to 10 with frequency 5, 11 to 20 with frequency 9, 21 to 30 with frequency 12, 31 to 40 with frequency 8, 41 to 50 with frequency 6. Using the interpolation method, estimate (a) the median, (b) the lower quartile, (c) the interquartile range, correct to one decimal place.
- Cumulative frequencies: 5, 14, 26, 34, 40.
- Median position is n over 2 equals 20, which falls in the class 21 to 30 with lower boundary 20.5, frequency 12 and cumulative frequency before it of 14.
- Median equals 20.5 plus ((20 minus 14) divided by 12) times 10 equals 20.5 plus 5 equals 25.5.
- Lower quartile position is n over 4 equals 10, in class 11 to 20: 10.5 plus ((10 minus 5) divided by 9) times 10 equals 16.1 to one decimal place.
- Upper quartile position is 30, in class 31 to 40: 30.5 plus ((30 minus 26) divided by 8) times 10 equals 35.5.
- Interquartile range equals 35.5 minus 16.1 equals 19.4.
Answer: (a) median = 25.5 marks (b) lower quartile = 16.1 marks (c) interquartile range = 19.4 marks
Where marks slip: B1 for the cumulative frequency column, then M1 A1 per measure. The whole question hinges on class boundaries: using 21 instead of 20.5 as the lower boundary loses the accuracy mark in every part.
Try one yourself: For 30 students with classes 1 to 10, 11 to 20, 21 to 30, 31 to 40 and frequencies 4, 8, 10, 8, estimate the median. [Answer: 23.5]
A family's monthly income of GHc 5,400 is shown on a pie chart. The sectors are food 150 degrees, rent 90 degrees, school fees 70 degrees and savings x degrees. Find (a) the value of x, (b) the amount spent on food, (c) the amount saved.
- Angles in a pie chart sum to 360 degrees: x equals 360 minus (150 plus 90 plus 70) equals 50 degrees.
- Each degree represents 5,400 divided by 360 equals GHc 15.
- Food: 150 times 15 equals GHc 2,250.
- Savings: 50 times 15 equals GHc 750.
Answer: (a) x = 50 degrees (b) GHc 2,250 (c) GHc 750
Where marks slip: M1 A1 for x, then M1 for the fraction of 360 method and A1 for each amount. Writing the value per degree, GHc 15, as its own line is the cleanest way to secure the method mark.
Try one yourself: In a pie chart of N18,000, the transport sector is 80 degrees. How much goes on transport? [Answer: N4,000]
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Solve my question →Quiz me on this topicQuestions students ask
Do I have to draw the cumulative frequency curve, or can I just interpolate?
Do what the question asks. If it says draw a cumulative frequency curve and use it, the graph itself carries marks, scales, plotted points at upper class boundaries, and a smooth curve. If it says calculate or estimate, interpolation is fine.
What accuracy should statistics answers be given to?
Follow the instruction in the question, commonly one or two decimal places for means and quartiles. If no accuracy is stated, one decimal place is a safe habit, and exact values like 51 kg should be left exact.
Are these genuine WAEC past questions on statistics?
No. They are original questions built in the WASSCE format, same table styles, same mark weighting, because real past questions are WAEC copyright. Practising these prepares you for the real ones without copying them.