CSEC MATHEMATICS · MODULE 2 · LESSON B1

Collecting Data: Samples, Frequency Tables, Bar Charts and Pie Charts

Population and sample, the four levels of measurement, building a frequency table, drawing and reading bar charts and pie charts.

Intermediate Secondary Level MathematicsM2 1.1M2 1.2M2 1.3M2 1.7≈ 35 min🎮 3 games
Before you start

By the end of this lesson you can…

Step 1 · Watch

Explainer video

5 narrated scenes. Press play, listen and read along — the points appear as they are explained. Use ‹ Prev / Next › or the scene bar to jump to any scene.

LESSON B1 · EXPLAINER

Collecting Data: Samples, Frequency Tables, Bar Charts and Pie Charts

Every poll, every weather report, every sales chart starts with the same question: how was the data collected, and how is it shown?

Narration uses your device’s built-in voice. No sound? Switch to “Captions only” — the captions advance on their own.

Step 2 · Read

Key notes

Copy these into your notebook in your own words — that is how they stick.

Population & sample

Population = whole group; sample = part measured. Statistic (sample) vs parameter (population). Random, representative samples avoid bias.

Levels of measurement

Nominal (names), ordinal (order), interval (equal gaps, no true zero), ratio (true zero).

Discrete vs continuous

Discrete: counted (siblings). Continuous: measured (height, time).

Frequency table

Tally → frequency; check Σf equals the number of items.

Bar chart

Equal widths, gaps, even scale, labelled axes and title.

Pie chart

Angle = f ÷ total × 360°; f = angle ÷ 360 × total; angles sum to 360°.

Reading diagrams

Find modes (tallest bar / biggest sector), compare categories, spot trends.

Misleading graphs

Truncated axes, uneven scales and 3-D effects distort the message.

EXAM TIPS & COMMON MISTAKES

  • Always add a total row and check the frequencies sum to the number of items collected.
  • In a pie chart show your working: f ÷ total × 360 for each sector, then check they add to 360°.
  • Bar chart: gaps between bars (discrete); histograms (Module 3) have no gaps.
  • Say what a graph shows in words — “most students have two siblings” — not only the numbers.
Play & practise

Games

3 quick games on this lesson. Earn XP and badges as you play — your best score for each game is saved. Games are for practice and do not change your exam readiness. More games in the Mathematics Arcade.

Step 3 · Practise

Paper 1 practice — multiple choice

8 items modelled on real CSEC Paper 1 questions. Choose one answer for each, then check. Aim for 80% or better. Work each item on paper first.

CSEC Paper 01 style · SO 1.1

1. A researcher interviews 50 students chosen at random from a school of 800 students. The 800 students are the

Answer: D. The whole group of interest is the population.
CSEC Paper 01 style · SO 1.7 (levels of measurement)

2. Exam grades A, B, C, D, E are an example of which level of measurement?

Answer: A. They can be ordered but the gaps are not equal.
CSEC Paper 01 style · SO 1.2

3. Which of the following is continuous data?

Answer: B. Height is measured and can take any value in a range.
CSEC Paper 01 style · SO 1.3

4. In a survey of 180 students, 45 chose cricket. In a pie chart, the angle of the cricket sector is

Answer: C. 45/180 × 360 = 90°.
Adapted from CSEC P1 May/June 2024 (pie chart item)

5. The pie chart shows how a student used 12 hours. The sector for Mathematics is 90°. The time spent on Mathematics is

Answer: D. 90/360 × 12 = 3 hours.
CSEC Paper 01 style · SO 1.2

6. A frequency table for 20 students shows frequencies 3, 6, x, 3, 1. The value of x is

Answer: C. 3 + 6 + x + 3 + 1 = 20 → x = 7.
CSEC Paper 01 style · SO 1.1

7. Which of the following would give the most biased sample of students for a survey on the school canteen?

Answer: A. Students who arrive at the canteen first are the ones who use it most, so they do not represent everyone.
CSEC Paper 01 style · SO 1.3

8. The angles in a pie chart must add up to

Answer: B. A full circle is 360°.
Step 4 · Apply

Paper 2 practice — structured questions

Write full answers, then reveal the mark scheme and tick the points you earned (16 marks in total). Show all your working — method marks count. Your answers are saved on this device.

CSEC Paper 02 style · Module 2 (Statistics 1)

Question 1 [9 marks]

The number of siblings of 20 students is recorded: 2, 1, 0, 3, 2, 1, 1, 2, 0, 4, 2, 1, 3, 2, 1, 0, 2, 1, 2, 3.

(a) Construct a frequency table for the data. [3]

MARK SCHEME — (a) (max 3)

(b) State the modal number of siblings and the type of data (discrete or continuous). [2]

MARK SCHEME — (b) (max 2)

(c) Calculate the angle for each sector in a pie chart of this data. [4]

MARK SCHEME — (c) (max 4)

CSEC Paper 02 style · Module 2 (Reading pie charts and sampling)

Question 2 [7 marks]

A pie chart shows the favourite subject of 72 students. The sectors are: Mathematics 100°, English 80°, Science 120°, Other 60°.

(a) How many students chose each subject? [4]

MARK SCHEME — (a) (max 4)

(b) A school has 1 200 students. The principal surveys the 30 students in one Form 5 class about the school canteen. Give TWO reasons why this sample may be biased. [2]

MARK SCHEME — (b) (max 2)

(c) Suggest a better way to choose a sample of 30 students. [1]

MARK SCHEME — (c) (max 1)

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Sources

Where this topic appears in CSEC papers

Find these in your own past-paper booklets for extra timed practice. Items above are written in the style of these papers; any adapted from a specific question say so.