Data Collection and Frequency Tables

Tally charts, frequency distribution tables, vertical/horizontal bar charts, and pie chart sector angles.

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Curated Video Lesson

Visual explanation and practical step-by-step walk-through

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Comprehensive Study Notes

Aligned with Ghana NaCCA & WAEC BECE syllabus standards

Topic Introduction & Real-World Context:

Data collection and presentation is the foundation of statistics. In an information-driven world, organizing raw figures into structured frequency tables, bar charts, and pie charts allows governments, health agencies, and schools to identify trends and make decisions. In BECE mathematics, constructing frequency distribution tables and drawing charts appear regularly in both papers.

What You Will Master in This Lesson (NaCCA Objectives):

Collect and record discrete data using tally marks.

Construct ungrouped frequency distribution tables from raw data.

Draw and interpret vertical and horizontal bar charts.

Calculate sector angles and interpret simple pie charts.

1. Raw Data and Tally Charts

Raw data consists of numbers or categories collected before any organization. • Tally Marks: Recorded in bundles of 5 (|||| with a slash across). This allows rapid counting. • Frequency (f): The number of times a particular score occurs. • Total Frequency (Σf or n): Sum of all frequencies, representing total sample size.

2. Constructing Bar Charts

A bar chart uses rectangular bars of equal width to show categorical frequencies: • The height (or length) of each bar represents the frequency. • Spaces between bars must be EQUAL. • Both axes must be clearly labeled (e.g. "Subject" on horizontal axis, "Number of Students" on vertical axis).

3. Pie Charts: Sector Angle Calculation

A pie chart is a circular statistical graphic divided into slices (sectors). The entire circle equals 360°. Formula for Sector Angle of a Category: Angle = (Frequency of category / Total Frequency) × 360° Check: The sum of all sector angles MUST equal 360°.

Common Mistakes Students Make in BECE Examinations:

⚠️Drawing touching bars for a bar chart (touching bars are for histograms, not bar charts!).

⚠️Miscounting raw data when making tally marks.

⚠️Sector angles not adding up to 360° due to rounding errors.

Teacher's BECE Exam Pro-Tips:

⭐Cross out numbers on the question paper as you tally them to ensure no scores are missed.

⭐Check that Σf matches the total count given in the question statement.

⭐Label axes with titles and units on your graph sheet.

Quick Revision Summary Checklist:

Tally marks are grouped in bundles of 5.

Bar chart: bars have equal width and equal spaces between them.

Pie chart sector angle = (f / Σf) × 360°.

Total angles in pie chart = 360°.

Step-by-Step Worked Examples (1)

Real BECE exam-standard problems with complete solution steps

Example 1: Sector Angle for Pie Chart

Problem StatementIn a class of 40 students, 10 prefer Football. What is the sector angle for Football in a pie chart?

Step-by-Step Solution:

Step 1: Formula: Angle = (Frequency / Total) × 360°.

Step 2: Angle = (10 / 40) × 360° = ¼ × 360° = 90°.

💡

Key Takeaway / Exam Rule: All sector angles in a pie chart must sum to 360°.

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