Mathematics · Interactive learning companion

Weighted Average: Frequency Distribution

Calculate a weighted mean from a frequency distribution without treating distinct values as equally frequent.

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📝 Description

Weighted Average: Frequency Distribution is a statistics activity for learning how repeated values and frequencies affect averages. Students practice reading frequency tables, applying weighted mean ideas, and connecting data representation with calculation. It supports exam revision and classroom practice.

📋 Instructions

Study each frequency distribution, calculate the required average, and answer the questions. Repeat rounds to improve accuracy with data tables.

🎓 Learning Guide: Weighted Average: Frequency Distribution

Learning focus: Calculate a weighted mean from a frequency distribution without treating distinct values as equally frequent.

Mathematics Interactive learning companion

Learning objectives

Interpret a frequency as the number of occurrences.
Use Σfx/Σf to calculate the arithmetic mean from a discrete frequency table.

Concepts and principles

For values x with frequencies f, mean = (Σfx)/(Σf).
A value occurring many times contributes proportionally more to the total than a rare value.

Examples and worked solutions

Values 2 and 4 occur 3 and 1 times respectively. Find the mean.: Worked solution: (2×3+4×1)/(3+1)=10/4=2.5.

Guided practice

From each displayed table, multiply each value by its frequency before summing.
Divide by the total frequency, not the number of distinct rows.

Expected observations and explanations

Averages of listed rows are generally wrong when the frequencies differ.

Assessment questions and answers

Why not divide by 2, the number of distinct values?: Answer: There are four observations altogether, as shown by the frequency total.

🎯 Categories

Mathematics Grade 9 Grade 10 Grade 12 Grade 11 CBSE

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