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MathidiaMathematics Academy
Statistics and data
Lesson 61 of 75
Introduction

Grouped frequency tables

Objective. Interpret grouped data and estimate totals.

  1. 1. Learn
  2. 2. Worked example
  3. 3. Practice
  4. 4. Feedback
  5. 5. Continue

Learn: the key idea

A grouped frequency table organises continuous or widely spread data into class intervals, such as 0–10 or 10–20, each paired with how many data values fall in that range. Because individual values are hidden within groups, totals like the estimated mean use the midpoint of each interval as a representative value. To estimate a total, multiply each midpoint by its frequency and sum these products. Example: for the interval 10–20 with frequency 4, the midpoint is 15, contributing 15 × 4 = 60 to the estimated total.

Worked example

A grouped frequency table shows 6 pupils scored between 20 and 30 marks. Find the midpoint used to estimate the total marks for this group.

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Bar chart of the values 6, 20, 30
  1. 1The interval boundaries are 20 and 30.
  2. 2Add the two boundaries together: 20 + 30 = 50.
  3. 3Divide by 2 to find the midpoint: 50 ÷ 2.
  4. 4The midpoint of this group is 25.

Answer: 25

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Practice

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Common mistake. Pupils often use the lower bound of each interval instead of the midpoint when estimating totals, which systematically underestimates the result; always average the interval's two boundary values first.

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