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📐 Mathematics - Class 7
Lesson 21 · Statistics

Frequency and Cumulative Frequency

MathematicsSubject
13 minEstimated read
Trading detail for shape

You give up knowing which mark belonged to whom, and in exchange you can see the shape of the whole set.

Tally marks and frequency

Group the tallies in fives, because a human eye counts fives far more reliably than eleven separate strokes.

Go through the data once, not once per value

Read the list once, in order. Always check at the end that the frequencies add up to the number of pieces of data you started with.

Grouping into classes

Six to ten classes usually works well: too few and the detail disappears, too many and the shape does not appear.

Classes must not overlap and must not leave gaps

0 to 10 then 10 to 20 leaves a mark of 10 in two classes. 0 to 9 then 11 to 20 leaves it in none. Every value must fit exactly one class.

Term What it means For the class 20 to 29
Class limitsThe smallest and largest values it holds20 and 29
Class sizeHow many values it covers10
Class markThe middle value24.5
FrequencyHow many pieces of data fall in itWhatever the tally gives
Grouping loses information for ever

Once you know seven students scored between 20 and 29, you no longer know whether they scored 20 or 29. Keep the original list.

Cumulative frequency answers a different question

Frequencies 3, 5, 7 and 4 give cumulative figures 3, 8, 15 and 19. The last one must equal the total number of pieces of data.

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Worked Example 1

Twenty students were asked how many brothers and sisters they have.

The raw data2, 1, 3, 0, 2, 4, 1, 2, 3, 1, 0, 2, 2, 5, 1, 3, 2, 1, 4, 2
Tally through the list onceRead in order, tallying in fives
The finished table0:2, 1:5, 2:7, 3:3, 4:2, 5:1
Check the total2+5+7+3+2+1 = 20, matching the students asked. Always do this check.
Worked Example 2

Forty test marks run from 12 to 67. Design suitable classes.

Find the rangeRange = 67 − 12 = 55
Choose the number of classes55 ÷ 6 is about 9, so use a class size of 10
Write the classes10–19, 20–29, 30–39, 40–49, 50–59, 60–69
Check for overlaps and gapsAfter 19 comes 20: nothing missed, nothing repeated.
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Activity 21.1

Survey your own class

What you needA question everyone can answer with a number, paper ruled into three columns.
Choose your questionNumber of people at home, minutes to reach school, or height in centimetres.
MethodCollect every answer in a list first, then tally through it once, in order.
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1

A frequency table trades individual detail for a shape you can see at a glance.

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1What is a frequency table for, and what does it cost you?
2Why should you tally through the data in order rather than searching for each value?
3What is wrong with the classes 0 to 10, 10 to 20, 20 to 30?
4How do you decide how many classes to use?
5What is cumulative frequency, and what kind of question does it answer?

Question 1 of 10

1A frequency table is useful because it
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Slide 1 of 4
Unit 21 · Frequency Tables

Frequency Tables

Mathematics · Grade 7

What You Will Be Able To Do

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Build a frequency table from raw data, using tally marks

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Design classes that do not overlap and do not leave gaps

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Work out cumulative frequency and use it to answer questions

⚖️

Say what a table shows you, and what it can never show you again

“

You give up knowing which mark belonged to whom, and in exchange you can see the shape of the whole set.

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Presenter notes: Open by reading out forty test marks as a list, slowly, and then asking the class what they learned from it. The honest answer is nothing, because nobody can hold forty numbers in mind at once. Then show the same forty marks as a table and ask again. That contrast is the entire justification for this unit and it takes about two minutes to demonstrate.