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Grade 10 · Core Mathematics · Lesson 4 of 16

Constructing Frequency Distribution Tables for Grouped and Ungrouped Data

A Grade 10 Core Mathematics CBE lesson from the sub-strand Statistics I. In it, learners prepare an ungrouped frequency distribution table from raw discrete data using tally marks.

Strand Statistics and ProbabilitySub-strand Statistics ILesson code 10CM-31-L440 minutes · 3 slides

KICD learning outcome (b)

Draw a frequency distribution table for grouped and ungrouped data.

By the end of this lesson, learners should be able to

  1. Prepare an ungrouped frequency distribution table from raw discrete data using tally marks.
  2. Group continuous or large discrete data into equal class intervals to construct a frequency distribution table.
  3. Identify class limits, class intervals, and modal classes from grouped data tables.

Key vocabulary

Frequency
The total number of times a specific value occurs in a dataset.
The frequency of scoring two goals in the handball dataset is four.
Class interval
A range of values used to group continuous or large discrete numerical data.
The class interval 70–74 includes all vehicle speeds measured within that range.
Modal class
The class interval that contains the highest frequency in a grouped dataset.
The modal class for M-Pesa transactions is 20–24 with a frequency of seven.

Lesson preview

Slide 1 · Ungrouped Frequency Distribution TablesOpening · 12 min
An ungrouped frequency distribution table showing tally marks and exact frequencies for goals scored.
Figure 1: An ungrouped frequency distribution table showing tally marks and exact frequencies for goals scored.

When summarising discrete data with few unique values, we use an ungrouped frequency distribution table. The table consists of three main columns: the variable value, tally marks, and the frequency f. Tallies are written in groups of five using four vertical strokes and one diagonal cross-stroke. Counting the tallies yields the exact frequency of each raw score, providing a clear visual summary of the entire collection. Use Figure 1 to identify the three main columns used in an ungrouped frequency table.

  • Ungrouped frequency distribution tables organise distinct discrete data values without grouping them into ranges.
  • A tally column uses vertical stroke marks to count how many times each raw score appears.
  • The frequency f represents the total count of tally marks for a specific individual score.
  • Summing all frequencies in the table gives the total number of observations in the dataset.
Worked example. Step 1: Identify distinct score values in ascending order: 0, 1, 2, 3, 4. Step 2: Tally each match score into column 2: 0: || (2) 1: |||| (4) 2: |||| (4) 3: ||| (3) 4: || (2) Step 3: Write down the corresponding frequency values in column 3 and sum them: ∑f=2+4+4+3+2=15. Answer: Frequency distribution table: Goals 0 (f=2), Goals 1 (f=4), Goals 2 (f=4), Goals 3 (f=3), Goals 4 (f=2); Total frequency = 15..

Check question: In a survey of 16 families, the number of pets per family is recorded as: 0, 1, 2, 1, 0, 3, 2, 1, 1, 0, 2, 1, 3, 1, 2, 1. What is the frequency of families having exactly 1 pet?

  1. 3
  2. 4
  3. 7
  4. 8
Show answer

7. To find the frequency of families with exactly 1 pet, tally the number of times 1 appears in the dataset. The occurrences are at the 2nd, 4th, 8th, 9th, 12th, 14th, and 16th positions. Counting the occurrences of the number 1 gives a total frequency of 7.

Slide 2 · Grouped Frequency Distribution Tables with Specified IntervalsPractice · 14 min
A grouped frequency distribution table summarising vehicle speeds using tally marks and equal class intervals.
Figure 2: A grouped frequency distribution table summarising vehicle speeds using tally marks and equal class intervals.

Teach the full lesson on the projector

This lesson, and every other Grade 1–10 CBE lesson, comes ready to project with the EAP ClassKit. It runs without electricity or internet.

  • All 3 slides with diagrams and class activities
  • Teacher notes, SNE adaptations and assessment checks
  • Homework and the other 15 lessons in this sub-strand
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All 16 lessons in Statistics I

  1. 1Gathering Data from Practical SituationsCollect data from real-life sources
  2. 2Frequency Distribution Tables for Ungrouped and Grouped DataDraw a frequency distribution table for grouped and ungrouped data
  3. 3Drawing Grouped Frequency Distribution TablesDraw a frequency distribution table for grouped and ungrouped data
  4. 4Constructing Frequency Distribution Tables for Grouped and Ungrouped DataDraw a frequency distribution table for grouped and ungrouped data
  5. 5Calculating Averages and Middle Values of Raw DataDetermine mean, mode and median of grouped and ungrouped data
  6. 6Determining Median of Data and Introduction to Grouped Data MeanDetermine mean, mode and median of grouped and ungrouped data
  7. 7Determining Mean, Modal Class, and Median of Grouped DataDetermine mean, mode and median of grouped and ungrouped data
  8. 8Determining Mean, Mode, and Median of Grouped and Ungrouped DataDetermine mean, mode and median of grouped and ungrouped data
  9. 9Representing Data Using Histograms and Frequency PolygonsRepresent data using histograms and frequency polygons
  10. 10Constructing Histograms and Frequency PolygonsRepresent data using histograms and frequency polygons
  11. 11Advanced Data Representation: Histograms and Frequency PolygonsRepresent data using histograms and frequency polygons
  12. 12Interpreting Data from Histograms and Frequency PolygonsInterpret data from histograms and frequency polygons
  13. 13Interpreting Histograms and Frequency PolygonsInterpret data from histograms and frequency polygons
  14. 14Interpreting Histograms and Frequency PolygonsInterpret data from histograms and frequency polygons
  15. 15Data Collection, Organisation, and Informed Decision MakingPromote data collection, organisation and representation for informed decision making
  16. 16Data Interpretation and Decision MakingPromote data collection, organisation and representation for informed decision making