Grade 10 · Core Mathematics · Lesson 13 of 16

Interpreting Histograms and Frequency Polygons

A Grade 10 Core Mathematics CBE lesson from the sub-strand Statistics I. In it, learners construct a frequency distribution table from a histogram or frequency polygon.

Strand Statistics and ProbabilitySub-strand Statistics ILesson code 10CM-31-L1340 minutes · 3 slides

KICD learning outcome (e)

Interpret data from histograms and frequency polygons.

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

Construct a frequency distribution table from a histogram or frequency polygon
Identify the modal class from visual distributions
Calculate the mean of grouped data presented in histograms and frequency polygons

Key vocabulary

Modal class: The class interval that contains the highest frequency in a grouped frequency dataset.; The modal class for avocado bag masses is 30–34 kg with sixteen bags.
Grouped mean: An estimate of the average found using class midpoints and their frequencies.; The grouped mean mass of avocado bags was calculated as 32.2 kg.
Class midpoint: The middle value of a grouped class interval found by averaging upper and lower limits.; The class midpoint for petrol purchases between 12.5 and 17.5 litres is 15 litres.
Frequency polygon: A line graph connecting class midpoints plotted against their respective frequency values.; The frequency polygon shows milk supply levels across forty local dairy farmers.

Lesson preview

Slide 1 · Extracting Frequency Tables and Means from HistogramsModel · 12 min

Figure 1: A histogram displays the frequency of various bag masses in kilograms, highlighting the tallest bar as the modal class.

Histograms present continuous grouped data where rectangle widths match class boundaries and height reflects frequency. To find summary measures, extract a frequency table from the graph. The class interval with the tallest bar identifies the modal class. For the mean, multiply each class midpoint by its frequency, sum these products, and divide by total frequency.

Histograms display continuous grouped data using adjoining vertical bars drawn over exact class boundaries.
The modal class corresponds directly to the bar with the greatest height on the histogram.
Class midpoints are determined by averaging the lower and upper limits of each interval.
Calculating the grouped mean requires dividing the sum of midpoint-frequency products by the total frequency.

Worked example. Step 1: List classes, midpoints (

x

), and frequencies (

f

). 20–24:

x = 22, f = 6

25–29:

x = 27, f = 4

30–34:

x = 32, f = 18

35–39:

x = 37, f = 12

40–44:

x = 42, f = 2

Step 2: Identify the modal class with highest

f

f = 18

corresponds to class 30–34 kg. Step 3: Compute

f \times x

for each class and sum.

(6 \times 22) + (4 \times 27) + (18 \times 32) + (12 \times 37) + (2 \times 42) = 132 + 108 + 576 + 444 + 84 = 1344

Step 4: Calculate total frequency

N = 6 + 4 + 18 + 12 + 2 = 42

. Step 5: Divide total product by

N

Mean = \frac{1344}{42} = 32 kg

. Answer: (a) Table prepared; (b) Modal class = 30–34 kg; (c) Mean mass = 32 kg..

Check question: A histogram has class intervals 10–14, 15–19, and 20–24 with frequencies 4, 10, and 6 respectively. What is the grouped mean?

15.5
17
17.5
19.5

Show answer

17.5. The midpoints ( $x$ ) of the intervals are 12, 17, and 22. The products $f \times x$ are: $4 \times 12 = 48$ , $10 \times 17 = 170$ , and $6 \times 22 = 132$ . The sum $\sum f x = 350$ . The total frequency $N = 4 + 10 + 6 = 20$ . The grouped mean is $\frac{350}{20} = 17.5$ .

Slide 2 · Interpreting Data from Frequency PolygonsPractice · 14 min

Figure 2: A frequency polygon shows petrol purchases, with frequencies plotted at class midpoints and connected by straight lines.

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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