Interpreting Histograms and Frequency Polygons

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

1. Extract class frequencies and sub-group counts from histograms and frequency polygons.
2. Calculate demographic percentages and grouped means from graph representations.
3. Estimate the median of grouped data from combined statistical diagrams.

Key vocabulary

Demographic Group

A specific sub-population categorised by shared characteristics such as age or score ranges.

We calculated the percentage of the youth demographic group from the sub-county histogram.

Class Midpoint

The middle numerical value of a class interval used to compute grouped averages.

The class midpoint of 35 was multiplied by its frequency of 12.

Linear Interpolation

A mathematical method used to estimate intermediate values within a specific class interval.

Using linear interpolation, we estimated the median test mark to be 32.86.

Lesson preview

Slide 1 · Extracting Group Totals and Percentages from HistogramsModel · 12 min

Histograms display continuous numerical data using adjacent vertical bars over class boundaries. The height of each bar represents the frequency of that class interval. By combining frequencies across adjacent intervals, we can determine totals for specific sub-groups, such as age brackets or performance categories, and calculate their percentages relative to the total population.

• Histograms allow direct reading of frequencies from column heights across specified continuous class intervals.
• Sub-group totals are found by adding frequencies of adjacent bars covering the desired range.
• Percentages for specific demographic categories are calculated relative to the total dataset frequency.
• Upper and lower class boundaries define exact thresholds for filtering data groups correctly.

Worked example. Step 1: Total population $N=10+25+20+15+10=80$ residents. Step 2: Identify bars for 30 years and above: 30–40 (20), 40–50 (15), and 50–60 (10). Total = $20+15+10=45$ residents. Step 3: Identify youth bars (10–30 years): 10–20 (10) and 20–30 (25). Total youth = $10+25=35$ residents. Step 4: Calculate youth percentage: $\left(\frac{35}{80}\right)\times 100\mathrm{\%}=43.75\mathrm{\%}$. Answer: (a) 45 residents; (b) 43.75%.

Check question: A histogram shows test scores for 40 learners: 0–10 (4), 10–20 (8), 20–30 (14), 30–40 (10), 40–50 (4). Find the number of learners who scored 20 marks or higher, and find the percentage of learners who scored below 20 marks.

1. 28 learners; 30%
2. 24 learners; 30%
3. 28 learners; 70%
4. 12 learners; 70%

Show answer

28 learners; 30%. Learners scoring 20 or higher are in 20–30 (14), 30–40 (10), and 40–50 (4), giving $14+10+4=28$ learners. Learners below 20 are in 0–10 (4) and 10–20 (8), giving $4+8=12$ learners. The percentage of learners scoring below 20 marks is $\left(\frac{12}{40}\right)\times 100\mathrm{\%}=30\mathrm{\%}$.

Slide 2 · Calculating Mean and Identifying Mode from Frequency PolygonsPractice · 14 min

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