Data Interpretation and Decision Making

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

1. Extract total frequency, specific interval counts, and calculate the mean from a frequency graph.
2. Calculate age bracket percentages from demographic histograms to inform community resource allocation.
3. Formulate and justify data-driven decisions based on statistical representations.

Key vocabulary

Informed Decision

A choice made after collecting, organising, and analysing relevant numerical data and statistical graphs.

The soft drink manufacturing company made an informed decision after calculating a mean sales volume.

Frequency Polygon

A line graph joining class-midpoint frequencies, closed on the horizontal axis at both ends.

The polygon peaked at midpoint 25.5, so class 21–30 crates had most outlets.

Demographic Data

Socioeconomic statistics describing population characteristics such as age groups, income levels, or gender distributions.

Sub-county officers used demographic data to allocate funding for elderly healthcare and youth training.

Class Interval

A range of numerical values used to group continuous data into manageable demographic categories.

The census histogram used a class interval of twenty to thirty-nine years for the youth bracket.

Lesson preview

Slide 1 · Interpreting Frequency Graphs for Commercial DecisionsModel · 18 min

Statistical representations such as frequency graphs condense raw data into actionable insights for decision making. For example, a soft drink manufacturing company analyses sales data across different flavours or bottle sizes using frequency graphs to determine consumer preferences. The information obtained can be used to make operational decisions, such as deciding to manufacture a popular brand in large quantities to meet high market demand while reducing production of slower-selling lines, thereby optimising profit and inventory management.

• Frequency polygons provide a clear visual display of distribution trends and peak activity across grouped data intervals.
• Summing category frequencies yields total participants, enabling percentage calculations across specific customer volume ranges.
• Statistical information obtained from frequency graphs enables a soft drink manufacturing company to produce popular brands in large quantities.
• Data-driven decisions help businesses optimise product inventory, staffing levels, and customer service efficiency.

Worked example. Total outlets $N=12+28+40+16+4=100$. Outlets selling between 11 and 30 crates = $28+40=68$ outlets. Find class midpoints ($x$): 5.5, 15.5, 25.5, 35.5, 45.5. Calculate $\sum fx=(12\times 5.5)+(28\times 15.5)+(40\times 25.5)+(16\times 35.5)+(4\times 45.5)=66+434+1020+568+182=2270$. Mean volume $\bar{x}=\frac{2270}{100}=22.7\text{ crates}$. Answer: Total outlets = 100; outlets selling 11–30 crates = 68; mean volume = $22.7\text{ crates}$..

Check question: A soft drink manufacturing company's frequency graph shows that 68 out of 100 outlets sell between 11 and 30 crates of a tropical brand monthly. What is this proportion as a percentage, and what informed decision should the company make regarding brand production?

1. $68\mathrm{\%}$; manufacture the tropical brand in large quantities to satisfy the strong market demand.
2. $68\mathrm{\%}$; reduce production because the brand does not sell over 30 crates in most outlets.
3. $32\mathrm{\%}$; base production solely on the few outlets selling over 40 crates.
4. $32\mathrm{\%}$; stop manufacturing the tropical brand completely because demand is too low.

Show answer

$68\mathrm{\%}$; manufacture the tropical brand in large quantities to satisfy the strong market demand. The percentage of outlets selling 11-30 crates is $\frac{68}{100}\times 100\mathrm{\%}=68\mathrm{\%}$. Since a large majority ($68\mathrm{\%}$) of the retail outlets show high sales, the data indicates strong market demand. This justifies an informed decision to manufacture the tropical brand in large quantities to meet retail needs and optimise profit.

Slide 2 · Analysing Demographic Data for Community PlanningPractice · 22 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.

• Both 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