Topic
Statistics
Sub-Topic
Statistics presentations and measures of central tendency
General Competences
Critical Thinking, Problem Solving, Analytical Thinking
Specific Competences
Apply statistics in making informed decisions in real life
Learning Activities
Collecting data from the environment using various ways
Expected Standard
Statistics applied in making informed decisions in real life appropriately
References
Secondary education ordinary level form 1-4
Critical Thinking, Problem Solving, Analytical Thinking
Lesson Goal
By the end of this lesson, learners should be able to collect data from the school environment using tally and survey methods, present the data in a frequency table, and calculate the mean, median, and mode of the data set in order to draw simple conclusions that can inform everyday decisions.
Rationale
This lesson develops Critical Thinking, Problem Solving, and Analytical Thinking by building on learners' prior knowledge of counting, ordering numbers, and simple arithmetic from primary school, extending these skills into formal statistical presentation and the calculation of measures of central tendency. Understanding how to collect, organise, and interpret data is essential for making informed decisions in learners' daily lives – for example, comparing prices at the market, analysing class test scores, or interpreting local rainfall patterns. Using a learner-centred, inquiry-based approach grounded in the 5E instructional model, the lesson engages learners in hands-on data collection from the environment and guides them to apply statistical concepts to real-life Zambian contexts, thereby developing both the specific competence of applying statistics in making informed decisions and the broader competences of critical and analytical thinking.
Prior Knowledge / Prerequisite Knowledge
Form 1 learners are expected to know how to count and tally objects, perform basic addition and division, read and interpret simple tables, and understand the concept of "most common" from primary school Mathematics (Grades 5–7). This prior knowledge will be activated at the start of the lesson through an oral hook about a market vendor, followed by targeted questions asking learners to recall how they count items and what "average" means in everyday language, thus bridging their existing understanding to the formal statistical concepts of mean, median, and mode.
Learning Environment
- Natural Environment: The school compound and surrounding community provide an immediate, authentic context for data collection – e.g., counting different types of trees, recording the number of learners wearing school shoes versus sandals, or noting crop types in the school garden. The teacher can refer to these local features during the EXPLORE phase to make data collection meaningful and relevant.
- Artificial Environment: The classroom is arranged into groups of 5–6 learners with desks pushed together to form shared workstations. Each workstation displays a large chart paper for recording group data, and a central "Data Corner" board on the wall shows a class tally chart and a pre-prepared example of a frequency table and measures of central tendency. Chairs face the front briefly during the EXPLAIN phase, then return to group configuration for ELABORATE.
- Technological Environment: A basic calculator (one per group, if available) supports calculation of the mean; alternatively, the teacher may use a projector or smartphone with a calculator app displayed on a screen to demonstrate step-by-step calculation. A short 2-minute video clip (downloaded offline or on a memory stick) showing a Zambian market vendor using records to decide what to sell can be shown during the ENGAGE phase to spark curiosity.
Teaching and Learning Materials / Resources
- Chart paper (one sheet per group) and marker pens for recording data
- Pre-printed tally sheets and frequency table templates (one per learner)
- Data cards with pre-collected local datasets (e.g., rainfall in Lusaka, crop yields in Mkushi) for the ELABORATE phase
- A large class tally chart poster with sticky notes or magnets
- Worksheet with guided questions for each phase
- A 2-minute video clip of a Zambian market vendor discussing stock decisions (teacher-prepared or sourced locally)
- Calculators (one per group, if available)
- Coloured counters or bottle tops for hands-on demonstration of median and mode
Cross-Cutting Issues
- Financial Education: The lesson uses a market vendor scenario in which learners calculate the mean number of tomatoes sold per day to decide how many to stock next week. This directly embeds financial decision-making into statistical analysis, teaching learners that data can guide spending, pricing, and stock management in real-life business contexts.
- Environmental Sustainability: During the EXPLORE phase, learners collect data from the school environment (e.g., types of trees, waste bins, water points). The teacher guides them to reflect on how such data can be used to monitor environmental resources, reduce waste, and promote sustainable practices within the school community – connecting statistical thinking to ecological awareness.
Lesson Progression (Model: 5E Model of Instruction)
| Phase |
Teacher Activities |
Learner Activities |
Assessment Criteria |
| INTRODUCTION |
ENGAGE 6 min |
- Hook: "Good morning, learners! Imagine you are a vegetable vendor at Lusaka's City Market. Every day you sell tomatoes, and at the end of the week you want to know how many tomatoes you usually sell each day so you can decide how many to bring next week. How could you figure that out?" (Pause for 2–3 responses.)
- Prior Knowledge Questions: Ask: "How do we count and record the number of items we see around us?" and "What does the word 'average' mean to you? Can you give me an example from everyday life?" and "Can you name one way to organise numbers so they are easy to read?"
- Lesson Goal: "Today we are going to learn how to collect data from our environment, present it in a frequency table, and calculate the mean, median, and mode — the three measures of central tendency — so that we can make informed decisions just like that market vendor."
- Note: Do NOT teach the new concept yet — this phase is purely about igniting curiosity and surfacing prior knowledge.
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- Learners respond to the hook by sharing their ideas about counting and averaging, drawing on everyday experiences. (Develops: Critical Thinking)
- Learners answer prior knowledge questions orally, demonstrating recall of counting, tallying, and the everyday meaning of "average". (Develops: Analytical Thinking)
- Learners listen to and repeat the lesson goal in their own words, showing awareness of what they will learn. (Develops: Communication)
- Learners raise questions or express curiosity about the topic, such as asking how vendors actually use numbers. (Develops: Critical Thinking)
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- Learners accurately recall what "average" means in an everyday context.
- Learners confidently explain one way they have counted or organised numbers before.
- Learners appropriately restate the lesson goal in their own words.
- Learners clearly articulate at least one question or curiosity about the topic.
|
| DEVELOPMENT |
EXPLORE 8 min |
- Learning Activities: "Now you will collect data from our school environment using different methods. Each group will choose one of the following: (a) count the number of learners wearing black shoes vs. brown shoes, (b) count the number of different tree types in the school compound, or (c) survey 10 learners on their favourite local fruit. You will use tally marks to record your data on the chart paper provided."
- Investigation Setup: "In your groups of 5–6, decide which data you will collect. Take your tally sheet and chart paper. You have 4 minutes to collect your data outside or in the classroom corridors. Remember to count carefully and record every observation using tally marks. Return to your seats when the timer sounds."
- Facilitation: Walk around among groups without lecturing. Ask guiding questions: "How are you keeping track of your counts?" and "What will you do if two items have the same tally?" and "How will you make sure your counts are accurate?"
- Observation: Note which groups are using tally marks correctly and which groups need a guiding nudge to stay organised.
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- Learners decide on a data collection method as a group and begin collecting data using tally marks on their chart paper. (Develops: Collaboration, Analytical Thinking)
- Learners record observations systematically, using tally marks for each item counted or surveyed. (Develops: Analytical Thinking)
- Learners discuss findings within their group, comparing counts and checking for accuracy. (Develops: Collaboration, Critical Thinking)
- Learners write a brief summary on their chart paper of what they observed and how many items they counted. (Develops: Communication, Analytical Thinking)
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- Learners correctly use tally marks to record data from the environment.
- Learners accurately transfer their observations onto chart paper in an organised format.
- Learners appropriately discuss and verify group counts with peers.
- Learners clearly write a short summary of their collected data.
|
EXPLAIN 8 min |
- Learner Sharing: "Group 1, what did you discover? Group 2, what method did you use? Let's hear your findings." Invite 2–3 groups to share their collected data with the class before teaching.
- Formalisation: "What you have created is called a tally table. When we organise tally marks into a table with numbers, we call it a frequency table. The numbers that describe the centre of the data are called measures of central tendency: the mean (the total divided by the number of items), the median (the middle value when data is ordered), and the mode (the value that appears most often)." Write definitions on the board with examples.
- Worked Example: On the board, write: "Data set: 4, 6, 6, 8, 10. Step 1 – total = 34; Step 2 – number of items = 5; Step 3 – mean = 34 ÷ 5 = 6.8. Ordered: 4, 6, 6, 8, 10 → median = 6. Mode = 6 (appears twice)." Think aloud at each step.
- Guided Questions: Ask: "What is the mean of 2, 4, 6? (Answer: 4)" and "What is the median of 1, 3, 5, 7? (Answer: 4)" and "What is the mode of 3, 3, 4, 5, 5, 5? (Answer: 5)." Build on responses.
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- Learners share their group's data and method with the class, describing what they found. (Develops: Communication, Collaboration)
- Learners write formal definitions of tally table, frequency table, mean, median, and mode in their exercise books. (Develops: Analytical Thinking)
- Learners follow the worked example on the board, copying each step and checking their understanding. (Develops: Problem Solving)
- Learners attempt the three guided questions orally or on a mini-whiteboard, and self-check or peer-check answers. (Develops: Critical Thinking, Problem Solving)
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- Learners clearly describe their group's data collection method and findings.
- Learners accurately record the formal definitions of statistical terms.
- Learners correctly follow the worked example step by step.
- Learners correctly calculate mean, median, and mode in guided questions.
|
ELABORATE 12 min |
- New Task: "Now turn to the data card on your desk. It shows the daily rainfall (in mm) recorded in Mongu for two weeks in January: 12, 15, 10, 18, 14, 20, 16, 13, 17, 19, 11, 14, 15, 13. As a group, complete the following: (a) organise the data into a frequency table, (b) calculate the mean, (c) find the median, and (d) identify the mode. Then write one sentence about what this data tells a farmer planning when to plant maize."
- Instructions: "Work with your group. You have 7 minutes. Use your exercise books to show all working. I will be walking around to listen to your discussions — I am not giving answers, only prompts."
- Facilitation: Walk around, observe, and offer probing questions only: "How did you order the data to find the median?" and "What does the mode tell you about the most common rainfall amount?"
- Extension: For groups that finish early: "Create a second frequency table using your group's original collected data and calculate its mean, median, and mode. Compare the two sets of results."
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- Learners read the new task aloud within their group and discuss what each part requires. (Develops: Analytical Thinking, Collaboration)
- Learners organise the rainfall data into a frequency table and calculate the mean, median, and mode using the steps taught. (Develops: Problem Solving, Analytical Thinking)
- Learners record all working and final answers in their exercise books, showing step-by-step calculations. (Develops: Problem Solving)
- Selected learners present their group's frequency table, calculated measures, and the sentence advising the farmer to the class, followed by peer discussion. (Develops: Communication, Critical Thinking)
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- Learners accurately identify the task requirements through group discussion.
- Learners correctly construct a frequency table and calculate the mean, median, and mode from the rainfall data.
- Learners independently record complete working and correct answers in their exercise books.
- Learners logically justify their advice to the farmer based on the calculated measures of central tendency.
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| CONCLUSION |
EVALUATE 6 min |
- Consolidation Questions: Ask: "What is the difference between the mean and the median of a data set?" and "Why might a market vendor use the mode when deciding which vegetable to stock the most of?" and "How does a frequency table help us see patterns in data?"
- Learner-Led Summary: Invite 2–3 learners to summarise the key learning points in their own words. Affirm correct responses and gently correct any misconceptions.
- Link Forward: "Next week we will learn how to draw bar graphs and pie charts from the frequency tables we made today. This will help us present data visually."
- Homework: "For homework, collect any set of 10 numbers from your home or community — for example, the ages of your family members, the prices of 10 different items at the market, or the number of steps to 10 different places. Bring the data to our next class. Write the data in your exercise book and calculate the mean, median, and mode. Due next lesson."
- Closure: "Well done, everyone! Today you became data collectors and decision-makers. I am proud of your teamwork and thinking."
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- Learners respond to consolidation questions individually or as a class, demonstrating their understanding of mean, median, mode, and frequency tables. (Develops: Critical Thinking, Analytical Thinking)
- Learners summarise the key learning points in their own words when invited by the teacher. (Develops: Communication)
- Learners record the homework task in their exercise books, ensuring they understand what data to collect. (Develops: Problem Solving)
- Learners reflect briefly on what they found most interesting or most challenging about collecting and analysing data. (Develops: Critical Thinking)
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- Learners correctly explain the difference between mean, median, and mode in consolidation responses.
- Learners accurately summarise the key concepts taught during the lesson.
- Learners appropriately note the homework instructions for completion.
- Learners clearly articulate one or more reflections on the learning experience.
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Class Exercise
Instructions to learners: Answer all five questions in your exercise book. Show all working where applicable. Time allowed: 10 minutes.
- Multiple Choice Question — Which measure of central tendency is found by adding all the values and dividing by the total number of values?
A) Median
B) Mode
C) Mean
D) Range
- Fill-in-the-Blank — A ________ table organises data by listing each value alongside the number of times it occurs, often using tally marks to count frequencies.
- Short Answer Question — Explain in one sentence how you would find the median of a data set that has an even number of values. Give an example with the numbers 4, 8, 10, and 14.
- Problem-Solving Question — The following are the distances (in kilometres) that 8 learners travel to school each day: 3, 5, 2, 7, 5, 4, 6, 4.
a) Present this data in a frequency table.
b) Calculate the mean distance.
c) Identify the mode.
- Application and Analysis Question (Real-Life Zambian Context) — A small-scale baker in Matero, Lusaka, recorded the number of loaves of bread she sold each day for one week: Monday 45, Tuesday 52, Wednesday 48, Thursday 55, Friday 50, Saturday 62, Sunday 38.
a) Calculate the mean number of loaves sold per day.
b) Based on the mean, how many loaves should the baker prepare each day to meet average demand without producing too many left unsold? Explain your reasoning.
c) If the mode of the data is 45, what does that tell you about the sales pattern?
Answer Key (For Teacher Use Only)
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Question 1 — Multiple Choice Question
Answer: C) Mean
Marks: 1 mark for correct letter.
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Question 2 — Fill-in-the-Blank
Answer: frequency
Marks: 1 mark for the correct word.
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Question 3 — Short Answer Question
Answer: When a data set has an even number of values, the median is the average (mean) of the two middle numbers. For 4, 8, 10, 14, the two middle numbers are 8 and 10, so the median is (8 + 10) ÷ 2 = 9.
Marks: 1 mark for correct explanation; 1 mark for correct example and calculation. Total: 2 marks.
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Question 4 — Problem-Solving Question
Answer:
a) Frequency table: Value 2 → 1, 3 → 1, 4 → 2, 5 → 2, 6 → 1, 7 → 1.
b) Mean = (3 + 5 + 2 + 7 + 5 + 4 + 6 + 4) ÷ 8 = 36 ÷ 8 = 4.5 km
c) Mode = 4 and 5 (both appear twice) → bimodal
Marks: 1 mark for correct frequency table; 1 mark for correct mean calculation; 1 mark for correct mode(s). Total: 3 marks.
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Question 5 — Application and Analysis Question (Real-Life Zambian Context)
Answer: