P6 Mathematics - Term II

Topic 6: Data Handling

Lesson 4: Simple Statistics - Mean, Median, and Mode

Duration: 45 minutes

Learning Objectives

By the end of this lesson, you will be able to:

• Define mean, median, and mode
• Calculate the mean (average) of a set of data
• Find the median (middle value) of a set of data
• Identify the mode (most common value) of a set of data
• Understand when each measure is useful

What are Statistics?

Statistics are special numbers that help us understand a whole set of data

Why use statistics?

• Summarize lots of data with one number
• Find the "typical" or "representative" value
• Make comparisons easier
• Help us make decisions

Example: What's the average test score in our class?

Three Important Statistics

Today we learn three measures:

1. Mean = The average of all numbers
2. Median = The middle number when arranged in order
3. Mode = The number that appears most often

Each tells us something different!

Understanding the Mean

Mean = Average value

The formula:

Mean = Sum of all values ÷ Number of values

In words:
Add up all the numbers, then divide by how many numbers there are

Example 1: Calculating the Mean

Test scores: 60, 70, 80, 70, 90

Four-step problem solving:

Understand: Find the average test score
Plan: Add all scores, divide by how many scores
Work: (60 + 70 + 80 + 70 + 90) ÷ 5 = 370 ÷ 5 = 74
Answer: The mean score is 74 marks

Example 2: Ages

Ages of family members: 8, 12, 35, 38, 5

Calculate the mean:

Sum = 8 + 12 + 35 + 38 + 5 = 98
Number of values = 5
Mean = 98 ÷ 5 = 19.6 years

(Approximately 20 years)

Practice: Calculate the Mean

Numbers: 10, 15, 20, 25, 30

Find the mean!

Work in your exercise book. Show all your steps:

1. Add all the numbers
2. Count how many numbers
3. Divide sum by count

Answer: Mean Practice

Numbers: 10, 15, 20, 25, 30

Solution:
Sum = 10 + 15 + 20 + 25 + 30 = 100
Count = 5 numbers
Mean = 100 ÷ 5 = 20

The mean is 20!

Understanding the Median

Median = The middle value when numbers are arranged in order

Steps to find the median:

1. Arrange all numbers from smallest to largest
2. Find the middle number
3. That's the median!

The median divides the data in half

Example 3: Median with Odd Numbers

Heights of 5 learners (cm): 130, 125, 135, 128, 132

Step 1: Arrange in order

125, 128, 130, 132, 135

Step 2: Find the middle

125, 128, [130], 132, 135

Median = 130 cm

Median with Even Numbers

Test scores: 50, 60, 70, 80, 90, 85

Step 1: Arrange in order

50, 60, 70, 80, 85, 90

Step 2: Find the two middle numbers

50, 60, [70, 80], 85, 90

Step 3: Calculate their mean
Median = (70 + 80) ÷ 2 = 75

Understanding the Mode

Mode = The value that appears most often

How to find the mode:

1. Look at all your numbers
2. Count how many times each number appears
3. The number that appears most is the mode

Example: In 5, 7, 5, 9, 5, the mode is 5 (appears 3 times)

Example 4: Finding the Mode

Shoe sizes: 35, 36, 37, 36, 38, 36, 39

Count each size:

• 35 appears 1 time
• 36 appears 3 times ✓
• 37 appears 1 time
• 38 appears 1 time
• 39 appears 1 time

Mode = 36 (most common shoe size)

Special Cases of Mode

Sometimes data has:

No mode: All numbers appear the same number of times
Example: 5, 10, 15, 20 (each appears once)

Two modes (bimodal): Two numbers both appear most often
Example: 2, 3, 2, 4, 3 (both 2 and 3 appear twice)

This is okay!

Comparing All Three Statistics

Same data, three different answers:

Data: 12, 15, 12, 18, 20, 15, 12

• Mean = (12+15+12+18+20+15+12) ÷ 7 = 104 ÷ 7 ≈ 14.9
• Median = Arrange: 12,12,12,15,15,18,20 → 15
• Mode = 12 (appears three times)

All three are different!

When to Use Each Statistic

Mean:

• Good for finding typical value
• But affected by very high or low numbers

Median:

• Good when there are extreme values
• Not affected by unusually high or low numbers

Mode:

• Good for finding most popular choice
• Best for categories (like favorite color)

Example: When Median is Better

Test scores: 20, 70, 75, 80, 85, 90, 95

Mean = 73.6 (pulled down by the 20)
Median = 80 (middle value, not affected)

Question: Which better shows typical performance?

Answer: Median! One poor score shouldn't represent the whole group.

Practice All Three Statistics

Data: 8, 10, 8, 12, 15, 10, 8

Calculate in your exercise book:

1. Mean
2. Median
3. Mode

Show all your working!

Answers: All Three Statistics

Data: 8, 10, 8, 12, 15, 10, 8

Mean: (8+10+8+12+15+10+8) ÷ 7 = 71 ÷ 7 ≈ 10.1

Median: Arrange: 8,8,8,10,10,12,15 → 10

Mode: 8 (appears three times)

How did you do?

Summary: Mean, Median, Mode

Remember these definitions:

Mean = Sum ÷ Count (the average)
Median = Middle value when arranged in order
Mode = Most common value

Each statistic tells a different story about the same data!

Real-Life Uses

Where are these statistics used?

• Schools: Average test scores, typical performance
• Sports: Average goals, median age of players
• Business: Average sales, most popular product
• Weather: Mean temperature, most common rainfall
• Health: Average weight, typical blood pressure

Statistics help us make sense of data everywhere!

Looking Ahead

Tomorrow's lesson:
We will learn about range and complete data analysis

Range = Highest value - Lowest value

We'll use all four measures together:
Mean, Median, Mode, and Range!

Homework

Assignment:

1. Practice calculations - Find mean, median, and mode:

   a) Ages: 11, 12, 11, 13, 12, 11, 14
   b) Prices (shillings): 500, 600, 500, 700, 800, 500
   c) Daily rainfall (mm): 10, 15, 20, 25, 30

2. Real data collection:
   Collect ages of 7 people in your family/neighborhood

   • Calculate mean age
   • Find median age
   • Identify mode (if any)

3. Reflection:
   In your own words, explain what the mean tells us about data

Expected time: 25-30 minutes