Mean, Median, Mode and Range

Lesson 3 of 4: Data Handling

In this lesson:

• Calculate the mean, median, and mode of a data set
• Find the range
• Choose the right measure for any situation

What You Will Be Able To Do

By the end of this lesson, you will:

1. Calculate the mean as sum ÷ count
2. Find the median — always ordering first
3. Identify the mode (most frequent value)
4. Calculate the range as highest − lowest
5. Choose the right measure and explain why

Which Number Tells the Story?

Five students sat a maths test and scored:

6, 8, 7, 9, 10 (out of 10)

The teacher wants to write one number to report how the class did.

Which single number should she choose — and why?

Let's Check Two Skills First

Before we start, make sure both of these are working:

Add:

Divide:

Work both out in your exercise book, then continue.

Fair Sharing: The Idea Behind the Mean

What if the five students pooled their marks and shared equally?

Total marks:

Share equally among 5 students:

Each student would have 8 marks.

The Mean: Sum ÷ Count

Two steps — both matter:

1. Add all the values
2. Divide by how many there are

Sanity check: the mean must sit between the lowest and highest values. A mean outside that range means an error somewhere.

Finding the Mean: Class Test Scores

Data: 6, 8, 7, 9, 10

Step 1 — Add:

Step 2 — Divide by count:

Mean = 8 ✓ (sits between 6 and 10 — passes the sanity check)

Your Turn: Find the Mean

Trader's daily sales: 12, 15, 18, 15

1. Add:
2. Divide by 4:

Work it out, then advance.

Sum = 60, Mean = 15

Always Order the Data First

As given: 3, 7, 5, 9, 4

In order (smallest → largest): 3, 4, 5, 7, 9

The middle value of the ordered list is 5.

A median read from an unordered list is only right by chance.

Median: Middle of the Ordered List

Step 1: Order smallest → largest — Step 2: Find the middle

Odd count (5 values) → one middle value:

Find the Flaw in This Method

Student's working on 3, 7, 5, 9, 4:

"5 values → 3rd position → 3rd value is 5. Median = 5."

Right answer — wrong method. Why does it fail?

Never ordered! For 8, 2, 6, 4, 1: same method gives 6; true median is 4.

Even Count: Average the Two Middles

Data: 3, 4, 5, 7, 9, 10 (six values — two middles)

Odd count → one middle. Even count → average the two middles.

Mode Is the Most Frequent Value

Data: 4, 5, 5, 6, 5, 8 → 5 appears 3 times (most)

Mode = 5 (frequency counts, not size — 8 is bigger, not the mode)

No mode if all values differ. Two modes if two values tie for most frequent.

Quick Check: Median and Mode

Data: 2, 6, 3, 6, 4

Find:

1. The median (remember to order first!)
2. The mode

Work it out before advancing.

Ordered: 2, 3, 4, 6, 6 → Median = 4
Mode = 6 (appears twice)

Range: How Spread Out Is the Data?

Mean, median, and mode describe the centre.

Range describes how spread out the data is:

Range is not a measure of centre — it measures variation.

Compute the Range from Ordered Data

Data (already ordered): 3, 4, 5, 7, 9

Since we ordered for the median, the ends are already the highest and lowest.

Always subtract: highest − lowest (not lowest − highest)

Same Mean Does Not Mean Same Spread

Both sets have mean = 5, but their ranges differ:

The mean alone doesn't tell the whole story.

Quick Check: Range of Test Scores

Data: 6, 8, 7, 9, 10 (our original class scores)

What is the range?

Work it out, then advance.

Highest = 10, Lowest = 6
Range = 10 − 6 = 4

When One Outlier Distorts the Mean

Monthly earnings (ten-thousands of shillings): 2, 3, 3, 4, 88

Mean = 20, but 4 of 5 people earn 4 or less. Which number is fairer?

Outliers Pull the Mean, Not the Median

• Outlier pulls the mean toward it
• Median resists — determined by position, not magnitude

With an outlier, the median is usually the fairer summary.

Which Measure Fits Each Situation?

Your Turn: All Four Measures

Data: 2, 3, 3, 4, 88 — work it out in your exercise book:

1. Find the mean
2. Find the median (order first)
3. Find the mode
4. Which — mean or median — better represents a typical person? One sentence, with a reason.

Full Model Answer: 2, 3, 3, 4, 88

Best summary: Median (3) — 4 of 5 people earn ≤ 3; outlier 88 pulls the mean to 20.

Four Mistakes to Watch For

Four Measures, Four Different Questions

• Mean — fair share; for sharing a total
• Median — middle of ordered list; use with outliers
• Mode — most frequent; "most common" situations
• Range — highest − lowest; spread

Know your question before picking a measure.

Next — Lesson 4: Frequency → probability.