P6 Mathematics - Term II

Topic 6: Data Handling

Lesson 5: Range and Data Analysis

Duration: 45 minutes

Today's Learning Objectives for Range

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

• Define and calculate range
• Understand what range tells us about spread
• Use all four statistics together
• Compare data sets using statistics
• Make informed conclusions from analysis

Reviewing Our Three Statistics So Far

What we learned yesterday:

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

All three tell us about typical or central values

A Problem for Us to Consider

Look at these two data sets:

Set A: 48, 49, 50, 51, 52 (test scores)
Set B: 20, 40, 50, 60, 80 (test scores)

Both have mean = 50

Question: Are these data sets the same?

Introducing Range as a Statistic

Range measures how spread out the data is

The formula is simple:

Range = Highest value - Lowest value

Range tells us:

• Small range = values close together (consistent)
• Large range = values spread out (varied)

Calculating Range for Two Sets

Set A: 48, 49, 50, 51, 52

Highest = 52
Lowest = 48
Range = 52 - 48 = 4

Set B: 20, 40, 50, 60, 80

Highest = 80
Lowest = 20
Range = 80 - 20 = 60

Now we can see the difference!

What a Range Value Tells Us

Small range (like 4):

• Values are close together
• Data is consistent, steady

Large range (like 60):

• Values are spread out
• Data is varied, inconsistent

Example 1: Temperature Range This Week

Temperatures last week:
24°C, 26°C, 25°C, 27°C, 26°C, 25°C, 24°C

Calculate the range:

Highest = 27°C
Lowest = 24°C
Range = 27 - 24 = 3°C

Interpretation: Temperatures were very consistent!

Example 2: Range in Market Prices

Price of matooke in different markets (shillings):
15,000, 18,000, 12,000, 22,000, 14,000

Calculate the range:

Highest = 22,000 shillings
Lowest = 12,000 shillings
Range = 22,000 - 12,000 = 10,000 shillings

Interpretation: Prices vary a lot between markets!

Practice Calculating a Range Now

Learner heights (cm):
145, 150, 142, 155, 148, 152

In your exercise book:

1. Arrange the heights in order
2. Find the highest height
3. Find the lowest height
4. Calculate the range
5. Write what it tells us

You have 2 minutes!

The Answer for Height Range

Heights arranged: 142, 145, 148, 150, 152, 155 cm

Calculation:
Highest = 155 cm
Lowest = 142 cm
Range = 155 - 142 = 13 cm

Interpretation: There's a 13 cm difference between the tallest and shortest learner.

Doing a Complete Data Analysis

Now we have FOUR statistics:

1. Mean - Average value
2. Median - Middle value
3. Mode - Most common value
4. Range - Spread of values

Together, they give a complete picture of the data!

Worked Example: A Complete Analysis

Stall A mangoes sold per day:
20, 22, 21, 23, 20, 22, 20 → arranged: 20, 20, 20, 21, 22, 22, 23

• Mean ≈ 21.1, Median = 21, Mode = 20, Range = 3

Very consistent sales, around 20-21 per day

Comparing Two Different Data Sets

Stall A: Mean ≈ 21, Median = 21, Mode = 20, Range = 3

Stall B: 10, 25, 18, 30, 15, 28, 16
Mean ≈ 20.3, Median = 18, Mode = None, Range = 20

Similar means, but Stall A is far more consistent (range 3 vs 20)!

Practice a Complete Data Analysis

Test scores for Learner X:
70, 75, 72, 74, 69

Test scores for Learner Y:
85, 60, 75, 90, 55

Calculate all four statistics for each learner, then compare!

Answers for the Learner Comparison

Learner X: Mean = 72, Median = 72, Mode = None, Range = 6

Learner Y: Mean = 73, Median = 75, Mode = None, Range = 35

Similar averages, but X is consistent (range 6) while Y varies a lot (range 35)!

When Is Range Especially Important?

Range matters when:

• Checking consistency (should scores be similar?)
• Quality control (should products be uniform?)
• Identifying problems (why such variation?)
• Comparing reliability (which is more predictable?)
• Planning (what's the worst and best case?)

Summary Table of All Four Statistics

Use all four for complete analysis!

Real-Life Applications of Range Values

Where is range used?

• Weather (temperature range each day)
• Business (price range for products)
• Sports (score ranges showing consistency)
• Quality control (acceptable variation in products)
• Health (normal range for blood pressure, temperature)
• Education (grade ranges, performance variation)

Common Range Mistakes to Avoid

• Adding instead of subtracting
• Wrong highest/lowest value
• Not arranging data first
• Not interpreting what range means

Take time to check your work! ✓

Summary of Today's Key Points

Today we learned:

• Range = Highest - Lowest
• Range shows how spread out data is
• Small range = consistent data
• Large range = varied data
• Use all four statistics together for complete analysis:
  Mean, Median, Mode, Range
• Compare data sets using statistics

Looking Ahead to Our Probability Lesson

Tomorrow's lesson:
We will learn about probability - the chance of events happening!

What is probability?

• How likely is something to happen?
• Probability of flipping heads on a coin
• Probability of picking a red ball from a bag

New topic, exciting concepts!

Homework: Compare Two Shops' Prices

Shop A: 1500, 1600, 1500, 1700, 1500, 1800 shillings
Shop B: 1200, 1800, 1500, 2000, 1400, 1600 shillings

For each shop, calculate mean, median, mode, range.
Which shop is better for buying? Why?

Homework: Collect Data and Reflect

1. Collect at least 7 values (temperatures, bread prices, or attendance)
2. Calculate all four statistics and explain what they show
3. Explain why range is important, with a real-life example

Expected time: 30 minutes