P6 Mathematics - Term II

Topic 6: Data Handling

Lesson 5: Range and Data Analysis

Duration: 45 minutes

Learning Objectives

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

• Define and calculate the range of a data set
• Understand what range tells us about data spread
• Use all four statistics together to analyze data
• Compare different data sets using statistics
• Make informed conclusions based on statistical analysis

Review: Three Statistics

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 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

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

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 Range Tells Us

Small range (like 4):

• Values are close together
• Data is consistent
• Performance is steady
• Little variation

Large range (like 60):

• Values are spread out
• Data is varied
• Performance is inconsistent
• Lots of variation

Example 1: Temperature

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: 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: Calculate Range

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!

Answer: 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.

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!

Example: Complete Analysis

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

Full analysis:

• Arrange: 20, 20, 20, 21, 22, 22, 23
• Mean ≈ 21.1
• Median = 21
• Mode = 20
• Range = 23 - 20 = 3

What does this tell us? Sales are very consistent, around 20-21 mangoes per day.

Comparing 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 = 30 - 10 = 20

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

Practice: Complete 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: Learner Comparison

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

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

Comparison:
Both have similar averages, but Learner X is very consistent (range = 6) while Learner Y is inconsistent (range = 35) - some very high scores, some very low.

When Range is 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?)

Statistics Summary Table

Use all four for complete analysis!

Real-Life Applications

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 Mistakes to Avoid

Watch out for:

• Adding instead of subtracting (range = subtract!)
• Not finding the correct highest/lowest
• Forgetting to arrange data first (makes it easier)
• Not interpreting what range means
• Ignoring range when comparing data sets

Take time to check your work! ✓

Summary: 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

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

Assignment:

1. Complete analysis practice:
   Shop A prices: 1500, 1600, 1500, 1700, 1500, 1800 shillings
   Shop B prices: 1200, 1800, 1500, 2000, 1400, 1600 shillings

   For each shop, calculate: mean, median, mode, range
   Compare the shops - which is better for buying? Why?

2. Real data collection:
   Collect data (at least 7 values):

   • Daily temperatures, OR
   • Prices of bread in different shops, OR
   • Daily attendance in your class

   Calculate all four statistics and write what they tell you

3. Reflection:
   Explain why range is important. Give a real-life example.

Expected time: 30 minutes