Chapter 8: Data, Statistics, and Probability
Data, Statistics and Probability
Read data carefully, calculate averages with meaning, and describe probability using evidence.
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Workbook pages
Fun Maths Book 3 pages 89-100
Read graphs, draw bar graphs from frequency tables, calculate averages and reason with probability.
Think first
Good mathematicians decide what the question is asking before they calculate.
- 1What does each scale mark or data value represent?
- 2Do we need mean, median, mode or range?
- 3Have the data values been sorted when needed?
- 4How many favourable outcomes are there compared with all possible outcomes?
Visual teaching
See the method
A frequency table rises into a bar chart, data cards sort into order and a probability scale marks impossible, unlikely, even chance, likely and certain.
Worked examples
Find the mean of 12, 8, 15, 5.
Step 1: What are we trying to find?
We need the mean, which is the equal-share average.
Why: The mean shows what each value would be if the total were shared equally.
Step 2: What is the total?
12 + 8 + 15 + 5 = 40.
Why: The mean starts by combining all the data.
Step 3: How many values are there?
There are 4 values.
Why: We divide by the number of data values.
Be careful: Do not divide by the largest number in the list.
Step 4: Now calculate the mean.
40 รท 4 = 10.
Why: Sharing 40 equally across 4 values gives 10.
Common mistake: Adding correctly but dividing by the wrong number.
Find the median of 4, 9, 2, 7, 8.
Step 1: What does median mean?
The median is the middle value after the data is ordered.
Why: Ordering matters because the middle depends on position.
Step 2: Sort the values.
2, 4, 7, 8, 9.
Why: Sorting makes the middle value clear.
Be careful: Do not choose the middle value from the unsorted list.
Step 3: Choose the middle value.
There are 5 values, so the 3rd value is the middle.
Why: Two values are below it and two values are above it.
Common mistake: Forgetting to put the data in order first.
A bag has 9 green counters and 1 yellow counter. Describe the chance of green.
Step 1: What information is given?
There are 9 green counters and 1 yellow counter, so 10 counters in total.
Why: Probability compares favourable outcomes with total outcomes.
Step 2: Is green certain?
No. Yellow is still possible.
Why: Certain means every outcome would be green.
Step 3: Which probability word fits best?
Green is likely because 9 out of 10 counters are green.
Why: A high chance that is not certain is described as likely.
Common mistake: Calling green certain because it is much more common.
Guided practice
Find the range of 6, 14, 9, 3, 11.
Independent practice
Your turn
What should you check first on a bar graph?
Find the median of 4, 9, 2, 7, 8.
If an event cannot happen, its probability is...
Mini checkpoint
Check your thinking
What should you check first on a bar graph?
Find the mean of 6, 10, 14, 18.
A spinner has 3 red sections and 1 blue section. What is P(blue)?
Key idea
Data work is about reading carefully before calculating. Check graph scales, sort data for the median, share totals for the mean, and justify probability with outcomes.
Parent signal
If graph answers are wrong, check whether the child read the vertical scale correctly.