Probability and interpreting statistics
Probability quantifies uncertainty and statistics summarises data. Both reward careful reading: the wording tells you which technique the question wants.
Lesson overview
What you'll learn in this lesson
Use proportional reasoning, probability and statistics to interpret and solve problems.
Key learning points
- • Probability rules
- • Tree and Venn diagrams
- • Averages and spread
This lesson at a glance
- 30 minutes
- 20 parts to scroll through
- 4 quick checks
- Marked quiz at the end
- Gentle pace: short sittings with pauses
Words to know
Scroll down — the lesson carries on below
Watch & discover
Part 1 of 20
Visual introductionPicture this
Probability and interpreting statistics
Probability quantifies uncertainty and statistics summarises data. Both reward careful reading: the wording tells you which technique the question wants.
In a nutshell
Use proportional reasoning, probability and statistics to interpret and solve problems.
Learning cycle
Part 2 of 20
Learning cycle 1 of 2
Part 1 · Probability rules
A short piece of teaching, then a check to make sure it has landed.
Explore the idea
Part 3 of 20
Learn
Probability rules
Probabilities of all outcomes sum to 1, so P(not A) = 1 − P(A). For independent events happening together, multiply. For mutually exclusive alternatives, add. 'At least one' is nearly always easiest as 1 minus the probability of none.
Reset break
Part 4 of 20
Pause
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Stretch, get a drink, look out of the window. There is no timer and nothing is counting down — your place is saved, so you can come back in five minutes or tomorrow.
Explore the idea
Part 5 of 20
Learn
Tree and Venn diagrams
On a tree diagram, multiply along branches and add between them. Without replacement, the second set of denominators decreases by one, and this is where most marks are lost. A Venn diagram handles overlapping categories: fill the intersection first, then work outwards.
Quick check
Part 6 of 20
Quick check
Part 7 of 20
Reset break
Part 8 of 20
Pause
That's sitting 2 of 5 done
Stretch, get a drink, look out of the window. There is no timer and nothing is counting down — your place is saved, so you can come back in five minutes or tomorrow.
Learning cycle
Part 9 of 20
Learning cycle 2 of 2
Part 2 · Averages and spread
A short piece of teaching, then a check to make sure it has landed.
Explore the idea
Part 10 of 20
Learn
Averages and spread
The mean uses every value but is distorted by outliers; the median is resistant and better for skewed data; the mode suits categories. For grouped data, use midpoints to estimate the mean and say it is an estimate. Range and interquartile range describe spread, with the IQR ignoring extremes.
Quick check
Part 11 of 20
Reset break
Part 12 of 20
Pause
That's sitting 3 of 5 done
Stretch, get a drink, look out of the window. There is no timer and nothing is counting down — your place is saved, so you can come back in five minutes or tomorrow.
Quick check
Part 13 of 20
Explore the idea
Part 14 of 20
Worked example
Worked answer: a bag holds 5 red and 3 blue counters. Two are taken without replacement. Find P(both red) (3 marks)
P(first red) = 5/8 (1). After removing a red counter, 4 reds remain out of 7 counters, so P(second red) = 4/7 (1). Multiplying along the branches: 5/8 × 4/7 = 20/56 = 5/14 (1). Using 5/8 twice would answer a different question, one with replacement.
Challenge round
Part 15 of 20
Game · Sort it
Which of these are true?
Drag each card into the right column. Tap a card first if dragging is fiddly.
True
Not true
Reset break
Part 16 of 20
Pause
That's sitting 4 of 5 done
Stretch, get a drink, look out of the window. There is no timer and nothing is counting down — your place is saved, so you can come back in five minutes or tomorrow.
Challenge round
Part 17 of 20
Game · Fill the gaps
Finish the sentences
Choose the word that belongs in each gap.
'At least one' is nearly always easiest as 1 minus the ____ of none.
Challenge round
Part 18 of 20
Game · Recall cards
P(not A) equals
Card 1 of 4
Mastery quiz
Part 19 of 20
Marked quiz
End of lesson quiz: Probability and interpreting statistics
4 questions, marked with the reasoning shown. No timer.
1. P(not A) equals
2. On a tree diagram you
3. Which average is least affected by an outlier?
4. The mean from grouped data is an estimate because
Lesson round-up
Part 20 of 20
Lesson round-up
Ready when you are
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