1. Which measure is most affected by one extremely large value?
- Median
- Mean
- Mode always
Check the answer and reasoning
Mean
The mean includes the magnitude of every observation.
MATH / IGCSE
Statistics and probability
Tables, histograms, cumulative frequency and scatter diagrams summarise data. Means use all values; medians describe the middle and may resist extreme values.
Learning objectives
- Explain statistics and probability using a concrete example.
- Apply the worked method and justify each step.
- Recognise the limitation described in the final check.
The big idea
Tables, histograms, cumulative frequency and scatter diagrams summarise data. Means use all values; medians describe the middle and may resist extreme values.
Probabilities lie between 0 and 1. Tree diagrams multiply conditional branch probabilities along a path and add mutually exclusive paths; independence must be justified.
Equations and relationships
Applies when A and B are independent.
Worked example
Two fair coins are tossed. Find P(two heads).
Follow the solution
The independent probabilities multiply: 1/2 × 1/2 = 1/4.
Investigate and explain
Predict the worked result before calculating. Change one input, record the new result, and explain which assumptions still hold.
Related interactive model. Compare its assumptions with the explanation; it is not a complete syllabus lesson.
Check your understanding
2. Two fair coins are tossed. Find P(two heads).
- 1/2
- 1
- 1/4
Check the answer and reasoning
1/4
The independent probabilities multiply: 1/2 × 1/2 = 1/4.
3. Does correlation by itself establish causation?
- No
- Yes
- Only if the graph slopes upward
Check the answer and reasoning
No
A hidden variable or coincidence may explain an association; causal evidence needs a suitable design.