This area covers four skills that make data and chance questions routine: reading frequency tables, finding mean, median and mode, listing outcomes systematically, and comparing experimental with theoretical probability.
How do the parts connect?
- Reading frequency tables: what each row and the frequency column mean.
- Calculating mean, median and mode: three ways to describe one table.
- Listing outcomes systematically: the set of possibilities behind a probability.
- Comparing experimental and theoretical probability: why real results differ from the ideal.
The last page brings the others together, since experimental results come from a table and the theory comes from a list of outcomes.
What does one short example look like?
An original question: a student tosses two coins 20 times and records the number of heads: 0 heads 4 times, 1 head 11 times, 2 heads 5 times.
From the table, the total is 4 + 11 + 5 = 20, and the most common result (mode) is 1 head. The experimental probability of two heads is 5/20 = 1/4. The list of outcomes HH, HT, TH, TT gives a theoretical probability of 1/4 for two heads.
The two probabilities match here, but the experimental probability of one head is 11/20 = 0.55, while theory says 2/4 = 0.5. Real trials wobble around the theory. That single example used a table, a mode, an outcome list and a comparison.
Who should start where?
| Symptom | Start with |
|---|---|
| Totals from a table are wrong | Frequency tables |
| Mix up mean, median and mode | Mean, median and mode |
| Always missing one outcome | Listing outcomes |
| Do not see why results differ from theory | Experimental and theoretical probability |
Go back to all foundation skills or try the prerequisite gap finder if you are not sure.
These skills return in SPM Mathematics statistics and probability, and in Science when averaging repeated readings. If you want a teacher beside you, online one-to-one Mathematics tuition begins with a one-hour trial class (from RM50).