Statistics and Probability
Statistics and Probability tests mean, median, mode for grouped data, and classical probability. Statistics summarises data; probability measures chance.
Core rules
- Mean by direct method: Σfixi/Σfi, where xi is the class mark.
- Median for grouped data: l + [(n/2 - cf)/f]×h, with l the lower limit of the median class, cf the cumulative frequency before it, f its frequency, and h the class size.
- Mode for grouped data: l + [(f1-f0)/(2f1-f0-f2)]×h.
- Empirical relation for moderately skewed data: 3 median = mode + 2 mean.
- Probability of an event E: P(E)=number of favourable outcomes/total outcomes. Also 0≤P(E)≤1 and P(not E)=1-P(E).
Worked example
A die is rolled once. Find the probability of getting an even number. Favourable outcomes are 2,4,6, so there are 3. Total outcomes are 1 to 6, so 6. P(even)=3/6=1/2. The complement is P(odd)=1-1/2=1/2, which agrees with the three odd outcomes 1,3,5.
Traps
In grouped data, use class marks, not class limits, for the mean. Identify the median class using n/2, not n. The mode formula uses the modal class and neighbouring frequencies. In probability, total outcomes must be equally likely; do not count impossible or repeated outcomes.