Statistics and Probability
Statistics and Probability tests mean, median and mode of grouped data and simple probability. The exam expects correct class intervals, cumulative frequencies and a probability between 0 and 1.
Core rules
- Mean (direct): Σf_ix_i/Σf_i.
- Median: l + [(n/2 − cf)/f]×h, where l is lower limit of median class, cf cumulative frequency before it, f its frequency, h class size.
- Mode: l + [(f1−f0)/(2f1−f0−f2)]×h.
- Empirical relation: 3 median = mode + 2 mean (approximate).
- Probability P(E)=number of favourable outcomes/total outcomes; 0≤P(E)≤1; P(not E)=1−P(E).
Worked example
Classes 0–10, 10–20, 20–30, 30–40 have frequencies 5, 8, 12, 5. Total n=30, n/2=15. Cumulative frequencies: 5, 13, 25, 30; median class is 20–30, with l=20, cf=13, f=12, h=10. Median=20+[(15−13)/12]×10=20+20/12≈21.67.
Traps
Use class boundaries, not just midpoints, in median and mode. The cumulative frequency “cf” is the total before the median class, not including it. In probability, count all equally likely outcomes; a die has 6 outcomes even if only even numbers interest you. Probability cannot exceed 1. Do not use the empirical relation as an exact formula.