Statistics and Probability
Statistics and Probability
Statistics and Probability tests data collection and representation, averages and spread, cumulative frequency and box plots, scatter graphs, probability rules, tree diagrams and conditional probability.
Core rules
- Mean = total of values ÷ number of values. For grouped data, use midpoints. Median is the middle value after ordering; mode is the most frequent.
- Cumulative frequency plots estimate the median and quartiles at cumulative frequencies n/2, n/4 and 3n/4.
- In a histogram, frequency density = frequency ÷ class width; area represents frequency.
- Probability of an event lies between 0 and 1; P(not A) = 1 − P(A). For mutually exclusive events, add probabilities.
- For independent events, multiply probabilities. For events without replacement, adjust the denominator and numerator after each selection.
Worked example
A bag has 5 red and 3 blue counters. Two are taken without replacement. P(first red, second blue) = (5/8) × (3/7) = 15/56. P(both red) = (5/8) × (4/7) = 20/56 = 5/14. The second fraction changes because one counter has been removed and not replaced.
Traps
- Using the original total for the second draw when selection is without replacement.
- Reading a cumulative frequency axis as if it were frequency.
- Finding the median from ungrouped raw data without ordering it first.
- Adding probabilities for events that are not mutually exclusive; subtract the overlap.