Statistics and Probability
What this domain tests
Statistics and Probability asks you to draw inferences from random samples, compare data sets using center and spread, and compute probabilities of simple and compound events. Expect mean absolute deviation, interquartile range, sample spaces, and simulations.
Core rules
- A random sample gives every member of the population an equal chance of selection; a biased sample over- or under-represents a group.
- Center: mean, median, mode. Spread: range, interquartile range (IQR = Q3 − Q1), and mean absolute deviation (MAD).
- MAD is the average of |data value − mean|; it measures typical distance from the mean.
- Probability of an event = favorable outcomes ÷ total equally likely outcomes, a value from 0 to 1.
- For independent events, P(A and B) = P(A) × P(B).
Worked example
A bag holds 3 red, 5 blue, and 2 green marbles, 10 total. P(red) = 3/10. With replacement, P(red then blue) = (3/10)(5/10) = 15/100 = 0.15. Without replacement, the second draw has only 9 marbles: (3/10)(5/9) = 15/90 = 1/6.
MAD for the data 2, 4, 6, 8: mean = 5. Deviations: 3, 1, 1, 3. MAD = (3 + 1 + 1 + 3) ÷ 4 = 2.
Traps that cost marks
- Comparing two data sets by their means alone while ignoring spread.
- Computing MAD from signed deviations that cancel to zero.
- Using without-replacement denominators when the problem states replacement.
- Assuming experimental results must exactly match theoretical probability in a small sample.
- Treating a non-random sample as representative of the whole population.