Data Analysis: Statistics, Counting, Probability, and Graphs
Core skills
Data analysis covers descriptive statistics (mean, median, mode, range, standard deviation, quartiles, interquartile range); interpreting bar, line, and circle graphs, scatterplots, and tables - often two or three linked questions per set; the normal distribution's 68–95–99.7 rule; counting via the fundamental counting principle, permutations, and combinations; probability including complements and independent events; and overlapping sets through Total = A + B − Both + Neither.
Traps
- With an even number of data values, the median is the average of the two middle values, not one of them.
- Adding a constant to every value shifts the mean and median but leaves the standard deviation and range unchanged; multiplying every value by k multiplies the standard deviation by |k|.
- Standard deviation measures spread only - two sets can share a mean and have very different spreads.
- At least one is almost always fastest as 1 − P(none).
- Ask whether order matters: if it does, it is a permutation; if only selection matters, it is a combination.
- On graph questions, check axis labels, units, and whether the scale starts at zero before estimating.
Worked example
A set of five numbers has mean 20, so its sum is 100. Adding a sixth value of 32 gives a new mean of (100 + 32)/6 = 132/6 = 22. Rule of thumb: convert every mean back into a sum (sum = mean × count) before combining groups.