Statistics, Probability, and Data Analysis
What this domain tests
Statistics, Probability, and Data Analysis tests summarizing data with mean, median, mode, range, and interquartile range; reading displays; sampling and bias; basic probability; counting; and interpreting association and trends.
Core rules
- Mean is the sum divided by the count; median is the middle ordered value, averaging the two middle values for an even count; mode is most frequent. Outliers affect the mean more than the median.
- Range=max−min. Interquartile range IQR=Q3−Q1; it measures the middle 50% and resists outliers.
- Probability of an event = favorable outcomes / total equally likely outcomes, between 0 and 1. For independent events, P(A and B)=P(A)P(B). For mutually exclusive events, P(A or B)=P(A)+P(B).
- A random sample supports generalization only to the population sampled; biased sampling, such as voluntary response, undermines inference.
- On scatterplots, describe direction, strength, and form; correlation does not prove causation.
Worked example
A bag has 3 red, 2 blue, and 5 green marbles. One marble is drawn, replaced, then another is drawn. P(red then blue)= (3/10)(2/10)=6/100=3/50. Because the first marble is replaced, the draws are independent. Without replacement, the second probability would change to 2/9.
Traps
Do not call the most frequent value the median. In probability, “or” is not always addition unless events are mutually exclusive; subtract the overlap. Replacement changes denominators and independence. A graph with a truncated axis can exaggerate differences. A mean of grouped data uses class midpoints and is an estimate.