Statistics and Probability: Data Analysis and Chance
Data analysis starts with questions: who was surveyed, how, and is the sample representative? A population is the whole group; a sample is part of it. Samples chosen conveniently or by voluntary response can be biased. Classify data as categorical (categories) or numerical, and numerical data as discrete (counted) or continuous (measured).
Choose graphs deliberately: bar graphs compare categories, histograms show numerical data grouped in intervals, line graphs show change over time, circle graphs show parts of a whole (percentages must total 100%), and stem-and-leaf plots keep every value visible while ordering the data.
The mean is the sum divided by the count; the median is the middle value of ordered data; the mode is the most frequent value. The range (maximum minus minimum) describes spread. An outlier can pull the mean far from the median, which is why the median often better describes a typical value.
Probability is a number from 0 (impossible) to 1 (certain), often written as a fraction, decimal, or percent. Find it by counting favourable outcomes over all equally likely outcomes in the sample space. Experimental probability comes from trials and may differ from theoretical probability, especially with few trials; past results do not change the theoretical chance next time.
Traps: finding the median without ordering the data first (with an even count, average the two middle values); reporting a mode when every value appears once; and comparing circle-graph slices as if they were raw counts.
Worked example: for 4, 7, 9, 12, 13, the mean is 45 ÷ 5 = 9, the median is 9, and the range is 9. The probability of rolling a number greater than 4 on a fair die is 2/6 = 1/3.