Statistics and Probability: Data Displays, Averages, and Chance
What you must understand
This strand covers collecting and organizing data, reading and constructing graphs, describing a data set with mean, median, mode, and range, and expressing probability as a fraction, decimal, or percent between 0 and 1. You should be able to read bar graphs, line graphs, pictographs, and circle graphs, choose an appropriate display, and interpret what a graph shows. Probability of an event equals the number of favourable outcomes divided by the total number of equally likely outcomes.
Traps to watch for
- Mean versus median: the mean is affected by outliers, while the median is the middle value of an ordered list; always sort the data before finding the median.
- Even-sized data sets: the median is the average of the two middle values.
- Range: it is the largest value minus the smallest, not a count of values.
- Scale reading: check the axis intervals on a graph before stating a value; a bar may represent 5 units, not 1.
- Probability complements: the probability of an event not happening is 1 minus the probability that it happens.
- Misleading graphs: unequal intervals or a truncated axis can exaggerate differences.
Worked example
A data set is 4, 7, 7, 9, 13. Ordered already, the median is the middle value, 7. The mode is 7 because it appears most often. The mean is (4 + 7 + 7 + 9 + 13) ÷ 5 = 40 ÷ 5 = 8. The range is 13 − 4 = 9. If a bag holds 3 red and 5 blue marbles, the probability of drawing red is 3/8 = 0.375 = 37.5%, and the probability of not drawing red is 5/8.
Rule of thumb
Before computing any average, order the data and count the values; before reading any graph, check the axis scale and intervals.