Statistics and Probability: Data Analysis and Chance
What you must understand
Data analysis in Grade 5 includes reading and constructing tables, line plots, bar graphs, double bar graphs, and line graphs, and choosing a graph that fits the data. You must find mean, median, mode, and range for small data sets, describe the shape of a set (clusters, gaps, outliers), and interpret what the numbers say about the situation. Probability work uses the language of chance (impossible, unlikely, equally likely, likely, certain), expresses probability as a fraction of equally likely outcomes, and compares predicted results with experimental results.
Traps to watch
- Confusing mean and median: the mean is the sum divided by the count; the median is the middle value after ordering.
- Finding the median without ordering the data first, or forgetting to average the two middle values when the count is even.
- Reading a graph with a broken or non-zero axis and assuming the bars show the full size of the quantity.
- Treating a spinner's sectors as equally likely when they are different sizes.
- Believing past results change future chance in independent events.
Worked example
Data: 3, 5, 5, 7, 10. Mean = (3 + 5 + 5 + 7 + 10) ÷ 5 = 30 ÷ 5 = 6. Median = 5 (middle of the ordered list). Mode = 5 (most frequent). Range = 10 − 3 = 7. A bag has 3 red and 5 blue marbles, so the probability of red is 3/8.
Rule of thumb
Always order the data before finding the median, and count total outcomes before writing a probability fraction.