Data, Statistics and Probability: Tables, Charts, Averages
What you must be able to do
Read and interpret tables, bar charts, line graphs, pie charts and histograms. For a data set, compute the mean (sum ÷ count), the median (middle value when ordered), the mode (most frequent value) and the range (maximum − minimum). Know that the mean is affected by extreme values while the median is not.
For a pie chart, each sector's angle is (frequency/total)·360°. For grouped data, use class midpoints when estimating a mean.
For probability, P(event) = favourable outcomes ÷ all equally likely outcomes, always between 0 and 1. The complement rule: P(not A) = 1 − P(A). For two independent events, multiply the probabilities.
Traps that appear in questions
- Forgetting to order the data before finding the median.
- With an even count, forgetting to average the two middle values.
- Reporting a probability greater than 1 or a percentage not divided by 100.
- Reading a bar chart's axis with an inconsistent scale.
- Confusing "at least one" with "exactly one" in counting problems.
Rule of thumb
Before computing any average, sort the data and count how many values you have; write the count down.
Worked example
Data: 4, 7, 7, 9, 13. Mean = 40/5 = 8; median = 7; mode = 7; range = 9. The probability of picking a 7 at random is 2/5.