Summarising data with averages and measuring chance
Statistics organises data so that patterns can be seen. The mean is the sum of the values divided by how many there are, the median is the middle value once the data is arranged in order, and the mode is the value that occurs most often. For grouped data in a frequency table, the mean is Σfx ÷ Σf using the class marks as x, and the median and mode are found with formulas based on the median class and the modal class. Bar graphs, histograms and frequency polygons show the same data visually.
Probability measures how likely an event is, on a scale from 0 for impossible to 1 for certain. When all outcomes are equally likely, P(E) = number of favourable outcomes ÷ total number of outcomes, so the probability of drawing a king from a pack of 52 cards is 4/52 = 1/13. The complement rule says P(not E) = 1 − P(E), so the chance of not rolling a six is 5/6. With two dice there are 36 equally likely outcomes, and the chance of a total of 7 is 6/36 = 1/6.
Why it matters
Averages are used to report marks, cricket scores, rainfall and incomes, and choosing the right one matters: the median is not pulled up by a few very large values. Probability is used in weather forecasts, insurance, quality checks in factories and games of chance. Both topics continue in Class 11 with measures of spread, standard deviation and conditional probability.
Key terms
- Mean
- The sum of all observations divided by the number of observations.
- Median
- The middle observation when the data is arranged in ascending or descending order.
- Mode
- The observation that appears most often in a data set.
- Probability of an event
- The number of favourable outcomes divided by the total number of equally likely outcomes.