Statistics and Data Handling
Statistics and Data Handling
This domain tests organising data, calculating mean, median and mode, and reading bar graphs, histograms and frequency polygons.
Core rules
- Mean = sum of observations ÷ number of observations. For grouped data, mean = Σfx / Σf, where x is the class mark.
- Median: arrange data in order. For n odd, median = ((n+1)/2)th value; for n even, median = average of the (n/2)th and (n/2+1)th values.
- Mode = the value or class with the highest frequency. A data set may have no mode or more than one mode.
- In a bar graph, bars have gaps and categories can be non-numeric. In a histogram, bars touch and show continuous class intervals.
Worked example
Find the mean, median and mode of 4, 7, 7, 9, 13. Mean = (4 + 7 + 7 + 9 + 13) ÷ 5 = 40 ÷ 5 = 8. The data are already in order and n = 5, so median = (5+1)/2 = 3rd value = 7. The value 7 occurs twice, more than any other, so mode = 7.
Traps
- Always sort the data before finding the median; 13, 4, 9, 7, 7 has median 7, not 9.
- The mean is affected by extreme values; the median is not.
- Do not call the highest frequency the mode - the mode is the value (or class) with that frequency.
- When class intervals are unequal, histogram bar heights need frequency density, not raw frequency.