Data analysis
What you must understand
Data analysis in Foundation Mathematics is about describing a data set clearly and choosing the right summary for the question. Know the difference between categorical data (names or labels, such as eye colour or transport mode) and numerical data, which is either discrete (counted, such as number of siblings) or continuous (measured, such as height). You must be able to read and construct frequency tables, bar charts, dot plots, stem-and-leaf plots and histograms, and to describe a distribution by its shape (symmetric, skewed, with outliers), centre and spread.
Know the three averages and when each is appropriate: the mean (sum divided by count), the median (middle value of an ordered list) and the mode (most frequent value). Know the range and the interquartile range as measures of spread, and be able to find quartiles by splitting an ordered list into halves.
Traps to watch
- Forgetting to order the data before finding the median or quartiles.
- Confusing the number of data values with the number of categories on a chart axis.
- Reading a histogram as if the bar height were the data value rather than the frequency.
- Reporting a mean for categorical data, or a mode as if it were a measure of centre for continuous data with no repeats.
- Using the mean when an outlier drags it away from the typical value - the median is then safer.
Worked example
The data set 4, 7, 7, 9, 12, 15, 20 has n = 7. The median is the 4th value, 9. The lower half is 4, 7, 7, so Q1 = 7; the upper half is 12, 15, 20, so Q3 = 15. The IQR is 15 − 7 = 8. The mean is 74 ÷ 7 ≈ 10.6, which is above the median because 20 pulls it upward - a good illustration of why the median is preferred when outliers are present.