Measures of central tendency
Mean, median, mode.
Mean (). Sum / count.
- Raw: .
- Frequency: .
- Grouped: use class MIDPOINTS as .
Median. Ordered middle value.
- Raw: th value if odd; average of two middle if even.
- Grouped: from cumulative frequency curve (interpolate).
Mode. Most frequent value. For grouped data: modal class (class with highest frequency density if widths differ).
When to use each.
- Mean: most informative; uses all data; sensitive to outliers.
- Median: robust to outliers.
- Mode: useful for categorical data.
Example. from grouped data 0-10 freq 4, 10-20 freq 12, 20-30 freq 9, 30-40 freq 5.
- Midpoints 5, 15, 25, 35.
- .
- .
- .
Cambridge tip. For grouped data, ALWAYS use midpoints.
- Mean uses all data.
- Median is robust.
- Mode for categorical.
See the full worked example for measures of central tendency and variation β