What you'll learn
How to calculate and choose between the three averages.
The three averages
- Mean = sum of values ÷ number of values. Uses all data but is affected by outliers.
- Median = the middle value when ordered. Not affected by outliers.
- Mode = the most common value. The only average for categorical data.
From tables
- Frequency table: mean = Σ(fx) ÷ Σf.
- Grouped data: use class midpoints to estimate the mean; identify the modal class and the class containing the median.
Choosing an average
- Use the median with skewed data or outliers; the mean for symmetric data; the mode for categories.
Exam tips
- Show the Σ(fx) and Σf clearly for frequency-table means.
- State it is an estimate of the mean for grouped data.
Common mistakes
- Forgetting to divide by Σf (dividing by the number of rows instead).
- Using class widths instead of midpoints.