Averages & Interpreting Data — Year 9 Revision Notes
These notes cover the three averages and the range, finding averages from frequency tables, and estimating the mean of grouped data — all at Year 9 (Stage 9) level.
The three averages and the range
The mean is the total divided by how many values, the median is the middle value when ordered, and the mode is the most common value. The range (largest − smallest) measures spread, not average. Each average is useful in different situations.
Key Facts & Formulas
- mean = total ÷ number of values
- range = largest − smallest
Tips
- Order the data before finding the median.
- The range is a measure of spread, not an average.
Averages from a frequency table
For a frequency table, the mean is Σ(value × frequency) ÷ Σ(frequency). Multiply each value by its frequency, add the results, and divide by the total frequency. The mode is the value with the highest frequency, and the median is found by counting to the middle position.
Key Facts & Formulas
- mean = Σfx ÷ Σf
- median position = (n + 1) ÷ 2
Tips
- Multiply value by frequency, then divide by total frequency.
- Do not divide by the number of rows.
Estimating the mean of grouped data
When data is grouped into classes, use the midpoint of each class as the value. Multiply each midpoint by its frequency, add the products, and divide by the total frequency. Because exact values are unknown, this gives an estimated mean.
Key Facts & Formulas
- midpoint = (lower + upper) ÷ 2
- estimated mean = Σ(midpoint × f) ÷ Σf
Tips
- Use the midpoint of each class, not the class width.
- Call the answer an estimate of the mean.
Revision Checklist
- I can find the mean, median, mode and range of a data set
- I can find averages from a frequency table
- I can estimate the mean of grouped data using midpoints
- I can compare two data sets using an average and the range
Frequently Asked Questions
Which average should I use?
Use the mode for the most common or most popular item, the median when there are extreme values that would distort the mean, and the mean when you want to use all the data and there are no big outliers. The right choice depends on the data and the question.
Build strong foundations in Averages & Interpreting Data
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