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Averages and range
Averages summarise data in one number. Each average has strengths, and the range shows how spread out the data is.
The averages
Mean: add the values and divide by how many.
Median: the middle value when ordered (the ([n + 1]/2)th value).
Mode: the most common value.
Range: largest − smallest.
Median: the middle value when ordered (the ([n + 1]/2)th value).
Mode: the most common value.
Range: largest − smallest.
Frequency tables
Mean = total of (value × frequency)total frequency
For grouped data, use the midpoint of each group to estimate the mean.
For grouped data, use the midpoint of each group to estimate the mean.
Choosing an average
The mean uses every value but is affected by outliers (extreme values). The median is not affected by outliers.
Find the median of 7, 3, 9, 4, 12, 8.
- Order: 3, 4, 7, 8, 9, 12
- Two middle values: 7 and 8
- (7 + 8) ÷ 2
Answer: 7.5
Mean = total ÷ count; median = middle of ordered data; mode = most common; range = largest − smallest. From a table, mean = Σ(value × f) ÷ Σf.
The interactive lesson includes the diagrams for this topic.
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