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Measuring How Spread Out Data Is
Measuring How Spread Out Data Is
Two football teams have the same average age of 25 years. Team A has players aged: 24, 25, 25, 26, 25. Team B has players aged: 18, 22, 25, 28, 32. Which team has more consistent ages?
While both teams have the same mean age, Team A's ages are much more consistent (closer together) than Team B's. We need measures of spread to describe this difference - that's where range and interquartile range come in!
What is the range?: The range is the difference between the highest value and the lowest value in a dataset.
Range = Highest value - Lowest value
Mathematics glossary
- What is the range?
- The range is the difference between the highest value and the lowest value in a dataset. Range = Highest value - Lowest value
- What are quartiles?
- Quartiles are values that divide an ordered dataset into four equal parts: - Q1 (Lower quartile): 25% below - Q2 (Median): 50% below - Q3 (Upper quartile): 75% below
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Exam Tips for Range and IQR
- Always arrange data in order before finding quartiles
- Be careful with even/odd numbers when finding medians of halves
- Don't include the median when splitting data into halves for large datasets
- Show your working - especially when finding Q1 and Q3
- Check your answer makes sense - IQR should be less than range
- Units matter - range and IQR have the same units as the original data
- Use IQR for comparisons when asked about consistency or spread
Now try it yourself
Quiz · Question 1 of 12
The range of a set of data is calculated by:
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