Data types, displays, spread and the effect of outliers.
Example 1
A survey records favourite sport for each of 50 students. What type of variable is this?
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Answer: Categorical nominal
- Sport names are categories without a natural order.
- The variable is categorical nominal.
Example 2
In a sample of 110, weekly household incomes are strongly right-skewed, with a few exceptionally high incomes. Which pair gives a resistant summary of centre and spread?
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Answer: Median and interquartile range
- Extreme values can strongly affect the mean, standard deviation and range.
- Median and interquartile range depend on ordered positions and provide a resistant summary.
Example 3
The interquartile range of a data set is 3. Every value is multiplied by 8, then 5 is added. Find the new interquartile range.
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Answer: 24
- Multiplying by 8 multiplies differences by 8.
- Adding 5 shifts all values equally, leaving spread unchanged.
- New IQR=3×8=24.