What's covered
Key facts
Mode, median and mean
Comparisons of averages must be context-based interpretations (for example, "on average students at Britstone scored higher"), not just a statement that two numbers differ.
Outliers
Outlier boundaries may need to be calculated so that outliers can be identified and marked separately on a box plot.
Range, quartiles and percentiles
The interdecile range is the 90th percentile minus the 10th percentile, so it covers the middle 80% of the data.
Skewness
With positive skew, values above the median have a greater spread than values below the median.
Standard deviation and standardised scores
An alternative formula is standard deviation = square root of (sum of x squared / n - (sum of x / n) squared).
Weighted mean and geometric mean
Geometric mean = the nth root of (value1 x value2 x ... x valuen).
Mode, median and mean
Removing one very large value lowers the mean but may leave the median and the mode unchanged.
Outliers
Outliers may be genuine unusual values or may be the result of errors in recording data.
Range, quartiles and percentiles
An interpercentile range is one percentile minus another, for example the 10th to 90th or 2.5th to 97.5th interpercentile range.
Skewness
Positive skew could be indicated by mean > median > mode.
Practice questions with answers
A taste of the 62 questions in this topic, answers marked. Sign up to practise the full set with spaced repetition.
A shop wants to know which shoe size to stock the most of. Which average should it use?
- •The mean
- •The median
- ✓The mode
- •The range
An outlier is found in a set of survey data. What should be considered before removing it?
- ✓Whether it is a recording error or a genuine value
- •Whether it is the highest value in the data
- •Whether removing it will raise or lower the mean
- •Whether the data set has an odd number of values
A data set contains one extreme value. Why is the interquartile range a better measure of spread than the range?
- •It can be found without ordering data
- •It is always larger than the range
- •It uses every value in the data set
- ✓It uses only the middle 50% of the data
A distribution has positive skew. Which order of the averages is most likely?
- •mean = median = mode
- ✓mean > median > mode
- •median > mean > mode
- •mode > median > mean
Ava scored 65 in Maths (mean 55, sd 5) and 70 in English (mean 60, sd 10). Which statement is correct?
- •She did equally well in both subjects
- •She did relatively better in English
- ✓She did relatively better in Maths
- •They cannot be compared without medians
When is the geometric mean more useful than the arithmetic mean?
- ✓When averaging growth rates or index numbers
- •When every value is equally important
- •When the data include non-numeric categories
- •When the data set has an even number of values
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