Data summaries
Choose an average that fits the data and interpret it with an appropriate measure of spread.
What you will learn
- Find the median of ordered data.
- Explain why a mean may be affected by outliers.
Order before selecting a position
The median divides ordered data into two halves. For an odd number n of values, it is at position (n+1)/2. For an even number, average the two central values. A position is an index into the sorted list, not the numerical answer.
The mean uses every value and can move strongly when an extreme observation is added. The median depends on order and is often more resistant to an outlier.
A centre does not describe everything
Two data sets can have the same mean but very different variability. The range is maximum minus minimum; other measures describe spread around the centre. When comparing distributions, discuss both typical value and spread, and use the context's units.
For a frequency table, treat frequencies as repeated observations. The total number of observations is the sum of frequencies, not the number of rows.
Worked example
Find the median of 8, 3, 15, 9, 7, 10.
Show the worked solution
- Sort the data: 3,7,8,9,10,15.
- There are six values; select positions 3 and 4.
- Average 8 and 9.
Answer 8.5
Common mistakes
- Do not find a median from an unsorted list.
- The median of an even-sized set need not be one of its observations.
What can you explain now?
Which changes more when 100 replaces 10 in 2,4,6,8,10: mean or median?
Compare with the explanation
The mean
The median stays 6. The mean rises from 6 to 24.
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These lessons teach the topics represented in our current practice sets. They are not a complete course for every paper or option in the qualification.
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