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Choosing the right measure: mean, median or mode sheet
3-mark answer frame

For a grouped data set, the mean is 26.4 and the median is 25.8. (i) Find the mode using the empirical relation. (ii) Which measure would you use to describe the most common value, and why?

How to lay out the answer. Follow the frame, then write it in your own words.

  1. 1 · Write what is given and what is to be found. Given: mean = 26.4, median = 25.8. To find: the mode, and the right measure for the most common value.
  2. 2 · Write the relation. 3 Median = Mode + 2 Mean, so Mode = 3 Median − 2 Mean.
  3. 3 · Substitute. Mode = 3 × 25.8 − 2 × 26.4 = 77.4 − 52.8 = 24.6.
  4. 4 · Choose the measure. The mode, because it is the value that occurs most often.
  5. 5 · Check and box the answer. Check: Mode + 2 Mean = 24.6 + 52.8 = 77.4 = 3 × 25.8. Box: Mode = 24.6.

Scoring tip: Write the empirical relation first, then rearrange it before you substitute.