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In a frequency table the classes are written in the inclusive form 10–19, 20–29, 30–39 and so on. What are the true class boundaries of the class 20–29, and what is its class size?

Competition practiceData & Probability
  • ABoundaries 20 and 29, class size 9
  • BBoundaries 20 and 30, class size 10
  • CBoundaries 19.5 and 29.5, class size 10
  • DBoundaries 19.5 and 29.5, class size 9

Step-by-Step Solution

Inclusive classes leave a gap of 1 between 19 and 20, and that gap is shared equally between the neighbours: 0.5 is taken off the lower limit and added to the upper one. So the boundaries of 20–29 are 19.5 and 29.5 and the class size is 29.5 − 19.5 = 10, not the 29 − 20 = 9 that the printed limits suggest. The correction matters in practice, because histograms and the grouped median and mode formulas all work with boundaries rather than printed limits.
Answer: C) Boundaries 19.5 and 29.5, class size 10

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