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Question 31

Consider the four values 5, 6, 9 and 12. Which statements about the median of this data set are true? Select all that apply.

  1. The median must be one of the values in the data set.
  2. The median is 7.5.Correct answer
  3. The median is 9, the larger of the two central values.
  4. The median is not one of the four listed values.Correct answer
  5. The median is 8.5, the mean of 5 and 12.

Explanation

The values are already in order and the two central ones are 6 and 9, whose mean is 7.5, so that is the median even though 7.5 never appears in the list. Keeping 9 alone uses only the larger of the two central values, which leaves the result above the centre because the smaller central value is given no weight.

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Question 31: Consider the four values 5, 6, 9 and 12. Which statements… · Statistics and Probability · Questena