Multiple choice

If the mode of observations $5,4,4,3,5,x,3,4,3,5,4,3,5$ is $3$, then median of the observations is

  1. $3$
  2. $4$
  3. $5$
  4. $3.5$
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B Correct answer
Explanation

The mode is 3, meaning 3 appears most frequently. Counting the occurrences: 3 appears 4 times, 4 appears 4 times, 5 appears 4 times. Since the mode is 3, there must be more 3s. If x=3, then 3 appears 5 times. The set is 3,3,3,3,3,4,4,4,4,5,5,5,5. Median is the 7th term, which is 4.

AI explanation

The mode is the most frequent observation, so if the mode is 3, the value of x must be 3. The data set becomes 5, 4, 4, 3, 5, 3, 3, 4, 3, 5, 4, 3, 5. Arranging these values in ascending order yields 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 5, 5, 5. The median is the 7th value, which is 4.

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