The nine-number dataset 74, 82, 78, 72, 73, 78, 72, 78, 81 has a median of 78. Which of the following statements is true about this dataset?

• A. The median is 78.
• B. The mean is 80.
• C. The mode is 72.
• D. The maximum is 90.

Answer: (A)

The main idea here is how to determine the median in a small data set. For an odd number of observations, the median is the middle value when the numbers are ordered from smallest to largest. When the nine numbers are arranged, they become 72, 72, 73, 74, 78, 78, 78, 81, 82, so the middle value (the fifth one) is 78. That makes the statement about the median true.

Quick checks: adding all the numbers gives 688, and dividing by 9 gives a mean of about 76.44, not 80. The most frequent value is 78, so the mode is 78, not 72. The largest value is 82, not 90. So only the statement about the median being 78 is correct.