2026 · Q93
Consider the observations x, x + 4, 30, 33, 74, 78, 49, 52, 98, 85. If the median of the data is 67, then what is the value of x?
Elementary MathematicsStatistics
- A66
- B65
- C63
- DCannot be determined due to insufficient data
Explanation
With 10 observations the median is the mean of the 5th and 6th sorted values. Trying x = 65 gives the sorted list 30, 33, 49, 52, 65, 69, 74, 78, 85, 98, whose 5th and 6th values average to (65 + 69)/2 = 67 — matching the given median. Nearby values like x = 63 or 66 shift the median to 65 or 68, so x = 65 uniquely, option B.