If \(a\), \(b\) and \(c\) are the median, mode and range respectively of the data 9, 6, 5, 4, 3, 8, 4, 11, 10, 18, 13, 4, 9, 5, then what is the value of \(3a-2b+c\)?
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 28
All three measures come from the data arranged in order: the median is the middle value, the mode is the most frequent value and the range is largest minus smallest.
In ascending order: 3, 4, 4, 4, 5, 5, 6, 8, 9, 9, 10, 11, 13, 18 (14 values)
Median: average of the 7th (6) and 8th (8) values, \(a=\displaystyle\frac{6+8}{2}=7\)
Mode: 4 occurs 3 times, more than any other value, so \(b=4\)
Range: \(c=18-3=15\)
\(3a-2b+c=21-8+15=28\)
The value of \(3a-2b+c\) is 28.