If \(a\), \(b\) and \(c\) are the median, mode and range respectively of the data 10, 7, 6, 5, 4, 9, 5, 12, 11, 20, 14, 5, 10, 6, then what is the value of \(3a-2b+c\)?
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → 30
The median is the middle value of the ordered data (the average of the two middle values for an even count), the mode is the value that occurs most often, and the range is the largest value minus the smallest.
In ascending order: 4, 5, 5, 5, 6, 6, 7, 9, 10, 10, 11, 12, 14, 20
14 values, so the median is the average of the 7th and 8th: \(\displaystyle a=\frac{7+9}{2}=8\)
5 occurs three times, more than any other value, so \(b=5\)
Range \(c=20-4=16\)
\(3a-2b+c=3\times8-2\times5+16=24-10+16=30\)
The value of \(3a-2b+c\) is 30.