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
Arrange in as Ascending order = 3, 4, 4, 4, 5, 5, 6, 8, 9, 9, 10, 11, 13, 18
N = 14 which is even
Hence, median (a) = \(\frac{(\frac{n}{2})th\;term\;+\;(\frac{n}{2} +1)th\;term}{2}\)
= \(\frac{7th\;term\;+\;8th\;term}{2}\)
= \(\frac{6+8}{2}\) = 7
Mode = is most frequently occurring value in the list.
i.e. Mode (b) = 4
Range is the difference between the largest number and smallest number of data.
i.e. Range (c)= 18-3 = 15
Now, (3a-2b+c) = 3 ×7 - 2×4 + 15 = 21-8+15 = 28