What is the mean of the range, mode and median of the data given below ?
5, 10, 3, 6, 4, 8, 9, 3, 15, 2, 9, 4, 19, 11, 4

The correct answer is Option 2: 9.

Given data set:
5, 10, 3, 6, 4, 8, 9, 3, 15, 2, 9, 4, 19, 11, 4

First, let's arrange the data in ascending order:
2, 3, 3, 4, 4, 4, 5, 6, 8, 9, 9, 10, 11, 15, 19

Total number of terms (N) = 15

1. Range:
Range = Maximum value - Minimum value
Range = 19 - 2 = 17

2. Mode:
Mode is the value that appears most frequently in the data set.
Here, 4 appears 3 times (more than any other number).
So, Mode = 4

3. Median:
Since N = 15 (odd), the median is the ^{(N + 1)}/₂ th term.
Position of Median = ^{(15 + 1)}/₂ = 8th term
Looking at the sorted data, the 8th term is 6.
So, Median = 6

4. Mean of Range, Mode, and Median:
$\text{Mean}=\frac{\text{Range}+\text{Mode}+\text{Median}}{3}$

$\text{Mean}=\frac{17+4+6}{3}=\frac{27}{3}=9$

Hence, the mean of the range, mode, and median is 9.