What is the mean of the mode, median and range of the data given below ?
17, 8, 11, 13, 9, 14, 10, 11, 16, 23, 15, 7

The correct answer is Option 1 (13).

To find the mean of the mode, median, and range of the given data, we first need to calculate each of these three statistical measures step-by-step.

The given data set is:
17, 8, 11, 13, 9, 14, 10, 11, 16, 23, 15, 7

First, let's arrange the data set in ascending order:
7, 8, 9, 10, 11, 11, 13, 14, 15, 16, 17, 23

Total number of observations (n) = 12

Step 1: Find the Mode
The mode is the value that appears most frequently in the data set.
Looking at the ordered list, the number 11 appears twice, while all other numbers appear only once.
So, Mode = 11

Step 2: Find the Median
Since the number of observations n = 12 is even, the median is the average of the two middle terms, which are the 6th and 7th terms.

$\text{6th term}=11$

$\text{7th term}=13$

$\text{Median}=\frac{11+13}{2}=\frac{24}{2}=12$

Step 3: Find the Range
The range is the difference between the maximum value and the minimum value in the data set.

$\text{Maximum value}=23$

$\text{Minimum value}=7$

$\text{Range}=23-7=16$

Step 4: Find the Mean of Mode, Median, and Range
Now, we find the arithmetic mean of the three values obtained (Mode = 11, Median = 12, Range = 16):

$\text{Mean}=\frac{\text{Mode}+\text{Median}+\text{Range}}{3}$

$\text{Mean}=\frac{11+12+16}{3}$

$\text{Mean}=\frac{39}{3}=13$

Thus, the mean of the mode, median, and range is 13.