What is the mean of the range and median of the given data ?
11,16,14,7,11,23,10,30,20,33,19,12,17,14

Options

A. `20.5`
B. `25.5`
C. `24`
D. `19`

Answer

To solve the question, we need to find the mean of the range and median of the given data set. Here are the steps to arrive at the solution:

### Step 1: Arrange the Data in Increasing Order
We start by organizing the given data in ascending order. The data provided is:
11, 16, 14, 7, 11, 23, 10, 30, 20, 33, 19, 12, 17, 14.

Arranging this data in increasing order gives us:
7, 10, 11, 11, 12, 14, 14, 16, 17, 19, 20, 23, 30, 33.

### Step 2: Calculate the Range
The range is calculated by subtracting the minimum value from the maximum value in the data set.

- Maximum value = 33
- Minimum value = 7

So, the range is:
\[ \text{Range} = \text{Maximum} - \text{Minimum} = 33 - 7 = 26. \]

### Step 3: Calculate the Median
To find the median, we need to determine the middle value of the ordered data. Since there are 14 numbers (an even count), the median will be the average of the two middle numbers.

The two middle numbers in our ordered list are the 7th and 8th values:
- 7th value = 14
- 8th value = 16

Now, we calculate the median:
\[ \text{Median} = \frac{14 + 16}{2} = \frac{30}{2} = 15. \]

### Step 4: Calculate the Mean of the Range and Median
Now that we have both the range and the median, we can find the mean of these two values.

- Range = 26
- Median = 15

The mean is calculated as follows:
\[ \text{Mean} = \frac{\text{Range} + \text{Median}}{2} = \frac{26 + 15}{2} = \frac{41}{2} = 20.5. \]

### Final Answer
The mean of the range and median of the given data is **20.5**.

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