What is the mean of the range and median of the given data ? 9,8,7,5,11,10,13,16,15,23,19,7,9,11

Options

A. `15 . 25`
B. `13.5`
C. `14.25`
D. `14.5`

Answer

To find the mean of the range and median of the given data set: 9, 8, 7, 5, 11, 10, 13, 16, 15, 23, 19, 7, 9, 11, we will follow these steps:

### Step 1: Organize the Data
First, we need to arrange the data in ascending order.

**Data in ascending order:**
5, 7, 7, 8, 9, 9, 10, 11, 11, 13, 15, 16, 19, 23

### Step 2: Calculate the Median
To find the median, we need to determine the middle value of the ordered data. Since there are 14 data points (an even number), the median will be the average of the 7th and 8th values.

**Finding the 7th and 8th values:**
- 7th value = 10
- 8th value = 11

**Median Calculation:**
\[ \text{Median} = \frac{10 + 11}{2} = \frac{21}{2} = 10.5 \]

### Step 3: Calculate the Range
The range is found by subtracting the smallest value from the largest value in the data set.

**Finding the smallest and largest values:**
- Smallest value = 5
- Largest value = 23

**Range Calculation:**
\[ \text{Range} = 23 - 5 = 18 \]

### Step 4: Calculate the Mean of the Range and Median
Now we will find the mean of the range and median calculated in the previous steps.

**Mean Calculation:**
\[ \text{Mean} = \frac{\text{Range} + \text{Median}}{2} = \frac{18 + 10.5}{2} = \frac{28.5}{2} = 14.25 \]

### Final Answer
The mean of the range and median of the given data is **14.25**.

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