. Find the median of the given data:
24, 19, 13, 15, 12, 36, 21, 30

Options

A. `17`
B. `18`
C. `19`
D. `20`

Answer

To find the median of the given data set: 24, 19, 13, 15, 12, 36, 21, 30, we will follow these steps:

### Step 1: Arrange the data in ascending order
First, we need to sort the data from the smallest to the largest value.

**Data in ascending order:**
12, 13, 15, 19, 21, 24, 30, 36

### Step 2: Count the total number of observations
Next, we count how many numbers are in our data set.

**Total number of observations (n):**
8

### Step 3: Determine if n is odd or even
Since we have 8 observations, we note that this is an even number.

### Step 4: Use the median formula for even numbers
For an even number of observations, the median is calculated using the formula:
\[ \text{Median} = \frac{\text{(n/2)th observation} + \text{(n/2 + 1)th observation}}{2} \]
Here, n = 8, so we find:
\[ \text{Median} = \frac{\text{(8/2)th observation} + \text{(8/2 + 1)th observation}}{2} \]
This simplifies to:
\[ \text{Median} = \frac{\text{4th observation} + \text{5th observation}}{2} \]

### Step 5: Identify the 4th and 5th observations
From our sorted data:
- 4th observation = 19
- 5th observation = 21

### Step 6: Calculate the median
Now we substitute the values into the median formula:
\[ \text{Median} = \frac{19 + 21}{2} = \frac{40}{2} = 20 \]

### Final Answer
The median of the given data is **20**.

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