The median of 5,19,14,6,8,9,12,13,21 is

Options

A. 9
B. 13
C. 14
D. 12

Answer

To find the median of the given data set: 5, 19, 14, 6, 8, 9, 12, 13, 21, we will follow these steps:

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

**Sorted Data:** 5, 6, 8, 9, 12, 13, 14, 19, 21

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

**Total Count:** There are 9 numbers in total.

### Step 3: Determine if the count is odd or even
Since there are 9 numbers, we check if this count is odd or even.

**Count Type:** 9 is an odd number.

### Step 4: Use the median formula for an odd count
For an odd number of observations, the median is found using the formula:
\[ \text{Median} = \frac{N + 1}{2} \]
where \( N \) is the total number of observations.

**Calculation:**
\[ \text{Median Position} = \frac{9 + 1}{2} = \frac{10}{2} = 5 \]

### Step 5: Identify the median value
Now, we need to find the value at the 5th position in our sorted list.

**5th Term:** Looking at our sorted data:
1. 1st: 5
2. 2nd: 6
3. 3rd: 8
4. 4th: 9
5. 5th: 12

Thus, the median is 12.

### Final Answer
The median of the data set 5, 19, 14, 6, 8, 9, 12, 13, 21 is **12**.

---