Median of the data 10,21,5,6,4,12,14,3, is

Options

A. 16
B. 8
C. 4
D. None of these

Answer

To find the median of the given data set: 10, 21, 5, 6, 4, 12, 14, 3, 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:** 10, 21, 5, 6, 4, 12, 14, 3

**Ascending Order:** 3, 4, 5, 6, 10, 12, 14, 21

### Step 2: Count the number of data points
Next, we need to determine how many data points we have.

**Total number of data points (n):** 8

### Step 3: Determine if n is odd or even
Since the total number of data points (n) is 8, which is even, we will use the formula for finding the median in an even set of data.

### Step 4: Use the median formula for even data
The median for an even number of observations is calculated using the formula:

\[ \text{Median} = \frac{\text{(n/2)th term} + \text{(n/2 + 1)th term}}{2} \]

For our data:
- n = 8
- n/2 = 4
- n/2 + 1 = 5

### Step 5: Identify the 4th and 5th terms in the sorted data
From our sorted data (3, 4, 5, 6, 10, 12, 14, 21):
- 4th term = 6
- 5th term = 10

### Step 6: Calculate the median
Now, we can calculate the median using the identified terms:

\[ \text{Median} = \frac{6 + 10}{2} = \frac{16}{2} = 8 \]

### Conclusion
Thus, the median of the given data set is **8**.

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