Find the median of the following set of data. 42, 13, 76, 5, 21, 13, 37

Options

A. 33
B. 21
C. 33.5
D. 29

Answer

To find the median of the given set of data: 42, 13, 76, 5, 21, 13, 37, we will follow these steps:

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

**Data in ascending order:**
5, 13, 13, 21, 37, 42, 76

### Step 2: Count the number of data points.
Next, we count how many numbers are in our sorted list.

**Total number of data points (n):**
There are 7 numbers in total.

### Step 3: Determine if the number of data points is odd or even.
Since we have 7 data points, which is an odd number, we will use the formula for finding the median in an odd set.

### Step 4: Use the median formula for an odd number of data points.
The formula for the median when the number of data points (n) is odd is:
\[ \text{Median} = \frac{n + 1}{2} \text{th term} \]

**Calculating the position of the median:**
\[ \frac{7 + 1}{2} = \frac{8}{2} = 4 \]
This means the median is the 4th term in our sorted list.

### Step 5: Identify the 4th term in the sorted list.
Now, we look at our sorted data:
1. 5
2. 13
3. 13
4. 21
5. 37
6. 42
7. 76

The 4th term is **21**.

### Conclusion:
Thus, the median of the given set of data is **21**.

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