Find the median of the following data
`33,34, 28, 29, 72, 10, 8, 35`

Options

A. 29
B. 31
C. 33
D. 35

Answer

To find the median of the given data set \(33, 34, 28, 29, 72, 10, 8, 35\), 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**: \(8, 10, 28, 29, 33, 34, 35, 72\)

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

**Total numbers (N)**: \(8\)

### Step 3: Determine if N is odd or even
Since \(N = 8\) is even, we will use the formula for finding the median of an even set of numbers.

### Step 4: Use the median formula for even N
The formula for the median when \(N\) is even is:
\[ \text{Median} = \frac{\text{N/2 th term} + \text{(N/2 + 1) th term}}{2} \]
Here, \(N = 8\), so we calculate:
- \(N/2 = 8/2 = 4\)
- \(N/2 + 1 = 4 + 1 = 5\)

### Step 5: Identify the 4th and 5th terms in the sorted data
From the sorted data:
- 4th term = \(29\)
- 5th term = \(33\)

### Step 6: Calculate the median
Now we substitute the 4th and 5th terms into the median formula:
\[ \text{Median} = \frac{29 + 33}{2} = \frac{62}{2} = 31 \]

### Final Answer
The median of the given data is **31**.

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