The median of the following data is 25, 31, 22, 26, 35, 29, 20, 32

Options

A. 27.5
B. 29.5
C. 22.5
D. None of these

Answer

To find the median of the given data set, we will follow these steps:

### Step 1: Arrange the data in ascending order
First, we need to sort the data set in ascending order. The given data is:
25, 31, 22, 26, 35, 29, 20, 32

Arranging these numbers in ascending order, we get:
20, 22, 25, 26, 29, 31, 32, 35

### Step 2: Determine the number of observations
Next, we count the number of observations in the data set. In this case, there are 8 numbers.

### Step 3: Identify if the number of observations is odd or even
Since we have 8 observations, which is an even number, we will use the formula for finding the median in a data set with an even number of observations.

### Step 4: Find the two middle numbers
For an even number of observations, the median is the average of the two middle numbers. The two middle numbers in our sorted data are the 4th and 5th numbers:
- 4th number: 26
- 5th number: 29

### Step 5: Calculate the median
Now, we calculate the median using the formula:
\[ \text{Median} = \frac{\text{4th number} + \text{5th number}}{2} = \frac{26 + 29}{2} = \frac{55}{2} = 27.5 \]

Thus, the median of the given data set is **27.5**.

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