Find the median of the given data : 37, 31, 42, 43, 46, 25, 39, 45, 32

Answer

To find the median of the given data set: 37, 31, 42, 43, 46, 25, 39, 45, 32, we will follow these steps:

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

**Sorted data:** 25, 31, 32, 37, 39, 42, 43, 45, 46

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

**Number of observations (n):** 9

### Step 3: Determine if n is odd or even.
Since the number of observations (n) is 9, which is odd, we will use the formula for finding the median for an odd number of observations.

### Step 4: Use the median formula for odd n.
The formula to find the median when n is odd is:
\[ \text{Median} = \left(\frac{n + 1}{2}\right)^{th} \text{ observation} \]
Substituting n = 9 into the formula:
\[ \text{Median} = \left(\frac{9 + 1}{2}\right)^{th} \text{ observation} = \left(\frac{10}{2}\right)^{th} \text{ observation} = 5^{th} \text{ observation} \]

### Step 5: Find the 5th observation in the sorted data.
Now we look for the 5th number in our sorted list:
- 1st: 25
- 2nd: 31
- 3rd: 32
- 4th: 37
- 5th: 39

Thus, the 5th observation is 39.

### Conclusion: State the median.
The median of the given data set is **39**.

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