Find the median of the following data.
72, 93, 48, 36, 79, 23, 41, and 81.

Answer

To find the median of the given data set: 72, 93, 48, 36, 79, 23, 41, and 81, we can 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:** 23, 36, 41, 48, 72, 79, 81, 93

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

**Total number of observations (n):** 8

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

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

### Step 5: Identify the 4th and 5th observations.
From our sorted data:
- 4th observation = 48
- 5th observation = 72

### Step 6: Calculate the median.
Now we can substitute the 4th and 5th observations into the median formula:
\[ \text{Median} = \frac{48 + 72}{2} = \frac{120}{2} = 60 \]

### Final Answer:
The median of the given data set is **60**.

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