Find the median of the following data:
5, 2, 7, 9, 3, 2, 4, 8.

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 arrange the data in ascending order. The given data is:
5, 2, 7, 9, 3, 2, 4, 8.

Arranging this data in ascending order gives us:
2, 2, 3, 4, 5, 7, 8, 9.

### Step 2: Count the Number of Values
Next, we need to count the total number of values in the data set.
In this case, we have a total of 8 values.

### Step 3: Determine if the Number of Values is Even or Odd
Since we have 8 values, which is an even number, we will use the formula for finding the median for an even set of numbers.

### Step 4: Use the Median Formula for Even Numbers
The formula for finding the median when the number of observations (n) is even is:
\[ \text{Median} = \frac{\text{n/2 term} + \text{(n/2 + 1) term}}{2} \]
Here, n = 8.

Calculating the terms:
- n/2 = 8/2 = 4
- n/2 + 1 = 4 + 1 = 5

### Step 5: Identify the 4th and 5th Terms
Now, we will identify the 4th and 5th terms in the ordered data:
- The 4th term is 4.
- The 5th term is 5.

### Step 6: Calculate the Median
Now we can substitute these values into the median formula:
\[ \text{Median} = \frac{4 + 5}{2} = \frac{9}{2} = 4.5 \]

### Final Answer
Thus, the median of the given data set is **4.5**.

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