The median of the data `78,56,22,34,45,54,39,54, and 84` is

Options

A. `45`
B. `49.5`
C. `54`
D. `56`

Explanation

To find the median of the given data set `78, 56, 22, 34, 45, 54, 39, 54, and 84`, we will follow these steps:

### Step 1: Count the number of observations
First, we need to count how many numbers are in the data set.

**Calculation:**
- The numbers are: 78, 56, 22, 34, 45, 54, 39, 54, and 84.
- Total count = 9 observations.

### Step 2: Arrange the data in ascending order
Next, we need to arrange the data in ascending order (from smallest to largest).

**Ascending Order:**
- The sorted data is: 22, 34, 39, 45, 54, 54, 56, 78, 84.

### Step 3: Determine if the number of observations is odd or even
Since we have 9 observations, which is an odd number, we will use the formula for finding the median in an odd set of numbers.

### Step 4: Find the median position
For an odd number of observations, the median is located at the position given by the formula:
\[ \text{Median Position} = \frac{n + 1}{2} \]
where \( n \) is the number of observations.

**Calculation:**
- \( n = 9 \)
- Median Position = \( \frac{9 + 1}{2} = \frac{10}{2} = 5 \)

### Step 5: Identify the median value
Now, we find the value at the 5th position in the sorted data.

**Sorted Data:**
- 1st: 22
- 2nd: 34
- 3rd: 39
- 4th: 45
- 5th: 54 (This is the median)

### Conclusion
The median of the data set is **54**.

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