What is the median of the distribution 3, 7, 6, 9, 5, 4, 2?

Options

A. 5
B. 6
C. 7
D. 8

Explanation

To find the median of the distribution 3, 7, 6, 9, 5, 4, 2, we will follow these steps:

### Step 1: Arrange the data in ascending order.
First, we need to sort the numbers in ascending order. The given numbers are:
3, 7, 6, 9, 5, 4, 2.

When we arrange them in ascending order, we get:
2, 3, 4, 5, 6, 7, 9.

### Step 2: Count the total number of observations.
Next, we count how many numbers are in the distribution. In this case, there are 7 numbers.

### Step 3: Determine if the number of observations is odd or even.
Since we have 7 numbers, which is an odd number, we will use the formula for finding the median in a dataset with an odd number of observations.

### Step 4: Use the median formula.
The formula for finding the median when the number of observations (n) is odd is:
\[ \text{Median} = \frac{n + 1}{2} \]
Substituting n = 7 into the formula:
\[ \text{Median} = \frac{7 + 1}{2} = \frac{8}{2} = 4 \]

### Step 5: Identify the median value.
Now, we need to find the 4th number in our ordered list:
1. 2
2. 3
3. 4
4. 5 (This is the median)
5. 6
6. 7
7. 9

Thus, the median of the distribution is **5**.

### Final Answer:
The median of the distribution is **5**.

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