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

Options

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

Answer

To find the median of the distribution, we will follow these steps:

### Step 1: Arrange the data in ascending order
First, we need to sort the given numbers in ascending order. The numbers provided 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: Determine the number of observations
Next, we count the number of observations in the dataset. Here, we have:
2, 3, 4, 5, 6, 7, 9 (total of 7 numbers).

### Step 3: Find the median position
Since we have an odd number of observations (7), the median will be the middle number. The position of the median can be found using the formula:
Median position = (n + 1) / 2,
where n is the number of observations.

Substituting n = 7:
Median position = (7 + 1) / 2 = 8 / 2 = 4.

### Step 4: Identify the median
Now, we look for the 4th number in our sorted list:
2, 3, 4, 5, 6, 7, 9.

The 4th number is 5.

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

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