A variate X takes values 2, 9, 3, 7, 5, 4, 3, 2, 10.What is the median?

Options

A. 2
B. 4
C. 7
D. 9

Answer

To find the median of the given variate X, we will follow these steps:

### Step 1: List the values
The values given are:
\[ 2, 9, 3, 7, 5, 4, 3, 2, 10 \]

### Step 2: Arrange the values in ascending order
We need to sort these values from the smallest to the largest:
\[ 2, 2, 3, 3, 4, 5, 7, 9, 10 \]

### Step 3: Count the number of values
Now, we count how many values we have:
There are 9 values in total.

### Step 4: Determine if the count is odd or even
Since 9 is an odd number, we will use the formula for finding the median in a set with an odd number of observations.

### Step 5: Use the median formula
The formula for finding the median when the number of observations (n) is odd is:
\[ \text{Median} = \left( \frac{n + 1}{2} \right)^{th} \text{ term} \]
Substituting \( n = 9 \):
\[ \text{Median} = \left( \frac{9 + 1}{2} \right)^{th} \text{ term} = \left( \frac{10}{2} \right)^{th} \text{ term} = 5^{th} \text{ term} \]

### Step 6: Identify the 5th term in the ordered list
From our ordered list:
\[ 2, 2, 3, 3, 4, 5, 7, 9, 10 \]
The 5th term is:
\[ 4 \]

### Conclusion
Thus, the median of the given variate X is:
\[ \text{Median} = 4 \]

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