The median of the data 7, 21, 2, 17, 3, 13, 7, 4, 9, 7, 9 is :

Options

A. 4
B. 17
C. 7
D. 9

Answer

To find the median of the given data set \(7, 21, 2, 17, 3, 13, 7, 4, 9, 7, 9\), we will follow these steps:

### Step 1: Arrange the Data in Ascending Order
First, we need to sort the data in ascending order. The given data is:
\[ 7, 21, 2, 17, 3, 13, 7, 4, 9, 7, 9 \]

Arranging these numbers in ascending order gives:
\[ 2, 3, 4, 7, 7, 7, 9, 9, 13, 17, 21 \]

### Step 2: Count the Number of Data Points
Next, we count the total number of data points. In this case, we have:
\[ 11 \text{ data points} \]

### Step 3: Determine if the Number of Data Points is Odd or Even
Since we have an odd number of data points (11), we will use the formula for finding the median in a data set with an odd number of terms.

### Step 4: Find the Position of the Median
The position of the median can be calculated using the formula:
\[ \text{Median Position} = \frac{n + 1}{2} \]
where \(n\) is the number of data points. Here, \(n = 11\):
\[ \text{Median Position} = \frac{11 + 1}{2} = \frac{12}{2} = 6 \]

### Step 5: Identify the Median Value
Now, we find the value at the 6th position in our sorted data:
\[ \text{Sorted Data: } 2, 3, 4, 7, 7, 7, 9, 9, 13, 17, 21 \]
The 6th term is \(7\).

### Conclusion
Thus, the median of the data set is:
\[ \boxed{7} \]

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