The marks obtained by 13 student in a test are 10, 3, 10, 12, 6, 7, 9, 6, 7, 10, 8, 6, 7. The median of this data is?

Options

A. 7
B. 8
C. 9
D. 10

Explanation

To find the median of the given marks obtained by 13 students, we will follow these steps:

### Step 1: Organize the Data
First, we need to arrange the marks in ascending order. The given marks are:
10, 3, 10, 12, 6, 7, 9, 6, 7, 10, 8, 6, 7.

Arranging these in ascending order, we get:
3, 6, 6, 6, 7, 7, 7, 8, 9, 10, 10, 10, 12.

### Step 2: Count the Number of Observations
Next, we count the total number of observations. In this case, there are 13 marks.

### Step 3: Determine if the Number of Observations is Odd or Even
Since 13 is an odd number, we will use the formula for finding the median in an odd set of data.

### Step 4: Find the Position of the Median
The position of the median can be found using the formula:
\[ \text{Median Position} = \frac{n + 1}{2} \]
where \( n \) is the number of observations.

For our data:
\[ \text{Median Position} = \frac{13 + 1}{2} = \frac{14}{2} = 7 \]

### Step 5: Locate the Median
Now, we need to find the 7th value in our ordered list:
1. 3
2. 6
3. 6
4. 6
5. 7
6. 7
7. **7** (This is the 7th value)
8. 8
9. 9
10. 10
11. 10
12. 10
13. 12

### Conclusion
The median of the given data is **7**.

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