The marks secured in Mathematics test (out of 25) by 10 students are as follows
18, 25, 23, 20, 9, 15, 10, 5, 16, 24
Calculate the median

Answer

To calculate the median of the marks secured in the Mathematics test by 10 students, we will follow these steps:

### Step-by-Step Solution:

1. **List the Marks**: The marks secured by the students are:
- 18, 25, 23, 20, 9, 15, 10, 5, 16, 24

2. **Arrange the Marks in Ascending Order**: To find the median, we first need to arrange the marks from the smallest to the largest:
- 5, 9, 10, 15, 16, 18, 20, 23, 24, 25

3. **Count the Number of Students**: We have a total of 10 marks (students).

4. **Determine if the Number of Students is Even or Odd**: Since 10 is an even number, we will use the formula for finding the median of an even set of numbers.

5. **Use the Median Formula for Even Numbers**: The formula for finding the median when there is an even number of observations (n) is:
\[ \text{Median} = \frac{\text{(n/2)th observation} + \text{((n/2) + 1)th observation}}{2} \]
Here, n = 10.

6. **Calculate the Positions**:
- n/2 = 10/2 = 5
- (n/2) + 1 = 5 + 1 = 6

7. **Find the 5th and 6th Observations**: From our ordered list:
- 5th observation = 16
- 6th observation = 18

8. **Calculate the Median**:
\[ \text{Median} = \frac{16 + 18}{2} = \frac{34}{2} = 17 \]

### Final Answer:
The median of the marks is **17**.

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