The marks (out of 100) obtained by a group of students in Mathematics test are :
88, 74, 90, 88, 40, 46, 58, 96, 82, and 78. Find :
median of the marks obtained

Answer

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

### Step 1: List the marks
The marks obtained by the students are:
88, 74, 90, 88, 40, 46, 58, 96, 82, and 78.

### Step 2: Count the number of observations
We count the number of marks given:
1, 2, 3, 4, 5, 6, 7, 8, 9, 10.
So, the number of observations (n) is 10.

### Step 3: Arrange the marks in ascending order
Next, we arrange the marks in ascending order:
40, 46, 58, 74, 78, 82, 88, 88, 90, 96.

### Step 4: Determine if the number of observations is odd or even
Since we have 10 observations (which is even), we will use the formula for finding the median for an even number of observations.

### Step 5: Use the median formula for even observations
The formula for the median when n is even is:
\[ \text{Median} = \frac{\text{(n/2)th term} + \text{(n/2 + 1)th term}}{2} \]
Here, \( n = 10 \), so:
\[ \text{Median} = \frac{\text{(10/2)th term} + \text{(10/2 + 1)th term}}{2} = \frac{\text{5th term} + \text{6th term}}{2} \]

### Step 6: Identify the 5th and 6th terms
From our arranged list:
- The 5th term is 78.
- The 6th term is 82.

### Step 7: Calculate the median
Now, we can calculate the median:
\[ \text{Median} = \frac{78 + 82}{2} = \frac{160}{2} = 80. \]

### Final Answer
Thus, the median of the marks obtained is **80**.

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