In a mathematics test given to 15 students, the following marks (out of 100) are recorded: 41, 39, 48, 52, 46, 62, 54, 40, 96, 52, 98, 40, 42, 52, 60 Find the mean, median and mode of this data.

Answer

To find the mean, median, and mode of the given marks of 15 students, we will follow these steps:

### Step 1: Arrange the Data in Ascending Order
First, we need to arrange the marks in ascending order for easier calculation of median and mode.

**Given Marks:**
41, 39, 48, 52, 46, 62, 54, 40, 96, 52, 98, 40, 42, 52, 60

**Arranged Marks:**
39, 40, 40, 41, 42, 46, 48, 52, 52, 52, 54, 60, 62, 96, 98

### Step 2: Calculate the Mean
The mean is calculated using the formula:

\[ \text{Mean} = \frac{\text{Sum of all observations}}{\text{Total number of observations}} \]

**Sum of Observations:**
39 + 40 + 40 + 41 + 42 + 46 + 48 + 52 + 52 + 52 + 54 + 60 + 62 + 96 + 98 = 822

**Total Number of Observations:**
15

**Calculating Mean:**
\[ \text{Mean} = \frac{822}{15} = 54.8 \]

### Step 3: Calculate the Median
To find the median, we use the formula for the median position:

\[ \text{Median Position} = \frac{n + 1}{2} \]

Where \( n \) is the total number of observations.

**Calculating Median Position:**
\[ \text{Median Position} = \frac{15 + 1}{2} = 8 \]

The 8th observation in the arranged data is 52.

**Thus, the Median is:**
52

### Step 4: Calculate the Mode
The mode is the number that appears most frequently in the data set.

**Observations:**
- 39: 1 time
- 40: 2 times
- 41: 1 time
- 42: 1 time
- 46: 1 time
- 48: 1 time
- 52: 3 times
- 54: 1 time
- 60: 1 time
- 62: 1 time
- 96: 1 time
- 98: 1 time

**Finding the Mode:**
The number 52 appears 3 times, which is more than any other number.

**Thus, the Mode is:**
52

### Final Results
- **Mean:** 54.8
- **Median:** 52
- **Mode:** 52