The weights of 10 students (in kg) are
40, 52, 34, 47, 31, 35, 48, 41, 44, 38
Find the median weight.

Options

A. `45.5` kg
B. 40 kg
C. `40.5` kg
D. 45 kg

Answer

To find the median weight of the 10 students, we will follow these steps:

### Step 1: Arrange the data in ascending order
The weights of the students are given as:
40, 52, 34, 47, 31, 35, 48, 41, 44, 38

Arranging these weights in ascending order, we get:
31, 34, 35, 38, 40, 41, 44, 47, 48, 52

### Step 2: Determine the number of data points
We have a total of 10 weights (data points).

### Step 3: Identify if the number of data points is odd or even
Since we have 10 data points, which is an even number, we will use the formula for finding the median in an even set of numbers.

### Step 4: Use the median formula for even numbers
The formula for finding the median when the number of observations (n) is even is:
Median = (n/2 th term + (n/2 + 1) th term) / 2

Here, n = 10. So, we calculate:
- n/2 = 10/2 = 5
- n/2 + 1 = 5 + 1 = 6

### Step 5: Find the 5th and 6th terms in the ordered list
From our ordered list:
1st term = 31
2nd term = 34
3rd term = 35
4th term = 38
5th term = 40
6th term = 41
7th term = 44
8th term = 47
9th term = 48
10th term = 52

The 5th term is 40 and the 6th term is 41.

### Step 6: Calculate the median
Now, we substitute the values into the median formula:
Median = (40 + 41) / 2 = 81 / 2 = 40.5

### Conclusion
The median weight of the students is **40.5 kg**.

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