The weight of 12 students (in kg) are :
40,61,54,50,59,37,51,41,48,62,46 and 34.
Find the median weight.
If the weight of 62 kg is replaced by 35 kg, find the new median weight.

Answer

To find the median weight of the given data, we will follow these steps:

### Step 1: Arrange the data in ascending order
The weights of the 12 students are:
40, 61, 54, 50, 59, 37, 51, 41, 48, 62, 46, and 34.

Arranging these weights in ascending order:
34, 37, 40, 41, 46, 48, 50, 51, 54, 59, 61, 62.

### Step 2: Count the number of observations
We have a total of 12 weights. Since 12 is an even number, we will find the median by taking the average of the 6th and 7th terms.

### Step 3: Identify the 6th and 7th terms
From the ordered list:
- The 6th term is 48.
- The 7th term is 50.

### Step 4: Calculate the median
The median is calculated using the formula:
\[ \text{Median} = \frac{\text{6th term} + \text{7th term}}{2} = \frac{48 + 50}{2} = \frac{98}{2} = 49. \]

### Step 5: Replace the weight of 62 kg with 35 kg
Now, we replace 62 kg with 35 kg in the original list. The new weights are:
40, 61, 54, 50, 59, 37, 51, 41, 48, 35, 46, and 34.

### Step 6: Arrange the new data in ascending order
Arranging these new weights in ascending order:
34, 35, 37, 40, 41, 46, 48, 50, 51, 54, 59, 61.

### Step 7: Identify the new 6th and 7th terms
From the new ordered list:
- The 6th term is 46.
- The 7th term is 48.

### Step 8: Calculate the new median
The new median is calculated using the same formula:
\[ \text{New Median} = \frac{\text{6th term} + \text{7th term}}{2} = \frac{46 + 48}{2} = \frac{94}{2} = 47. \]

### Final Answers:
- The median weight of the original data is **49 kg**.
- The new median weight after replacing 62 kg with 35 kg is **47 kg**.

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