What is the median of the given data ?
41,43,46,50,85,61,76,55,68,95

Options

A. 61
B. 58
C. 57
D. 55

Answer

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

### Step 1: Arrange the Data in Ascending Order
First, we need to arrange the numbers in ascending order. The given data is:
41, 43, 46, 50, 85, 61, 76, 55, 68, 95

Arranging these numbers in ascending order, we get:
41, 43, 46, 50, 55, 61, 68, 76, 85, 95

### Step 2: Count the Number of Terms
Next, we will count the number of terms in the data set.
The arranged data has 10 terms:
1. 41
2. 43
3. 46
4. 50
5. 55
6. 61
7. 68
8. 76
9. 85
10. 95

### Step 3: Determine if the Number of Terms is Even or Odd
Since there are 10 terms, which is an even number, we will use the median formula for even numbers.

### Step 4: Use the Median Formula for Even Number of Terms
For an even number of terms, the median is calculated as the average of the two middle numbers. The middle terms can be found at positions n/2 and (n/2) + 1.

Here, n = 10:
- n/2 = 10/2 = 5 (5th term)
- (n/2) + 1 = 5 + 1 = 6 (6th term)

### Step 5: Identify the 5th and 6th Terms
From our arranged data:
- The 5th term is 55
- The 6th term is 61

### Step 6: Calculate the Median
Now, we will calculate the median by taking the average of the 5th and 6th terms:
Median = (5th term + 6th term) / 2
Median = (55 + 61) / 2
Median = 116 / 2
Median = 58

### Conclusion
Thus, the median of the given data is **58**.

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