Find the median of the given data set :
42, 45, 58, 87, 45, 54, 65, 12, 25, 25, 59, 60

Options

A. `49.5`
B. `59.5`
C. 54
D. 45

Answer

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

### Step 1: Arrange the Data in Ascending Order
First, we need to arrange the data set in ascending order. The given data set is:
42, 45, 58, 87, 45, 54, 65, 12, 25, 25, 59, 60

Arranging these numbers in ascending order gives us:
12, 25, 25, 42, 45, 45, 54, 58, 59, 60, 65, 87

### Step 2: Count the Number of Observations
Next, we count the total number of observations in the arranged data set.
The arranged data set has 12 numbers:
1. 12
2. 25
3. 25
4. 42
5. 45
6. 45
7. 54
8. 58
9. 59
10. 60
11. 65
12. 87

So, \( n = 12 \).

### Step 3: Determine the Median Position
Since the number of observations (n) is even, we will use the formula for finding the median:
\[ \text{Median} = \frac{\text{(n/2)th term} + \text{((n/2) + 1)th term}}{2} \]
Here, \( n = 12 \), so:
\[ \text{Median} = \frac{\text{(12/2)th term} + \text{((12/2) + 1)th term}}{2} = \frac{\text{6th term} + \text{7th term}}{2} \]

### Step 4: Identify the 6th and 7th Terms
From our arranged data set:
- The 6th term is 45
- The 7th term is 54

### Step 5: Calculate the Median
Now, we can calculate the median:
\[ \text{Median} = \frac{45 + 54}{2} = \frac{99}{2} = 49.5 \]

Thus, the median of the given data set is **49.5**.

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