What is the median of the numbers `4.6, 0, 9.3, -4.8, 7.6,2.3,12.7,3.5,8.2,6.1,3.9,5.2?`

Options

A. 3.8
B. 4.9
C. 5.7
D. 6

Explanation

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

### Step 1: List the Numbers
The numbers given are:
\[ 4.6, 0, 9.3, -4.8, 7.6, 2.3, 12.7, 3.5, 8.2, 6.1, 3.9, 5.2 \]

### Step 2: Arrange the Numbers in Ascending Order
We need to sort the numbers from the smallest to the largest:
1. Start with the smallest number: -4.8
2. Next is 0
3. Then 2.3
4. Followed by 3.5
5. Then 3.9
6. Next is 4.6
7. Followed by 5.2
8. Then 6.1
9. Next is 7.6
10. Followed by 8.2
11. Then 9.3
12. Finally, 12.7

Arranged in ascending order, the numbers are:
\[ -4.8, 0, 2.3, 3.5, 3.9, 4.6, 5.2, 6.1, 7.6, 8.2, 9.3, 12.7 \]

### Step 3: Count the Total Number of Values
Count the total number of values in the list:
- There are 12 values.

### Step 4: Determine if the Count is Even or Odd
Since the total number of values (12) is even, we will use the formula for finding the median for an even set of numbers.

### Step 5: Use the Median Formula
The median for an even number of observations is calculated using the formula:
\[ \text{Median} = \frac{(n/2)^{th} \text{ term} + ((n/2) + 1)^{th} \text{ term}}{2} \]
Where \( n \) is the total number of observations.

Here, \( n = 12 \):
- \( n/2 = 12/2 = 6 \)
- The 6th term is 4.6
- The 7th term is 5.2

### Step 6: Calculate the Median
Now, we calculate the median:
\[ \text{Median} = \frac{4.6 + 5.2}{2} = \frac{9.8}{2} = 4.9 \]

### Final Answer
The median of the given numbers is:
\[ \boxed{4.9} \]

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