The median of the data 3, 5, 9, 10, 11,4,5, 8, 12, 15 is

Options

A. 12
B. 8
C. 9
D. 8.5

Answer

To find the median of the given data set: 3, 5, 9, 10, 11, 4, 5, 8, 12, 15, we can follow these steps:

### Step 1: Arrange the data in ascending order.
First, we need to sort the numbers from smallest to largest.

**Sorted Data:**
3, 4, 5, 5, 8, 9, 10, 11, 12, 15

### Step 2: Count the number of observations.
Next, we count how many numbers are in the data set.

**Count of Observations (n):**
There are 10 numbers in total.

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

### Step 4: Use the median formula for even data sets.
The formula for the median when the number of observations (n) is even is:
\[ \text{Median} = \frac{\text{n/2th observation} + \text{(n/2 + 1)th observation}}{2} \]
Here, n = 10.

### Step 5: Identify the positions of the observations.
Calculate n/2 and (n/2 + 1):
- n/2 = 10/2 = 5
- (n/2 + 1) = 5 + 1 = 6

So, we need to find the 5th and 6th observations in our sorted data.

### Step 6: Find the 5th and 6th observations.
From our sorted data:
- 5th observation = 8
- 6th observation = 9

### Step 7: Calculate the median.
Now, substitute the values into the median formula:
\[ \text{Median} = \frac{8 + 9}{2} = \frac{17}{2} = 8.5 \]

### Final Answer:
The median of the data set is **8.5**.

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