Find the median of the following data 3,5,9,10,11,4,5,8,12,15

Options

A. 10
B. 9
C. 8
D. 8.5

Explanation

To find the median of the given data set: 3, 5, 9, 10, 11, 4, 5, 8, 12, 15, we will 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: Determine the number of observations (n).
Count the total number of data points.

**Total Observations (n):** 10

### Step 3: Identify if n is even or odd.
Since n = 10, which is even, we will use the formula for finding the median for an even number of observations.

### Step 4: Use the median formula for even n.
The formula for finding the median when n is even is:
\[ \text{Median} = \frac{\text{(n/2)th term} + \text{(n/2 + 1)th term}}{2} \]

### Step 5: Calculate the positions of the terms.
Here, we need to find the 5th and 6th terms because:
- n/2 = 10/2 = 5
- n/2 + 1 = 5 + 1 = 6

### Step 6: Find the 5th and 6th terms in the sorted data.
From our sorted data:
- 5th term = 8
- 6th term = 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 given data set is **8.5**.

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