Find the difference between the mean and the median of the set 3,8,10,15.

Answer

To solve the problem of finding the difference between the mean and the median of the set {3, 8, 10, 15}, we will follow these steps:

### Step 1: Calculate the Mean
The mean is calculated by adding all the numbers in the set and dividing by the total number of observations.

1. **Sum of the numbers**:
\[ 3 + 8 + 10 + 15 = 36 \]

2. **Number of observations (n)**:
\[ n = 4 \]

3. **Mean calculation**:
\[ \text{Mean} = \frac{\text{Sum of the numbers}}{n} = \frac{36}{4} = 9 \]

### Step 2: Calculate the Median
The median is the middle value of a data set. Since we have an even number of observations, the median will be the average of the two middle numbers.

1. **Arrange the numbers** (already arranged):
\[ 3, 8, 10, 15 \]

2. **Identify the middle numbers**:
The two middle numbers are 8 and 10.

3. **Median calculation**:
\[ \text{Median} = \frac{8 + 10}{2} = \frac{18}{2} = 9 \]

### Step 3: Find the Difference Between Mean and Median
Now that we have both the mean and the median, we can find the difference.

1. **Difference calculation**:
\[ \text{Difference} = \text{Mean} - \text{Median} = 9 - 9 = 0 \]

### Final Answer
The difference between the mean and the median of the set {3, 8, 10, 15} is **0**.

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