The difference between the mean and median of the data 66, 59, 68, 65, 62, 59, 58, 56, 63, 65 is:

Options

A. `0.4`
B. 1
C. `0.8`
D. `0.5`

Answer

To find the difference between the mean and median of the given data set (66, 59, 68, 65, 62, 59, 58, 56, 63, 65), we will follow these steps:

### Step 1: Calculate the Mean
1. **Sum the Numbers**: Add all the numbers together.
\[ 66 + 59 + 68 + 65 + 62 + 59 + 58 + 56 + 63 + 65 = 66 + 59 + 68 + 65 + 62 + 59 + 58 + 56 + 63 + 65 = 650 \]
2. **Count the Numbers**: Determine how many numbers are in the data set. There are 10 numbers.
3. **Calculate the Mean**: Divide the sum by the number of numbers.
\[ \text{Mean} = \frac{650}{10} = 65 \]

### Step 2: Calculate the Median
1. **Arrange the Data in Ascending Order**:
\[ 56, 58, 59, 59, 62, 63, 65, 65, 66, 68 \]
2. **Find the Middle Numbers**: Since there are 10 numbers (even), the median will be the average of the 5th and 6th numbers.
- The 5th number is 62 and the 6th number is 63.
3. **Calculate the Median**:
\[ \text{Median} = \frac{62 + 63}{2} = \frac{125}{2} = 62.5 \]

### Step 3: Find the Difference Between Mean and Median
1. **Calculate the Difference**:
\[ \text{Difference} = \text{Median} - \text{Mean} = 62.5 - 65 = -2.5 \]

### Final Answer
The difference between the mean and median of the data set is **-2.5**.

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