To solve the problem of finding out by how much the mean of the numbers 30, 56, 31, 55, 43, and 44 is less than the median, we will follow these steps: ### Step 1: Calculate the Mean The mean (average) is calculated by adding all the numbers together and then dividing by the total count of numbers. 1. **Add the numbers**: \[ 30 + 56 + 31 + 55 + 43 + 44 = 259 \] 2. **Count the numbers**: There are 6 numbers in total. 3. **Calculate the mean**: \[ \text{Mean} = \frac{\text{Total Sum}}{\text{Count}} = \frac{259}{6} \approx 43.1667 \] ### Step 2: Calculate the Median The median is the middle value when the numbers are arranged in ascending order. If there is an even number of observations, the median is the average of the two middle numbers. 1. **Arrange the numbers in ascending order**: \[ 30, 31, 43, 44, 55, 56 \] 2. **Find the middle values**: Since there are 6 numbers (even), the median will be the average of the 3rd and 4th numbers: - 3rd number: 43 - 4th number: 44 3. **Calculate the median**: \[ \text{Median} = \frac{43 + 44}{2} = \frac{87}{2} = 43.5 \] ### Step 3: Find the Difference Between the Median and the Mean Now that we have both the mean and the median, we can find the difference: 1. **Calculate the difference**: \[ \text{Difference} = \text{Median} - \text{Mean} = 43.5 - 43.1667 \approx 0.3333 \] ### Step 4: Compare with the Options The calculated difference is approximately 0.3333, which corresponds to option C (0.33). ### Explanation of Other Options - **Option A (0.75)**: This value is too high compared to our calculated difference. The mean is much closer to the median than this option suggests. - **Option B (0.50)**: This option is also higher than our calculated difference. The mean is less than the median, but not by this amount. - **Option D (0.17)**: This value is too low. The mean is not that far from the median, so this option does not reflect the actual difference. ### Summary of Key Points - The mean of the numbers is approximately 43.1667. - The median of the numbers is 43.5. - The difference between the median and the mean is approximately 0.3333. - The correct answer is option C (0.33). ### Revision Summary - **Mean Calculation**: Add all numbers and divide by the count. - **Median Calculation**: Arrange numbers in order and find the middle value(s). - **Difference**: Subtract the mean from the median to find how much less the mean is. - **Options Analysis**: Evaluate why other options do not match the calculated difference.