To calculate the mean deviation of the set of numbers \(7, 3, 14, 9, 7, 8\), we will follow a systematic approach. The mean deviation is a measure of how spread out the numbers are in relation to the mean of the set. Here’s how to do it step-by-step: ### Step 1: Calculate the Mean First, we need to find the mean (average) of the numbers. 1. **Sum the numbers**: \[ 7 + 3 + 14 + 9 + 7 + 8 = 48 \] 2. **Count the numbers**: There are 6 numbers in the set. 3. **Calculate the mean**: \[ \text{Mean} = \frac{\text{Sum of numbers}}{\text{Count of numbers}} = \frac{48}{6} = 8 \] ### Step 2: Calculate the Absolute Deviations Next, we find the absolute deviation of each number from the mean. The absolute deviation is the absolute value of the difference between each number and the mean. 1. For \(7\): \[ |7 - 8| = 1 \] 2. For \(3\): \[ |3 - 8| = 5 \] 3. For \(14\): \[ |14 - 8| = 6 \] 4. For \(9\): \[ |9 - 8| = 1 \] 5. For \(7\) (again): \[ |7 - 8| = 1 \] 6. For \(8\): \[ |8 - 8| = 0 \] ### Step 3: Sum the Absolute Deviations Now, we sum all the absolute deviations calculated in the previous step. \[ 1 + 5 + 6 + 1 + 1 + 0 = 14 \] ### Step 4: Calculate the Mean Deviation Finally, we calculate the mean deviation by dividing the total absolute deviation by the number of observations. \[ \text{Mean Deviation} = \frac{\text{Sum of absolute deviations}}{\text{Count of numbers}} = \frac{14}{6} = \frac{7}{3} \] ### Conclusion The mean deviation of the set of numbers \(7, 3, 14, 9, 7, 8\) is \(\frac{7}{3}\). ### Answer **Correct Option: D. \( \frac{7}{3} \)** ### Explanation of Other Options - **Option A: \( \frac{13}{6} \)**: This value does not represent the mean deviation as it is less than the calculated mean deviation of \( \frac{7}{3} \). - **Option B: \( \frac{5}{2} \)**: This value is approximately \(2.5\), which is also less than \( \frac{7}{3} \) (approximately \(2.33\)), making it incorrect. - **Option C: \( \frac{7}{6} \)**: This value is significantly lower than the calculated mean deviation, which confirms it is incorrect. ### Revision Summary - The mean deviation measures the average distance of each data point from the mean. - To calculate it, find the mean, then the absolute deviations, sum them, and divide by the number of observations. - The mean deviation for the set \(7, 3, 14, 9, 7, 8\) is \( \frac{7}{3} \). - Always check your calculations step-by-step to avoid common pitfalls in arithmetic.