To find the mean deviation of the numbers 1, 2, 3, and 4, we will follow a systematic approach. Let's break it down step-by-step. ### Step 1: Calculate the Mean The first step in finding the mean deviation is to calculate the mean (average) of the given numbers. **Formula for Mean:** \[ \text{Mean} = \frac{\text{Sum of all values}}{\text{Number of values}} \] **Calculating the Mean:** - Sum of the values: \(1 + 2 + 3 + 4 = 10\) - Number of values: \(4\) Now, plug these values into the formula: \[ \text{Mean} = \frac{10}{4} = 2.5 \] ### Step 2: Calculate the Absolute Deviations Next, we need to find the absolute deviations of each number from the mean. The absolute deviation is the absolute value of the difference between each number and the mean. **Calculating Absolute Deviations:** - For 1: \(|1 - 2.5| = | -1.5 | = 1.5\) - For 2: \(|2 - 2.5| = | -0.5 | = 0.5\) - For 3: \(|3 - 2.5| = |0.5| = 0.5\) - For 4: \(|4 - 2.5| = |1.5| = 1.5\) Now, we have the absolute deviations: - 1.5, 0.5, 0.5, 1.5 ### Step 3: Calculate the Mean of the Absolute Deviations Now, we will calculate the mean of these absolute deviations. **Formula for Mean of Absolute Deviations:** \[ \text{Mean Deviation} = \frac{\text{Sum of absolute deviations}}{\text{Number of values}} \] **Calculating the Mean Deviation:** - Sum of absolute deviations: \(1.5 + 0.5 + 0.5 + 1.5 = 4\) - Number of values: \(4\) Now, plug these values into the formula: \[ \text{Mean Deviation} = \frac{4}{4} = 1.0 \] ### Conclusion The mean deviation of the numbers 1, 2, 3, and 4 is **1.0**. ### Explanation of Options - **Option A (2.5)**: This is incorrect because it represents the mean of the numbers, not the mean deviation. - **Option B (2.0)**: This is incorrect as it does not correspond to any calculated value in our process. - **Option C (1.0)**: This is the correct answer, as we calculated the mean deviation to be 1.0. - **Option D (1.5)**: This is incorrect because it does not match the calculated mean deviation. ### Revision Summary - The mean of the numbers 1, 2, 3, and 4 is 2.5. - The absolute deviations from the mean are calculated by taking the absolute difference from the mean. - The mean deviation is the average of these absolute deviations. - The final mean deviation for the numbers 1, 2, 3, and 4 is 1.0.