Subjects statistics

Mean Absolute Deviation 9Cbfe1

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1. The problem asks us to find the mean height of the five black bars and then use that mean to calculate the mean absolute deviation (MAD) of the black bar heights. 2. The heights of the black bars are approximately: $10, 5, 4, 10,$ and $11$ units. 3. To find the mean height, use the formula for the mean: $$\text{Mean} = \frac{\text{Sum of all values}}{\text{Number of values}}$$ 4. Calculate the sum of the heights: $$10 + 5 + 4 + 10 + 11 = 40$$ 5. Divide by the number of bars (5): $$\text{Mean} = \frac{40}{5} = 8$$ 6. Now, calculate the absolute deviations from the mean for each bar: $$|10 - 8| = 2$$ $$|5 - 8| = 3$$ $$|4 - 8| = 4$$ $$|10 - 8| = 2$$ $$|11 - 8| = 3$$ 7. Find the mean absolute deviation (MAD) by averaging these absolute deviations: $$\text{MAD} = \frac{2 + 3 + 4 + 2 + 3}{5} = \frac{14}{5} = 2.8$$ 8. Rounded to the nearest tenth, the mean absolute deviation is $2.8$ units. **Final answers:** - Mean height = $8$ units - Mean absolute deviation = $2.8$ units