1. **State the problem:** We have two gardens, A and B, each with heights: 9, 10, 10, 11, 11, 12, 12, 13 feet. Both have a mean height of 11 feet.
2. **Find the distance between the means:** Since both means are 11 feet,
$$\text{Distance between means} = 11 - 11 = 0$$
3. **Find the Mean Absolute Deviation (MAD) for each garden:**
MAD is the average of the absolute differences between each data point and the mean.
For Garden A (and similarly for Garden B since data is identical):
Calculate absolute deviations:
$$|9 - 11| = 2, |10 - 11| = 1, |10 - 11| = 1, |11 - 11| = 0, |11 - 11| = 0, |12 - 11| = 1, |12 - 11| = 1, |13 - 11| = 2$$
Sum of absolute deviations:
$$2 + 1 + 1 + 0 + 0 + 1 + 1 + 2 = 8$$
Number of data points: 8
Calculate MAD:
$$\text{MAD} = \frac{8}{8} = 1$$
4. **Express the distance between the means as a multiple of the MAD:**
Since the distance between means is 0 and MAD is 1,
$$\text{Distance between means} = 0 \times \text{MAD}$$
**Final answers:**
- Distance between the means: 0 feet
- MAD for Garden A: 1 foot
- MAD for Garden B: 1 foot
- Distance between the means = 0 times the MAD
Garden Height 10F76B
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