Question

Question

Determine the mean absolute deviation of the following dataset. Round your answer to the nearest tenth.

{134,138,150,155,158,165}


(1 point)
Responses

56
56

11.2
11.2

9.3
9.3

150

Answer 1

To calculate the mean absolute deviation (MAD) of the dataset {134, 138, 150, 155, 158, 165}, follow these steps:

1. Calculate the mean of the dataset: \[ \text{Mean} = \frac{134 + 138 + 150 + 155 + 158 + 165}{6} = \frac{900}{6} = 150 \]

2. Calculate the absolute deviations from the mean:

   • For 134: \( |134 - 150| = 16 \)
   • For 138: \( |138 - 150| = 12 \)
   • For 150: \( |150 - 150| = 0 \)
   • For 155: \( |155 - 150| = 5 \)
   • For 158: \( |158 - 150| = 8 \)
   • For 165: \( |165 - 150| = 15 \)

   So the absolute deviations are: \[ 16, 12, 0, 5, 8, 15 \]

3. Calculate the mean of the absolute deviations: \[ \text{Mean Absolute Deviation} = \frac{16 + 12 + 0 + 5 + 8 + 15}{6} = \frac{56}{6} \approx 9.3 \]

Rounding to the nearest tenth gives us: \[ \text{MAD} \approx 9.3 \]

Thus, the answer is 9.3.