The number of visitors to a museum per hour recorded in one day is 106, 122, 134, 150, 120, 92, 75. What is the mean absolute deviation for this dataset? Round the answer to the nearest tenth.(1 point)

Question

Responses

138.9
138.9

19.8
19.8

114.1
114.1

799.0

Answer 1

To calculate the Mean Absolute Deviation (MAD) for the given dataset, we follow these steps:

1. Calculate the mean of the dataset. The dataset is: 106, 122, 134, 150, 120, 92, 75.

   \[ \text{Mean} = \frac{106 + 122 + 134 + 150 + 120 + 92 + 75}{7} \] \[ \text{Mean} = \frac{799}{7} \approx 114.14 \]

2. Calculate the absolute deviations from the mean. \[ |106 - 114.14| \approx 8.14 \] \[ |122 - 114.14| \approx 7.86 \] \[ |134 - 114.14| \approx 19.86 \] \[ |150 - 114.14| \approx 35.86 \] \[ |120 - 114.14| \approx 5.86 \] \[ |92 - 114.14| \approx 22.14 \] \[ |75 - 114.14| \approx 39.14 \]

3. Sum the absolute deviations. \[ 8.14 + 7.86 + 19.86 + 35.86 + 5.86 + 22.14 + 39.14 \approx 138.9 \]

4. Calculate the mean absolute deviation. \[ \text{MAD} = \frac{138.9}{7} \approx 19.84 \]

Rounding to the nearest tenth gives us:

\[ \text{MAD} \approx 19.8 \]

Thus, the Mean Absolute Deviation for this dataset is 19.8.