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.

Answer 1

First, we find the mean of the dataset by adding all the values and then dividing by the number of values:
Mean = (106 + 122 + 134 + 150 + 120 + 92 + 75) / 7 = 799 / 7 = 114.1 (rounded to the nearest tenth)
Next, we find the deviation of each value from the mean, and take the absolute value of each deviation:
106 - 114.1 = -8.1
122 - 114.1 = 7.9
134 - 114.1 = 19.9
150 - 114.1 = 35.9
120 - 114.1 = 5.9
92 - 114.1 = -22.1
75 - 114.1 = -39.1
Taking the absolute value of each deviation:
|-8.1| = 8.1
|7.9| = 7.9
|19.9| = 19.9
|35.9| = 35.9
|5.9| = 5.9
|-22.1| = 22.1
|-39.1| = 39.1
Then, we find the mean of the absolute deviations by adding all the absolute deviations and then dividing by the number of values:
Mean of absolute deviations = (8.1 + 7.9 + 19.9 + 35.9 + 5.9 + 22.1 + 39.1) / 7 = 139.9 / 7 = 19.99 (rounded to the nearest hundredth)
Therefore, the mean absolute deviation for this dataset is approximately 20.0.