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.
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.
To find the mean absolute deviation (MAD) for the given dataset, follow these steps:
Step 1: Find the mean (average) of the dataset.
To do this, add up all the numbers in the dataset and divide the sum by the total number of values.
106 + 122 + 134 + 150 + 120 + 92 + 75 = 799
799 ÷ 7 = 114.1 (rounded to one decimal place)
Step 2: Find the absolute deviation of each number from the mean.
To do this, subtract the mean from each value in the dataset, and then take the absolute value (ignore the negative sign if any).
|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
Step 3: Find the average of the absolute deviations.
To do this, add up all the absolute deviations and divide the sum by the total number of values.
(8.1 + 7.9 + 19.9 + 35.9 + 5.9 + 22.1 + 39.1) ÷ 7 = 18.4 (rounded to one decimal place)
Therefore, the mean absolute deviation for the given dataset is 18.4 (rounded to one decimal place).