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)
Responses
138.9
138.9
114.1
114.1
799.0
799.0
19.8
To find the mean absolute deviation (MAD), first we need to find the mean of the dataset.
The mean is calculated by adding up all the numbers in the dataset and dividing by the total number of values:
Mean = (106 + 122 + 134 + 150 + 120 + 92 + 75) / 7
Mean = 799 / 7
Mean = 114.1
Next, we need to find the absolute deviation for each value. The absolute deviation is the absolute value of the difference between each value and the mean.
Absolute Deviation = |Value - Mean|
For the first value, the absolute deviation is |106 - 114.1| = 8.1
For the second value, the absolute deviation is |122 - 114.1| = 7.9
For the third value, the absolute deviation is |134 - 114.1| = 19.9
For the fourth value, the absolute deviation is |150 - 114.1| = 35.9
For the fifth value, the absolute deviation is |120 - 114.1| = 5.9
For the sixth value, the absolute deviation is |92 - 114.1| = 22.1
For the seventh value, the absolute deviation is |75 - 114.1| = 39.1
Now, we need to find the mean of these absolute deviations.
Mean of Absolute Deviations = (8.1 + 7.9 + 19.9 + 35.9 + 5.9 + 22.1 + 39.1) / 7
Mean of Absolute Deviations = 138.9 / 7
Mean of Absolute Deviations = 19.8
Therefore, the mean absolute deviation for this dataset is 19.8.
To calculate the mean absolute deviation (MAD) for a dataset, we need to follow these steps:
1. Find the mean of the dataset. The mean is calculated by adding up all the values in the dataset and dividing by the total number of values.
(106 + 122 + 134 + 150 + 120 + 92 + 75) / 7 = 799 / 7 = 114.1
2. Subtract the mean from each value in the dataset to determine the deviations from the mean. Take the absolute value of each deviation (i.e., remove any negative signs).
Deviations from the mean:
|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
3. Calculate the average of the absolute deviations. Add up all the absolute deviations and divide by the total number of values.
(8.1 + 7.9 + 19.9 + 35.9 + 5.9 + 22.1 + 39.1) / 7 = 138.9 / 7 = 19.8
Therefore, the mean absolute deviation for this dataset is 19.8 (rounded to the nearest tenth).
To calculate the mean absolute deviation for this dataset, follow these steps:
Step 1: Find the mean (average) of the dataset. Add up all the values and divide by the total number of values.
Mean = (106 + 122 + 134 + 150 + 120 + 92 + 75) / 7 = 799 / 7 = 114.1 (rounded to the nearest tenth)
Step 2: Find the difference between each value and the mean.
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: Take the absolute value of each difference.
|-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
Step 4: Find the mean of the absolute differences.
Mean Absolute Deviation = (8.1 + 7.9 + 19.9 + 35.9 + 5.9 + 22.1 + 39.1) / 7 = 139.9 / 7 = 19.9 (rounded to the nearest tenth)
Therefore, the mean absolute deviation for this dataset is 19.9.