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
114.1
114.1
19.8
19.8
799.0
799.0
138.9
To find the mean absolute deviation, we first need to find the mean of the dataset.
Mean = (106 + 122 + 134 + 150 + 120 + 92 + 75) / 7
Mean = 799 / 7
Mean = 114.1
Next, we find the deviation of each data point from the mean.
Deviation = |106 - 114.1| = 8.1
Deviation = |122 - 114.1| = 7.9
Deviation = |134 - 114.1| = 19.9
Deviation = |150 - 114.1| = 35.9
Deviation = |120 - 114.1| = 5.9
Deviation = |92 - 114.1| = 22.1
Deviation = |75 - 114.1| = 39.1
We then find the mean of these deviations.
Mean deviation = (8.1 + 7.9 + 19.9 + 35.9 + 5.9 + 22.1 + 39.1) / 7
Mean deviation = 139.9 / 7
Mean deviation ≈ 19.9
Therefore, the mean absolute deviation for this dataset is approximately 19.9.
again
I apologize for the mistake in my previous response. Let's calculate the mean absolute deviation correctly.
To find the mean absolute deviation, we first need to find the mean of the dataset.
Mean = (106 + 122 + 134 + 150 + 120 + 92 + 75) / 7
Mean = 799 / 7
Mean = 114.1
Next, we find the absolute deviation of each data point from the mean.
Absolute Deviation = |106 - 114.1| = 8.1
Absolute Deviation = |122 - 114.1| = 7.9
Absolute Deviation = |134 - 114.1| = 19.9
Absolute Deviation = |150 - 114.1| = 35.9
Absolute Deviation = |120 - 114.1| = 5.9
Absolute Deviation = |92 - 114.1| = 22.1
Absolute Deviation = |75 - 114.1| = 39.1
Now, we find the mean of these absolute deviations.
Mean absolute deviation = (8.1 + 7.9 + 19.9 + 35.9 + 5.9 + 22.1 + 39.1) / 7
Mean absolute deviation = 138.9 / 7
Mean absolute deviation ≈ 19.8
Therefore, the mean absolute deviation for this dataset is approximately 19.8.
To find the mean absolute deviation (MAD), follow these steps:
1. Find the mean (average) of the dataset. Sum up all the numbers and divide by the total count.
Mean = (106 + 122 + 134 + 150 + 120 + 92 + 75) / 7 = 799 / 7 ≈ 114.1
2. Subtract each number in the dataset from the mean and record the absolute value of the difference.
|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 these absolute differences. Sum up all the absolute differences and divide by the total count.
MAD = (8.1 + 7.9 + 19.9 + 35.9 + 5.9 + 22.1 + 39.1) / 7 ≈ 19.8
Therefore, the mean absolute deviation for this dataset is approximately 19.8.