Find the mean absolute deviation of the following dataset: 8.4, 9.4, 14.2, 5.6, 8.3, 9.0, 10.2. Round the answer to the nearest tenth.(1 point)
Responses
7.0
7.0
11.8
11.8
1.7
1.7
9.3
9.3
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
799.0
799.0
138.9
138.9
19.8
19.8
114.1
114.1
A dataset includes the point 34.6. The mean of the set is 32.1. What is the absolute deviation for this data point? Round the answer to the nearest tenth.(1 point)
Responses
32.1
32.1
−2.5
negative 2.5
2.5
2.5
34.6
2.5
Sarina tracks her time spent on homework each night for a week, in minutes. She collects the following times: 51, 60, 25, 15, 20, 5, 35. When she solves for the mean absolute deviation, what number will she use for the divisor?(1 point)
Responses
7
7
55
55
30.1
30.1
15.9
7
What is the sum of the absolute deviations in the following dataset: 68, 51, 75, 78, 94, 35? The mean is 66.8.(1 point)
Responses
95.4
95.4
401
401
59
59
15.9
15.9
X = {68, 51, 75, 78, 94, 35}
Mean = (68+51+75+78+94+35)/6 = 66.8
|68-66.8| = 1.2
|51-66.8| = 15.8
|75-66.8| = 8.2
|78-66.8| = 11.2
|94-66.8| = 27.2
|35-66.8| = 31.8
Sum of Absolute Deviations = 1.2 + 15.8 + 8.2 + 11.2 + 27.2 + 31.8 = 95.4
Therefore, the sum of the absolute deviations is 95.4. Answer: 95.4
To find the mean absolute deviation of a dataset, you need to follow these steps:
1. Find the mean of the dataset. To do this, add up all the numbers in the dataset and divide by the total number of values. In this case, the mean is (8.4 + 9.4 + 14.2 + 5.6 + 8.3 + 9.0 + 10.2) / 7 = 65.1 / 7 = 9.3.
2. Subtract the mean from each value in the dataset to find the deviations. For example, the deviation for the first value in the dataset (8.4) is 8.4 - 9.3 = -0.9.
3. Take the absolute value of each deviation. The absolute value of a number is its distance from zero, so it removes any negative sign. For example, the absolute value of -0.9 is 0.9.
4. Find the mean of the absolute deviations. Add up all the absolute deviations and divide by the total number of values. In this case, the mean absolute deviation is (0.9 + 0.1 + 4.9 + 3.7 + 0.8 + 0.3 + 0.9) / 7 = 11.6 / 7 = 1.7.
Therefore, the mean absolute deviation of the given dataset is 1.7 (rounded to the nearest tenth). So the correct response is "1.7."