Question

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

11.8
11.8

1.7
1.7

9.3
9.3

7.0
7.0

Answer 1

[AI-generated answer — Bot GPT 3.5]

To find the mean absolute deviation, we first need to find the mean of the dataset.

Mean = (8.4 + 9.4 + 14.2 + 5.6 + 8.3 + 9.0 + 10.2) / 7 = 9.8

Next, we find the absolute deviation of each data point from the mean:

|8.4 - 9.8| = 1.4
|9.4 - 9.8| = 0.4
|14.2 - 9.8| = 4.4
|5.6 - 9.8| = 4.2
|8.3 - 9.8| = 1.5
|9.0 - 9.8| = 0.8
|10.2 - 9.8| = 0.4

Now we find the mean of these absolute deviations:

Mean Absolute Deviation = (1.4 + 0.4 + 4.4 + 4.2 + 1.5 + 0.8 + 0.4) / 7 ≈ 2.4

Rounded to the nearest tenth, the mean absolute deviation is 2.4. The closest response is 1.7.

Answer 2

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

114.1
114.1

19.8
19.8

138.9

Answer 3

[AI-generated answer — Bot GPT 3.5]

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 = 114.1

Next, we find the absolute deviation of each data point 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

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 ≈ 19.8

Rounded to the nearest tenth, the mean absolute deviation is 19.8. The correct response is 19.8.

Answer 4

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

34.6
34.6

2.5
2.5

−2.5

Answer 5

[AI-generated answer — Bot GPT 3.5]

To find the absolute deviation for the data point 34.6 from the mean 32.1, we calculate:

|34.6 - 32.1| = 2.5

Rounded to the nearest tenth, the absolute deviation for the data point 34.6 is 2.5. The correct response is 2.5.

Answer 6

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

15.9
15.9

55
55

30.1
30.1

7

Answer 7

[AI-generated answer — Bot GPT 3.5]

To calculate the mean absolute deviation for the dataset, Sarina will use the total number of data points (in this case, the number of days in a week which is 7) as the divisor.

Therefore, she will use 7 as the divisor to calculate the mean absolute deviation. The correct response is 7.

Answer 8

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

59
59

95.4
95.4

15.9
15.9

401

Answer 9

[AI-generated answer — Bot GPT 3.5]

To find the sum of the absolute deviations for the dataset given the mean is 66.8:

1. Calculate the absolute deviation of each data point from the mean:

|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

2. Sum these absolute deviations:

1.2 + 15.8 + 8.2 + 11.2 + 27.2 + 31.8 = 95.4

Therefore, the sum of the absolute deviations in the dataset is 95.4. The correct response is 95.4.