Question

What is the mean absolute deviation of the following dataset: 4.8, 5.9, 6.2, 10.8, 1.2, 6.4? Round the answer to the nearest tenth. (1 point) E

Answer 1

[AI-generated answer — Bot GPT 3.5]

The mean absolute deviation is calculated by finding the absolute difference between each data point and the mean of the dataset, then finding the mean of those absolute differences.

First, find the mean of the dataset:
(4.8 + 5.9 + 6.2 + 10.8 + 1.2 + 6.4) / 6 = 35.3 / 6 = 5.883333... ≈ 5.9

Next, find the absolute differences between each data point and the mean:
|4.8 - 5.9| = 1.1
|5.9 - 5.9| = 0
|6.2 - 5.9| = 0.3
|10.8 - 5.9| = 4.9
|1.2 - 5.9| = 4.7
|6.4 - 5.9| = 0.5

Then, find the mean of these absolute differences:
(1.1 + 0 + 0.3 + 4.9 + 4.7 + 0.5) / 6 = 11.5 / 6 = 1.916666... ≈ 1.9

Therefore, the mean absolute deviation of the dataset is 1.9 (rounded to the nearest tenth).

Answer 2

The number of words Mr. Ahmad's students read per minute is 109, 89, 112, 98, 101, 105, 120, 106. What is the mean absolute deviation of the dataset?

Round the answer to the nearest tenth. (1 point)

Answer 3

[AI-generated answer — Bot GPT 3.5]

To calculate the mean absolute deviation (MAD), we need to follow these steps:

Step 1: Find the mean of the dataset:
Mean = (109 + 89 + 112 + 98 + 101 + 105 + 120 + 106) / 8
Mean = 840 / 8
Mean = 105

Step 2: Find the absolute difference between each data point and the mean:
|109 - 105| = 4
|89 - 105| = 16
|112 - 105| = 7
|98 - 105| = 7
|101 - 105| = 4
|105 - 105| = 0
|120 - 105| = 15
|106 - 105| = 1

Step 3: Find the mean of these absolute differences:
MAD = (4 + 16 + 7 + 7 + 4 + 0 + 15 + 1) / 8
MAD = 54 / 8
MAD = 6.75

Therefore, the mean absolute deviation of the dataset is 6.8 (rounded to the nearest tenth).

Answer 4

Data point: - Absolute Deviation:

5 - 17.3
10 - 12.3
45 - missing value
12 - 10.3
27 - missing value
34 - 12.7
The table lists Jude's data for how many people walk into a store each half hour. The mean is 22.3. Identify the absolute deviation for each missing value.
Round each value to the nearest tenth.

Answer 5

[AI-generated answer — Bot GPT 3.5]

To find the absolute deviation for the missing values, we will first calculate the absolute deviation for the given values and then use the mean to find the missing values.

Given data and their absolute deviation from the mean:
1. For 5: Absolute Deviation = |5 - 22.3| = 17.3
2. For 10: Absolute Deviation = |10 - 22.3| = 12.3
3. For 12: Absolute Deviation = |12 - 22.3| = 10.3
4. For 34: Absolute Deviation = |34 - 22.3| = 12.7

First, let's calculate the sum of the known absolute deviations:
17.3 + 12.3 + 10.3 + 12.7 = 52.6

The sum of absolute deviations represents the total deviation from the mean. To find the missing values, we can use the fact that the total deviation from the mean must be zero.

Let's assume the missing values are x and y. We know that the sum of all absolute deviations from the mean should be zero:

17.3 + 12.3 + x + 10.3 + y + 12.7 = 0
52.6 + x + y = 0
x + y = -52.6

Since there are two missing values, the total deviation must be divided between them. Let's assign x = 45 and y = 27:

45 - 27 = 18

Therefore, the absolute deviation for 45 is 18 and for 27 is also 18.

Answer 6

Wrong on both

Answer 7

[AI-generated answer — Bot GPT 3.5]

I apologize for the error in my previous response. Let's correct this:

Given data and their absolute deviation from the mean:
1. For 5: Absolute Deviation = |5 - 22.3| = 17.3
2. For 10: Absolute Deviation = |10 - 22.3| = 12.3
3. Missing Value x
4. For 12: Absolute Deviation = |12 - 22.3| = 10.3
5. Missing Value y
6. For 34: Absolute Deviation = |34 - 22.3| = 12.7

Since we have the mean absolute deviation as 22.3, the sum of absolute deviations from the mean should be zero:

17.3 + 12.3 + x + 10.3 + y + 12.7 = 0
52.6 + x + y = 0
x + y = -52.6

Since there are two missing values, the total deviation must be divided between them. Let's solve the equation:

From the equation x + y = -52.6, we can find one of the missing values. Let's solve for x by assuming y = 34:

x + 34 = -52.6
x = -52.6 - 34
x = -86.6

Now, let's find the other missing value (y) by assuming x = 45:

45 + y = -52.6
y = -52.6 - 45
y = -97.6

Therefore, the absolute deviation for the missing value 45 is 86.6, and for the missing value 27 is 97.6.

Answer 8

Both wrong again

Answer 9

[AI-generated answer — Bot GPT 3.5]

I apologize for the errors in my previous responses. Let's correct this calculation.

Given data and their absolute deviation from the mean:
1. For 5: Absolute Deviation = |5 - 22.3| = 17.3
2. For 10: Absolute Deviation = |10 - 22.3| = 12.3
3. Missing Value x
4. For 12: Absolute Deviation = |12 - 22.3| = 10.3
5. Missing Value y
6. For 34: Absolute Deviation = |34 - 22.3| = 12.7

Since the total deviation from the mean should be zero, we have:

17.3 + 12.3 + x + 10.3 + y + 12.7 = 0
52.6 + x + y = 0
x + y = -52.6

From this equation, we have to share a total deviation of -52.6 between x and y.

Let's assign a value to one of the missing values to solve for the other. We'll assume x = 45:

45 + y = -52.6
y = -52.6 - 45
y = -97.6

Now, let's assume y = 27:

x + 27 = -52.6
x = -52.6 - 27
x = -79.6

Therefore, the absolute deviation for the missing value 45 is 79.6, and for the missing value 27 is 97.6. Thank you for your patience.

Answer 10

No

Answer 11

[AI-generated answer — Bot GPT 3.5]

Let's correct the calculation for the absolute deviation of the missing values.

Given data and their absolute deviation from the mean:
1. For 5: Absolute Deviation = |5 - 22.3| = 17.3
2. For 10: Absolute Deviation = |10 - 22.3| = 12.3
3. Missing Value x
4. For 12: Absolute Deviation = |12 - 22.3| = 10.3
5. Missing Value y
6. For 34: Absolute Deviation = |34 - 22.3| = 12.7

Since the total deviation from the mean should be zero, we have:

17.3 + 12.3 + x + 10.3 + y + 12.7 = 0
52.6 + x + y = 0
x + y = -52.6

From this equation, we have to share a total deviation of -52.6 between x and y.

One approach is to assume x = 45 and y = 27 and then test if the total deviation equals zero:

45 - 52.6 = -7.6
27 - 52.6 = -25.6
-7.6 + -25.6 = -33.2

This does not equal zero, so let's use a different approach:

Let's set the two missing values as negative since the total deviation is negative:

x = -a
y = -b

Now, we need to find values a and b such that -a - b = -52.6:

a + b = 52.6

One possible solution is:
a = 27
b = 25.6

This way:
27 + 25.6 = 52.6

Therefore, the absolute deviation for the missing value is 27 and 25.6.