Question

bot, Here are the science test scores from Ms. O’Donnell’s class:

55, 60, 70, 70, 75, 75, 75, 80, 80, 85, 85, 85, 85, 90, 90, 95, 100

Find the MAD.

(1 point)
The MAD is
.

Answer 1

wrong

Answer 2

not it

Answer 3

The Mean Absolute Deviation (MAD) is the average amount by which data points deviate from the mean.

To find the MAD, we need to calculate the following steps:

Step 1: Find the mean (average) of the data set.
Step 2: Determine the deviation of each data point from the mean.
Step 3: Take the absolute value of each deviation.
Step 4: Find the average of all the absolute deviations.

Let's proceed with the calculations:

Step 1: Find the mean
To find the mean, we sum up all the data points and divide by the total count of data points.
Mean = (55 + 60 + 70 + 70 + 75 + 75 + 75 + 80 + 80 + 85 + 85 + 85 + 85 + 90 + 90 + 95 + 100) / 17
Mean = 1420 / 17
Mean = 83.53 (rounded to two decimal places)

Step 2: Determine the deviation of each data point from the mean
Deviation of each data point = data point - mean

Data point - Mean:
55 - 83.53 = -28.53
60 - 83.53 = -23.53
70 - 83.53 = -13.53
70 - 83.53 = -13.53
75 - 83.53 = -8.53
75 - 83.53 = -8.53
75 - 83.53 = -8.53
80 - 83.53 = -3.53
80 - 83.53 = -3.53
85 - 83.53 = 1.47
85 - 83.53 = 1.47
85 - 83.53 = 1.47
85 - 83.53 = 1.47
90 - 83.53 = 6.47
90 - 83.53 = 6.47
95 - 83.53 = 11.47
100 - 83.53 = 16.47

Step 3: Take the absolute value of each deviation
We take the absolute value of each deviation to remove any negative values.

Absolute deviations:
|-28.53| = 28.53
|-23.53| = 23.53
|-13.53| = 13.53
|-13.53| = 13.53
|-8.53| = 8.53
|-8.53| = 8.53
|-8.53| = 8.53
|-3.53| = 3.53
|-3.53| = 3.53
|1.47| = 1.47
|1.47| = 1.47
|1.47| = 1.47
|1.47| = 1.47
|6.47| = 6.47
|6.47| = 6.47
|11.47| = 11.47
|16.47| = 16.47

Step 4: Find the average of all the absolute deviations
Average of absolute deviations = sum of absolute deviations / total count of data points

Sum of absolute deviations = 28.53 + 23.53 + 13.53 + 13.53 + 8.53 + 8.53 + 8.53 + 3.53 + 3.53 + 1.47 + 1.47 + 1.47 + 1.47 + 6.47 + 6.47 + 11.47 + 16.47
Sum of absolute deviations = 156.36

Average of absolute deviations = 156.36 / 17
Average of absolute deviations = 9.19 (rounded to two decimal places)

Therefore, the Mean Absolute Deviation (MAD) is 9.19.

Answer 4

Apologies for the error in my response. Let's recalculate the Mean Absolute Deviation (MAD) correctly.

To find the MAD, we need to calculate the following steps:

Step 1: Find the mean (average) of the data set.
Step 2: Determine the deviation of each data point from the mean.
Step 3: Take the absolute value of each deviation.
Step 4: Find the average of all the absolute deviations.

Step 1: Find the mean
To find the mean, we sum up all the data points and divide by the total count of data points.
Mean = (55 + 60 + 70 + 70 + 75 + 75 + 75 + 80 + 80 + 85 + 85 + 85 + 85 + 90 + 90 + 95 + 100) / 17
Mean = 1415 / 17
Mean = 83.24 (rounded to two decimal places)

Step 2: Determine the deviation of each data point from the mean
Deviation of each data point = data point - mean

Data point - Mean:
55 - 83.24 = -28.24
60 - 83.24 = -23.24
70 - 83.24 = -13.24
70 - 83.24 = -13.24
75 - 83.24 = -8.24
75 - 83.24 = -8.24
75 - 83.24 = -8.24
80 - 83.24 = -3.24
80 - 83.24 = -3.24
85 - 83.24 = 1.76
85 - 83.24 = 1.76
85 - 83.24 = 1.76
85 - 83.24 = 1.76
90 - 83.24 = 6.76
90 - 83.24 = 6.76
95 - 83.24 = 11.76
100 - 83.24 = 16.76

Step 3: Take the absolute value of each deviation
We take the absolute value of each deviation to remove any negative values.

Absolute deviations:
|-28.24| = 28.24
|-23.24| = 23.24
|-13.24| = 13.24
|-13.24| = 13.24
|-8.24| = 8.24
|-8.24| = 8.24
|-8.24| = 8.24
|-3.24| = 3.24
|-3.24| = 3.24
|1.76| = 1.76
|1.76| = 1.76
|1.76| = 1.76
|1.76| = 1.76
|6.76| = 6.76
|6.76| = 6.76
|11.76| = 11.76
|16.76| = 16.76

Step 4: Find the average of all the absolute deviations
Average of absolute deviations = sum of absolute deviations / total count of data points

Sum of absolute deviations = 28.24 + 23.24 + 13.24 + 13.24 + 8.24 + 8.24 + 8.24 + 3.24 + 3.24 + 1.76 + 1.76 + 1.76 + 1.76 + 6.76 + 6.76 + 11.76 + 16.76
Sum of absolute deviations = 154.48

Average of absolute deviations = 154.48 / 17
Average of absolute deviations = 9.09 (rounded to two decimal places)

Therefore, the Mean Absolute Deviation (MAD) is 9.09.

Answer 5

Apologies for the confusion. Let's recalculate the Mean Absolute Deviation (MAD) correctly.

To find the MAD, we need to calculate the following steps:

Step 1: Find the mean (average) of the data set.
Step 2: Determine the deviation of each data point from the mean.
Step 3: Take the absolute value of each deviation.
Step 4: Find the average of all the absolute deviations.

Step 1: Find the mean
To find the mean, we sum up all the data points and divide by the total count of data points.
Mean = (55 + 60 + 70 + 70 + 75 + 75 + 75 + 80 + 80 + 85 + 85 + 85 + 85 + 90 + 90 + 95 + 100) / 17
Mean = 1380 / 17
Mean ≈ 81.18 (rounded to two decimal places)

Step 2: Determine the deviation of each data point from the mean
Deviation of each data point = data point - mean

Data point - Mean:
55 - 81.18 ≈ -26.18
60 - 81.18 ≈ -21.18
70 - 81.18 ≈ -11.18
70 - 81.18 ≈ -11.18
75 - 81.18 ≈ -6.18
75 - 81.18 ≈ -6.18
75 - 81.18 ≈ -6.18
80 - 81.18 ≈ -1.18
80 - 81.18 ≈ -1.18
85 - 81.18 ≈ 3.82
85 - 81.18 ≈ 3.82
85 - 81.18 ≈ 3.82
85 - 81.18 ≈ 3.82
90 - 81.18 ≈ 8.82
90 - 81.18 ≈ 8.82
95 - 81.18 ≈ 13.82
100 - 81.18 ≈ 18.82

Step 3: Take the absolute value of each deviation
We take the absolute value of each deviation to remove any negative values.

Absolute deviations:
|-26.18| ≈ 26.18
|-21.18| ≈ 21.18
|-11.18| ≈ 11.18
|-11.18| ≈ 11.18
|-6.18| ≈ 6.18
|-6.18| ≈ 6.18
|-6.18| ≈ 6.18
|-1.18| ≈ 1.18
|-1.18| ≈ 1.18
|3.82| ≈ 3.82
|3.82| ≈ 3.82
|3.82| ≈ 3.82
|3.82| ≈ 3.82
|8.82| ≈ 8.82
|8.82| ≈ 8.82
|13.82| ≈ 13.82
|18.82| ≈ 18.82

Step 4: Find the average of all the absolute deviations
Average of absolute deviations = sum of absolute deviations / total count of data points

Sum of absolute deviations ≈ 26.18 + 21.18 + 11.18 + 11.18 + 6.18 + 6.18 + 6.18 + 1.18 + 1.18 + 3.82 + 3.82 + 3.82 + 3.82 + 8.82 + 8.82 + 13.82 + 18.82
Sum of absolute deviations ≈ 186.18

Average of absolute deviations ≈ 186.18 / 17
Average of absolute deviations ≈ 10.95 (rounded to two decimal places)

Therefore, the Mean Absolute Deviation (MAD) is approximately 10.95.