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
.
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.
wrong
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.
not it
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.
To find the Mean Absolute Deviation (MAD) for the given set of numbers, follow these steps:
1. Calculate the mean (average) of the numbers:
55 + 60 + 70 + 70 + 75 + 75 + 75 + 80 + 80 + 85 + 85 + 85 + 85 + 90 + 90 + 95 + 100 = 1415
Mean = 1415 / 17 = 83.24 (rounded to two decimal places)
2. Find the deviation of each number from the mean by subtracting the mean from each number:
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
3. Find the absolute value of the deviation for each number:
|-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
4. Calculate the mean of the 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) / 17 = 102.12 / 17 = 6 (rounded to the nearest whole number)
Therefore, the Mean Absolute Deviation (MAD) for the given set of numbers is 6.
To find the Mean Absolute Deviation (MAD), follow these steps:
Step 1: Find the mean
To calculate the mean, add up all the test scores and divide by the total number of scores.
55 + 60 + 70 + 70 + 75 + 75 + 75 + 80 + 80 + 85 + 85 + 85 + 85 + 90 + 90 + 95 + 100 = 1420
1420 / 17 (number of scores) ≈ 83.5294 (mean)
Step 2: Find the absolute deviation for each score
To find the absolute deviation for each score, subtract the mean from each individual score, and take the absolute value (ignore the negative sign if any).
|55 - 83.5294| ≈ 28.5294
|60 - 83.5294| ≈ 23.5294
|70 - 83.5294| ≈ 13.5294
|70 - 83.5294| ≈ 13.5294
|75 - 83.5294| ≈ 8.5294
|75 - 83.5294| ≈ 8.5294
|75 - 83.5294| ≈ 8.5294
|80 - 83.5294| ≈ 3.5294
|80 - 83.5294| ≈ 3.5294
|85 - 83.5294| ≈ 1.4706
|85 - 83.5294| ≈ 1.4706
|85 - 83.5294| ≈ 1.4706
|85 - 83.5294| ≈ 1.4706
|90 - 83.5294| ≈ 6.4706
|90 - 83.5294| ≈ 6.4706
|95 - 83.5294| ≈ 11.4706
|100 - 83.5294| ≈ 16.4706
Step 3: Find the average of the absolute deviations
Add up all the absolute deviations, and divide by the total number of scores.
28.5294 + 23.5294 + 13.5294 + 13.5294 + 8.5294 + 8.5294 + 8.5294 + 3.5294 + 3.5294 + 1.4706 + 1.4706 + 1.4706 + 1.4706 + 6.4706 + 6.4706 + 11.4706 + 16.4706 = 165.2941
165.2941 / 17 ≈ 9.723
The Mean Absolute Deviation (MAD) is approximately 9.723.