1, 2, 2, 3, 3, 6, 7, 8, 10
mean absolute deviation.
To find the mean absolute deviation (MAD) of a set of numbers, follow these steps:
1. Find the mean (average) of the set of numbers.
Add the numbers together and divide by the total count. In this case:
(1 + 2 + 2 + 3 + 3 + 6 + 7 + 8 + 10) / 9 = 42 / 9 = 4.67 (rounded to 2 decimal places)
2. Calculate the absolute deviation for each number.
Subtract the mean from each number and take the absolute value. In this case:
|1 - 4.67| = 3.67
|2 - 4.67| = 2.67
|2 - 4.67| = 2.67
|3 - 4.67| = 1.67
|3 - 4.67| = 1.67
|6 - 4.67| = 1.33
|7 - 4.67| = 2.33
|8 - 4.67| = 3.33
|10 - 4.67| = 5.33
3. Find the average of the absolute deviations.
Add up the absolute deviations and divide by the total count. In this case:
(3.67 + 2.67 + 2.67 + 1.67 + 1.67 + 1.33 + 2.33 + 3.33 + 5.33) / 9 = 24.34 / 9 = 2.71 (rounded to 2 decimal places)
The mean absolute deviation (MAD) of the given set of numbers is 2.71.
To find the mean absolute deviation (MAD) for a set of numbers, follow these steps:
1. Find the mean (average) of the numbers.
Add all the numbers together and divide by the total count of numbers.
For example:
(1 + 2 + 2 + 3 + 3 + 6 + 7 + 8 + 10) / 9 = 42 / 9 = 4.6667 (rounded to 4.67)
2. Subtract the mean from each number to find the deviations.
For each number in the set, subtract the mean from it.
For example:
1 - 4.67 = -3.67
2 - 4.67 = -2.67
2 - 4.67 = -2.67
3 - 4.67 = -1.67
3 - 4.67 = -1.67
6 - 4.67 = 1.33
7 - 4.67 = 2.33
8 - 4.67 = 3.33
10 - 4.67 = 5.33
3. Find the absolute value of each deviation.
If any of the deviations are negative, convert them to their positive value.
For example:
Absolute deviation for -3.67 = 3.67
Absolute deviation for -2.67 = 2.67
Absolute deviation for -2.67 = 2.67
Absolute deviation for -1.67 = 1.67
Absolute deviation for -1.67 = 1.67
Absolute deviation for 1.33 = 1.33
Absolute deviation for 2.33 = 2.33
Absolute deviation for 3.33 = 3.33
Absolute deviation for 5.33 = 5.33
4. Find the mean (average) of the absolute deviations.
Add all the absolute deviations together and divide by the total count of numbers.
For example:
(3.67 + 2.67 + 2.67 + 1.67 + 1.67 + 1.33 + 2.33 + 3.33 + 5.33) / 9 = 24.97 / 9 = 2.7744 (rounded to 2.77)
So, the mean absolute deviation for the given set of numbers is 2.77.
To find the mean absolute deviation (MAD) of a set of numbers, you'll need to follow these steps:
1. Calculate the mean: Add up all the numbers in the set and then divide the sum by the total number of values. In this case, you have 1, 2, 2, 3, 3, 6, 7, 8, and 10. Adding them up gives us 42, and since there are 9 numbers, the mean is 42/9 = 4.67 (rounded to two decimal places).
2. Find the absolute deviation: For each number in the set, subtract the mean from the number and take the absolute value of the difference. In other words, find the distance between each number and the mean. For example, the absolute deviations for the first few numbers (1, 2, 2, 3, 3) would be 3.67, 2.67, 2.67, 1.67, and 1.67 respectively.
3. Calculate the mean of the absolute deviations: Add up all the absolute deviations and divide the sum by the total number of values. In this case, adding the absolute deviations (3.67, 2.67, 2.67, 1.67, 1.67, 1.67, 2.67, 3.67, and 5.33) gives us 24.49. Since there are 9 absolute deviations, the mean is 24.49/9 = 2.72 (rounded to two decimal places).
The mean absolute deviation (MAD) is the average distance between each number in the set and the mean. So in this case, the MAD is 2.72.