0, 0, 1, 2, 3, 3, 8, 9, 10
mean absolute deviation.
To find the mean absolute deviation, first calculate the mean of the given set of numbers:
0 + 0 + 1 + 2 + 3 + 3 + 8 + 9 + 10 = 36
36/9 = 4
Next, calculate the absolute deviation for each number by subtracting the mean from each number and taking the absolute value:
|0 - 4| + |0 - 4| + |1 - 4| + |2 - 4| + |3 - 4| + |3 - 4| + |8 - 4| + |9 - 4| + |10 - 4|
= 4 + 4 + 3 + 2 + 1 + 1 + 4 + 5 + 6
= 30
Finally, divide the sum of absolute deviations by the number of observations:
30/9 = 3.333
So, the mean absolute deviation of the given set of numbers is 3.333.
To find the mean absolute deviation (MAD) of a set of numbers, follow these steps:
Step 1: Find the mean of the set of numbers.
To find the mean, add up all the numbers in the set and divide the sum by the total count of numbers.
In this case, the numbers are:
0, 0, 1, 2, 3, 3, 8, 9, 10.
Sum = 0 + 0 + 1 + 2 + 3 + 3 + 8 + 9 + 10 = 36
Count = 9
Mean = Sum / Count = 36 / 9 = 4
Therefore, the mean of the set is 4.
Step 2: Find the absolute deviation from the mean for each number in the set.
To find the absolute deviation from the mean, subtract the mean from each number in the set and take the absolute value of the result.
Absolute Deviation = |Number - Mean|
For example, the absolute deviation from the mean for the first number 0 is |0 - 4| = 4.
Calculating the absolute deviation for each number in the set gives us the following values:
0: |0 - 4| = 4
0: |0 - 4| = 4
1: |1 - 4| = 3
2: |2 - 4| = 2
3: |3 - 4| = 1
3: |3 - 4| = 1
8: |8 - 4| = 4
9: |9 - 4| = 5
10: |10 - 4| = 6
Step 3: Find the mean of the absolute deviations.
To find the MAD, find the mean of all the absolute deviations calculated in step 2.
Sum of absolute deviations = 4 + 4 + 3 + 2 + 1 + 1 + 4 + 5 + 6 = 30
MAD = Sum of absolute deviations / Count = 30 / 9 = 3.33 (rounded to two decimal places)
Therefore, the mean absolute deviation (MAD) of the given set is approximately 3.33.
To find the mean absolute deviation (MAD) of a set of numbers, you need to follow these steps:
1. Find the mean (average) of the numbers in the set. To do this, add up all the numbers and divide the sum by the total number of numbers in the set.
For the given set: 0, 0, 1, 2, 3, 3, 8, 9, 10
The sum = 0 + 0 + 1 + 2 + 3 + 3 + 8 + 9 + 10 = 36
The total number of numbers in the set = 9
Mean = 36 / 9 = 4
2. Find the absolute value of the difference between each number in the set and the mean. To do this, subtract the mean from each number and take the absolute value (ignore negative signs).
For the given set, subtract the mean (4) from each number:
|0-4| = 4
|0-4| = 4
|1-4| = 3
|2-4| = 2
|3-4| = 1
|3-4| = 1
|8-4| = 4
|9-4| = 5
|10-4| = 6
3. Find the mean of the absolute differences calculated in step 2. This is the MAD.
Add up all the absolute differences and divide by the total number of numbers in the set:
MAD = (4 + 4 + 3 + 2 + 1 + 1 + 4 + 5 + 6) / 9
= 30 / 9
≈ 3.33
Therefore, the mean absolute deviation (MAD) of the given set of numbers is approximately 3.33.