109, 89, 112, 98, 101, 105, 120, 106. What is the mean absolute deviation of the dataset?
To find the mean absolute deviation (MAD) of a data set, we need to follow these steps:
1. Calculate the mean of the data set.
2. Find the absolute difference between each data point and the mean.
3. Calculate the mean of these absolute differences.
Let's apply these steps to the given data set:
1. Calculate the mean:
Mean = (109 + 89 + 112 + 98 + 101 + 105 + 120 + 106) / 8
Mean = 840 / 8
Mean = 105
2. Find the absolute difference:
|109 - 105| = 4
|89 - 105| = 16
|112 - 105| = 7
|98 - 105| = 7
|101 - 105| = 4
|105 - 105| = 0
|120 - 105| = 15
|106 - 105| = 1
3. Calculate the mean of the 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 approximately 6.75.
To find the mean absolute deviation (MAD) of a dataset, follow these steps:
1. Find the mean (average) of the dataset.
- Add up all the numbers: 109 + 89 + 112 + 98 + 101 + 105 + 120 + 106 = 840
- Divide the sum by the total number of values: 840 / 8 = 105
- The mean of the dataset is 105.
2. Subtract the mean from each number in the dataset, and take the absolute value of the difference.
- Subtract the mean from each number: |109-105|, |89-105|, |112-105|, |98-105|, |101-105|, |105-105|, |120-105|, |106-105|
- Simplifying, we get: 4, 16, 7, 7, 4, 0, 15, 1
3. Find the sum of the absolute differences.
- Add up all the absolute differences: 4 + 16 + 7 + 7 + 4 + 0 + 15 + 1 = 54
4. Divide the sum of the absolute differences by the total number of values in the dataset.
- Divide the sum by 8 (since there are 8 numbers in the dataset): 54 / 8 = 6.75
Therefore, the mean absolute deviation of the given dataset is 6.75.
To calculate the mean absolute deviation (MAD) of a dataset, follow these steps:
1. Find the mean (average) of the dataset. To do this, add up all the numbers in the dataset and divide by the total number of values. For the given dataset, the sum is 109 + 89 + 112 + 98 + 101 + 105 + 120 + 106 = 840. There are 8 numbers in the dataset, so the mean is 840/8 = 105.
2. Subtract the mean from each value in the dataset to get the deviations. For example, for the first number, 109, the deviation is 109 - 105 = 4. Repeat this step for each number in the dataset.
3. Take the absolute value of each deviation. This ensures that all deviations are positive. For example, the absolute value of 4 is 4.
4. Find the mean of the absolute deviations. Add up all the absolute deviations and divide by the total number of values. For the given dataset, the absolute deviations are: 4, 16, 7, 7, 4, 0, 15, 1. The sum of these values is 4 + 16 + 7 + 7 + 4 + 0 + 15 + 1 = 54. Divide 54 by 8 (the total number of values) to get the mean absolute deviation.
Therefore, the mean absolute deviation of the given dataset is 54/8 = 6.75.