To find the mean absolute deviation of the data, start by finding the mean of the data set.
Find the sum of the data values, and divide the sum by the number of data values.
Find the absolute value of the difference between each data value and the mean: |data value – mean|.
Find the sum of the absolute values of the differences.
Divide the sum of the absolute values of the differences by the number of data values.

Mean Deviation

Mean deviation, also known as average deviation or mean absolute deviation, is a statistical measure that calculates the average distance between each data point in a dataset and the mean of that dataset. It provides a measure of the dispersion or spread of the data values around the mean.

Calculation

The mean deviation is calculated by following these steps:

1. Find the mean of the dataset by summing all the values and dividing by the total number of values.

2. Calculate the absolute difference between each data point and the mean by subtracting the mean from each value and taking the absolute value of the result.

3. Sum all the absolute differences calculated in the previous step.

4. Divide the sum obtained in step 3 by the total number of values in the dataset.

Formula

The formula for calculating the mean deviation is as follows:

Mean deviation = Σ|X - X̄| / N

Where:
- Σ represents the sum of the values.
- X represents each individual value in the dataset.
- X̄ represents the mean of the dataset.
- N represents the total number of values in the dataset.

Example

Let's consider a dataset of exam scores: 85, 90, 92, 88, 95.

1. Calculate the mean: (85 + 90 + 92 + 88 + 95) / 5 = 90.

2. Calculate the absolute difference between each score and the mean:
- |85 - 90| = 5
- |90 - 90| = 0
- |92 - 90| = 2
- |88 - 90| = 2
- |95 - 90| = 5

3. Sum the absolute differences: 5 + 0 + 2 + 2 + 5 = 14.

4. Divide the sum by the total number of values: 14 / 5 = 2.8.

Therefore, the mean deviation of the dataset is 2.8.

Interpretation

The mean deviation provides a measure of the average deviation of the data points from the mean. A higher mean deviation indicates a greater dispersion or spread of the data values. In the example above, a mean deviation of 2.8 suggests that, on average, the exam scores deviate from the mean by approximately 2.8 units.

Limitations

While mean deviation is a useful measure of dispersion, it has some limitations:
- It does not consider the direction of deviations, only their magnitude.
- It treats positive and negative deviations equally, which may not always be desirable.
- It may not be suitable for datasets with outliers, as a single extreme value can significantly affect the mean deviation.

Conclusion

Mean deviation is a statistical measure that calculates the average distance between each data point and the mean of a dataset. It provides a measure of the dispersion or spread of the data values. By following the calculation steps and using the formula, you can easily calculate the mean deviation. However, it is important to consider the limitations of mean deviation and interpret the results in the context of the dataset being analyzed.