To find the mean deviation of a dataset, follow these steps based on the provided reference:
Steps to Calculate Mean Deviation
Here's a detailed breakdown of how to calculate the mean deviation:
- Calculate the Central Point:
- First, you need to determine a central point for your dataset. This can be the mean, median, or mode, depending on the context.
- The most common central point used is the mean. To calculate the mean, sum all the data values and divide by the total number of data points.
- Calculate Deviations:
- Next, subtract the value of the chosen central point (usually the mean) from each individual data point in your dataset. This gives you the deviation of each point from the center.
- Absolute Values:
- Take the absolute value of each deviation you calculated in the previous step. This ensures that all values are positive, as we are interested in the magnitude of the deviation, not the direction.
- Sum of Absolute Deviations:
- Now, add up all the absolute deviations you have obtained.
- Calculate Mean Deviation:
- Finally, divide the sum of the absolute deviations by the total number of data points in your original dataset. The result is the mean deviation.
Example
Let's say we have the following dataset: 4, 6, 8, 10, 12
- Mean: (4 + 6 + 8 + 10 + 12) / 5 = 40 / 5 = 8
- Deviations from the mean:
- 4 - 8 = -4
- 6 - 8 = -2
- 8 - 8 = 0
- 10 - 8 = 2
- 12 - 8 = 4
- Absolute values of deviations: 4, 2, 0, 2, 4
- Sum of absolute deviations: 4 + 2 + 0 + 2 + 4 = 12
- Mean deviation: 12 / 5 = 2.4
Thus, the mean deviation for the dataset is 2.4.
Summary
| Step | Action |
|---|---|
| 1 | Calculate the mean (or central point) |
| 2 | Subtract the mean from each data point |
| 3 | Take the absolute value of each difference |
| 4 | Sum the absolute values |
| 5 | Divide the sum by the number of data points |
This process gives a measure of how spread out the data is around the mean.
