The mean deviation is found by following a three-step process:
- Calculate the Mean: First, you must determine the average value of the given data set. This is done by summing all the values in the data set and dividing by the total number of values.
- Find the Absolute Deviations: Next, you subtract the calculated mean from each individual data point. After doing so, you take the absolute value of each of these differences (meaning you ignore any negative signs and treat all values as positive). The absolute deviation measures how far each data point is from the mean.
- Calculate the Mean of the Absolute Deviations: Finally, you find the mean of all the absolute deviations. This involves summing up all of the absolute deviation values and dividing by the total number of absolute deviations. The result is the mean deviation.
Here's a table summarizing the steps:
| Step | Action | Description |
|---|---|---|
| 1 | Find the mean value of the data set | Sum all values and divide by the number of values. |
| 2 | Find the absolute deviations | Subtract the mean from each data value, then take the absolute value (ignore negative signs). |
| 3 | Find the mean of absolute deviations | Sum all absolute deviations and divide by the number of absolute deviations (which equals the number of data points). |
Example
Let's say we have the data set: 5, 8, 10, 12, 15
- Step 1: Calculate the mean: (5 + 8 + 10 + 12 + 15) / 5 = 50 / 5 = 10
- Step 2: Calculate absolute deviations:
- |5 - 10| = 5
- |8 - 10| = 2
- |10 - 10| = 0
- |12 - 10| = 2
- |15 - 10| = 5
- Step 3: Calculate the mean of absolute deviations: (5 + 2 + 0 + 2 + 5) / 5 = 14 / 5 = 2.8
Therefore, the mean deviation for the data set is 2.8.
In summary, the mean deviation provides a measure of the average distance of the data points from the mean, giving an idea of how spread out the data is. This is useful in statistics to understand data variability.
