To find the deviation of data points, you first need to calculate the mean (average) of your dataset and then subtract the mean from each individual data point.
Steps to Calculate Deviation
Here's a breakdown of how to find the deviation:
-
Calculate the Mean:
- Add up all the values in your dataset.
- Divide the sum by the total number of values.
- This result is the mean (represented as in statistical formulas).
-
Find the Deviations:
- Subtract the calculated mean from each individual data point in your dataset.
- This difference is the deviation for that data point.
- Important: Data points below the mean will have negative deviations, while those above the mean will have positive deviations, as stated in the reference.
Example
Let's say we have the following data set: 5, 8, 6, 10, 11
-
Calculate the Mean:
- Sum: 5 + 8 + 6 + 10 + 11 = 40
- Count: 5
- Mean: 40 / 5 = 8
-
Find the Deviations:
- 5 - 8 = -3
- 8 - 8 = 0
- 6 - 8 = -2
- 10 - 8 = 2
- 11 - 8 = 3
Here's a table summarizing the process:
| Data Point | Deviation |
|---|---|
| 5 | -3 |
| 8 | 0 |
| 6 | -2 |
| 10 | 2 |
| 11 | 3 |
Understanding Deviations
- Positive Deviations: These indicate a data point that is greater than the mean.
- Negative Deviations: These indicate a data point that is less than the mean.
- Zero Deviation: This indicates a data point that is exactly the same as the mean.
Deviations are fundamental in statistics and are used to calculate measures like standard deviation, which provides information about the spread or variability of the data set.
