Based on the provided steps, the process is likely calculating the standard deviation or variance of a dataset. The question is asking what follows these steps:
- Step 1: Find the mean.
- Step 2: For each data point, find the square of its distance to the mean.
- Step 3: Sum the values from Step 2.
- Step 4: Divide by the number of data points.
The next step depends on whether you're calculating the variance or the standard deviation.
If Calculating Variance:
If you are calculating the population variance, Step 4 gives you the variance directly. Therefore, there is no 'next step'. The variance is a measure of how spread out the data is from the mean.
However, if calculating the sample variance, Step 4 would be dividing by (n-1) instead of n, where n is the number of data points. Again, once you perform this division, the result is the sample variance, and there is no further step.
If Calculating Standard Deviation:
If you are calculating the standard deviation, the next step is to find the square root of the result from Step 4.
Step 5: Take the square root of the value obtained in Step 4.
The standard deviation is the square root of the variance and provides a measure of the spread of the data in the original units. This makes it easier to interpret than the variance.
Example:
Let's say you have the following data points: 2, 4, 6, 8, 10.
- Mean: (2 + 4 + 6 + 8 + 10) / 5 = 6
- Squared distances from the mean: (2-6)^2 = 16, (4-6)^2 = 4, (6-6)^2 = 0, (8-6)^2 = 4, (10-6)^2 = 16
- Sum of squared distances: 16 + 4 + 0 + 4 + 16 = 40
- Variance (assuming population): 40 / 5 = 8
- Standard Deviation (assuming population): √8 ≈ 2.83
In summary, if you are calculating the variance, the provided steps are complete. If calculating the standard deviation, the final step is to take the square root of the result after dividing by the number of data points.
