Calculate SS, variance, and standard deviation for the following sample of n _ 4 scores: 3, 1, 1, 1. (Note: The computational formula works well with these scores.)
To calculate the SS (sum of squares), variance, and standard deviation for this sample, we need to follow a few steps:
1. Calculate the mean (average) of the scores:
- Add up all the scores: 3 + 1 + 1 + 1 = 6.
- Divide the sum by the number of scores (4): 6 / 4 = 1.5.
- The mean is 1.5.
2. Calculate the deviation from the mean for each score:
- For each score, subtract the mean from the score:
- Deviation for the first score: 3 - 1.5 = 1.5
- Deviation for the second score: 1 - 1.5 = -0.5
- Deviation for the third score: 1 - 1.5 = -0.5
- Deviation for the fourth score: 1 - 1.5 = -0.5
3. Calculate the squared deviation for each score:
- For each deviation, square it:
- Squared deviation for the first score: 1.5^2 = 2.25
- Squared deviation for the second score: (-0.5)^2 = 0.25
- Squared deviation for the third score: (-0.5)^2 = 0.25
- Squared deviation for the fourth score: (-0.5)^2 = 0.25
4. Calculate the SS (sum of squares):
- Add up all the squared deviations:
- SS = 2.25 + 0.25 + 0.25 + 0.25 = 3
5. Calculate the variance:
- Divide the SS by the number of scores (4):
- Variance = 3 / 4 = 0.75
6. Calculate the standard deviation:
- Take the square root of the variance:
- Standard Deviation = √(0.75) ≈ 0.866
So, the SS is 3, the variance is 0.75, and the standard deviation is approximately 0.866 for the given sample.