The scores of a group of five students are 4, 5, 6, 7, 8. The standard deviation is
https://www.easycalculation.com/statistics/standard-deviation.php
I should have pointed out that there are two types of deviation.
One is called Population Standard Deviation, where you divide by n, the number of data values
The other is the Standard Deviation, where you divide by n-1 , where n is the number of data values.
You can see examples of the use of each one at the bottom of the above webpage
To calculate the standard deviation, follow these steps:
1. Find the mean (average) of the scores.
- Add up all the scores: 4 + 5 + 6 + 7 + 8 = 30
- Divide the sum by the number of scores: 30 / 5 = 6
- The mean is 6.
2. Subtract the mean from each score and square the result.
- For the first score: (4 - 6)^2 = (-2)^2 = 4
- For the second score: (5 - 6)^2 = (-1)^2 = 1
- For the third score: (6 - 6)^2 = 0^2 = 0
- For the fourth score: (7 - 6)^2 = 1^2 = 1
- For the fifth score: (8 - 6)^2 = 2^2 = 4
3. Calculate the mean of the squared differences.
- Add up all the squared differences: 4 + 1 + 0 + 1 + 4 = 10
- Divide the sum by the number of scores: 10 / 5 = 2
- The mean of the squared differences is 2.
4. Take the square root of the mean of squared differences to get the standard deviation.
- The square root of 2 is approximately 1.414.
- Therefore, the standard deviation is 1.414.
So, the standard deviation of the scores is 1.414.