Shane04 wrote:
Mean of {1, 1, 1, 5} is 2. Three of the numbers are distance 1 away from mean and one number is distance 3 away from mean. Mean of {1, 5, 5, 5} is 4. Three of the numbers are distance 1 away from mean and one number is distance 3 away from mean. Sum of the squared deviations will be the same in both the cases and the number of elements is also the same in both the cases. Therefore, both these sets will have the same SD.
How do we conclude that these two sets have the same SD?
Does this mean that if we have the same number of elements in two sets at the same distance from their mean, their SD will be the same??
Thank you.
Yes. How do we calculate SD? We square the "difference of each term from the mean" and add these squares. Then we divide this sum by the number of terms. Then we take the square root of everything. So then what does the SD of any set depend on? The difference of each term from the mean and the number of terms.
If two sets have same number of terms, say 4 and if the difference of numbers from mean is 1, 1, 1, 3 and in the other set too, the difference of numbers from mean is 3, 1, 1, 1, the SDs will be the same no matter what the actual numbers are.
The two sets could be {1, 1, 1, 5} and {96, 100, 100, 100} too. They will still have the same SD.
For more on SD,
Check out this video:
https://youtu.be/0E6FQMzQVj0and this post
https://anaprep.com/sets-statistics-sta ... formation/