Is there a formula to calculate the standard deviation of a group or individual statistics
Example in a sporting fantasy league I can calculate the summary statistics of any one player.
Example
one player has a Mean 75, Standard deviation 26.
But what if I selected a group of 18 players with the same summary stats, can I estimate the summary statistics of this group?
The Mean I believe can just be multiplied
1350 (75*18),
but the standard deviation isn't as simple as using a multiplication?
To add to this- if the group of 18 players each had unique summary stats, can the groups summary stats also be explained/calculated? example
Player 1 – mean 75 sd 26
Player 2 – mean 100 sd 28
Player 3 – mean 105 sd 25
.
.
Player 18 – mean 72 sd 23
Any help would be great.
Thanks heaps
Best Answer
Well, it's complicated, because it depends on the distribution of the underlying statistic for each player. Let's assume we are talking about normal distributions. In that case (if the sample is large enough, you can ignore this constraint, and despite most data not being normally distributed, it's often somewhat close)