Will the standard deviation of all data in three unequally-sized groups each with different means be the same if each group has the same standard deviation?
For example, I have a data set as follows:
- Group 1, Makes up 30% of individuals, Mean = 12, SD = 3
- Group 2, Makes up 50% of individuals, Mean = 17, SD = 3
- Group 3, Makes up 20% of individuals, Mean = 11, SD = 3
I've been asked to calculate whether the SD for all individuals together is equal to 3, or larger than 3. My instinct is to say that it will be larger than 3 given that the the means are quite far apart, but can I be certain given just the information provided...? Any help here would be much appreciated.