Final answer:
When each observation is increased by 4, the standard deviation remains unchanged. When each observation is multiplied by 5, the standard deviation increases by a factor of 5.
Step-by-step explanation:
To find the changed standard deviation when each observation is increased by 4, we need to understand that standard deviation measures the spread or variability of the data. When each observation is increased by the same value, the spread of the data remains the same, so the standard deviation will remain unchanged. Therefore, the changed standard deviation in this case is 2.
When each observation is multiplied by 5, the spread of the data is increased by a factor of 5, so the standard deviation will also increase by a factor of 5. Therefore, the changed standard deviation in this case is 10.