Answer:
(a)
(b)
(c) The population standard deviation is multiplied by k
Step-by-step explanation:
Given
Solving (a): The population standard deviation
Start by calculating the mean
The population standard deviation is:
This gives:
Solving (b): Double the dataset and calculate the new population standard deviation
The new dataset is:
Start by calculating the mean
The population standard deviation is:
This gives:
Solving (c): What happens when the dataset is multiplied by k
In (a), we have:
In (b), when the dataset is doubled,
This implies that when the dataset is multiplied by k, the population standard deviation will be multiplied by the same factor:
i.e.