Answer:
The mean and standard deviation of the combined distribution is 16 and 7.192 respectively.
Step-by-step explanation:
We have given that a distribution consists of three components with frequencies 200, 250, and 300 having means 25, 10, and 15 and standard deviations 3, 4, and 5 respectively.
And we have to find the mean and standard deviation of the combined distribution.
Firstly let us represent some symbols;
= 200 = 25 = 3
= 250 = 10 = 4
= 300 = 15 = 5
Here, represent the means and represent the standard deviations.
Now, as we know that Mean of the combined distribution is given by;
Putting the above values in the formula we get;
= 16
Similarly, the formula for combined standard deviation is given by;
= 7.192
Hence, the mean and standard deviation of the combined distribution is 16 and 7.192 respectively.