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. Calculate the mean and standard deviation.

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.

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