# The combined mean of three groups is 12 and the combined mean of first two groups is 3.If the first ,second and third groups have 2,3 and 5 items respectively, then mean if third group is?

Please find below the solution to the asked query:

Given : The combined mean of three groups is 12 .

Let sum of observation of first group =

*x*

_{1}, sum of observation of second group =

*x*

_{2}and sum of observation of third group =

*x*

_{3},

Also given : the first ,second and third groups have 2 , 3 and 5 items respectively , So

$\frac{{x}_{1}+{x}_{2}+{x}_{3}}{10}=12$ ,

*x*

_{1}+

*x*

_{2}+

*x*

_{3}= 120 ---- ( 1 )

And

The combined mean of first two groups is 3.So

$\frac{{x}_{1}+{x}_{2}}{5}=3$ ,

*x*

_{1}+

*x*

_{2}= 15 ---- ( 2 )

Now we subtract equation 2 from equation 1 we get

*x*

_{3}= 105

Therefore,

Mean if third group = $\frac{105}{5}$ =

**21 ( Ans )**

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