Question

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 of the third group is

Answer 1

★ STATISTICS ★

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Explanation :-

If the combined mean of the first two groups combined (five total items) is 3, then that means the total value of the five items is 15. (If each item averages 3, and there are five items, the total would be 15.) 

The mean of all the items in the three groups (10 total items) is 12. That means the total value of the 10 items is 120. 

That means the total value of the items in the third group is 105. (120 total for all the groups -(Minus) 15 total for the first two groups equals 105.) Since there are five total items in the third group and the total is 105, that means the mean of the third group is 21. 

Calculations :-

Here, Total of all 3 groups $= 120$ 

So, Total of first 2 groups $= 15$ 
And, Total of 3rd group $= 105$ 

Thus, Mean for 3rd group $= \frac{105}{5}$ 
                                          $= 21$

∴ Mean for 3rd group is 21.

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Answer 2

Answer:

21

Step-by-step explanation:

The first , second and third groups have 2,3 and 5 items respectively.

The combined mean of three groups is 12

So, $12 =\frac{\text{First group+Second group +third group}}{2+3+5}$

$12\times 10=\text{First group+Second group +third group}$  ---A

$120=\text{First group+Second group +third group}$

Now we are given that  the combined mean of first two groups is 3

$3 =\frac{\text{First group+Second group}}{2+3}$

$3 \times 5=\text{First group+Second group}$

$15=\text{First group+Second group}$  ---B

A- B = Third group

$\text{First group+Second group +third group}-\text{First group+Second group}$  

$120-15$  

$105$  

Mean of third group = $\frac{\text{Sum}}{\text{No. of items}}$

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

Mean of third group = $21$

Hence then mean of the third group is is 21