Average.

[lenagmat]

If I know the average for one group, (for instance, the average grade for the first group = 68.2), and the average for the second group (for instance, the average grade for the second group = 73.5).
Could I say, that the average grade in two groups is - (68.2+73.5)/2 ?
And if not, why?

[Anurag@Gurome]

If I know the average for one group, (for instance, the average grade for the first group = 68.2), and the average for the second group (for instance, the average grade for the second group = 73.5).
Could I say, that the average grade in two groups is - (68.2+73.5)/2 ?
And if not, why?

No, unless both groups have same number of members.

For example if 1st group has x members and 2nd group has y members, then total grade for the 1st group = 68.2x and total grade for 2nd group = 73.5y

Hence, average grade in two groups = (68.2x + 73.5y)/(x + y)

Only if x = y, then average = (68.2x + 73.5x)/(x + x) = (68.2 + 73.5)/2

[lenagmat]

If I know the average for one group, (for instance, the average grade for the first group = 68.2), and the average for the second group (for instance, the average grade for the second group = 73.5).
Could I say, that the average grade in two groups is - (68.2+73.5)/2 ?
And if not, why?

No, unless both groups have same number of members.

For example if 1st group has x members and 2nd group has y members, then total grade for the 1st group = 68.2x and total grade for 2nd group = 73.5y

Hence, average grade in two groups = (68.2x + 73.5y)/(x + y)

Only if x = y, then average = (68.2x + 73.5x)/(x + x) = (68.2 + 73.5)/2

I understood with x and y, and I am sure that you are completly right, but I don't understand taking numbers: (very simple ex.):
(2+6)/2=4 - Av.
(3+5+4)/3=4 - Av.

(Av.+Av.)/2=(4+4)/2=4
(2+6+3+5+4)/5=4

I just can not understand why both answers are the same.

[neelgandham]

If I know the average for one group, (for instance, the average grade for the first group = 68.2), and the average for the second group (for instance, the average grade for the second group = 73.5).
Could I say, that the average grade in two groups is - (68.2+73.5)/2 ?
And if not, why?

No, unless both groups have same number of members.

For example if 1st group has x members and 2nd group has y members, then total grade for the 1st group = 68.2x and total grade for 2nd group = 73.5y

Hence, average grade in two groups = (68.2x + 73.5y)/(x + y)

Only if x = y, then average = (68.2x + 73.5x)/(x + x) = (68.2 + 73.5)/2

I understood with x and y, and I am sure that you are completly right, but I don't understand taking numbers: (very simple ex.):
(2+6)/2=4 - Av.
(3+5+4)/3=4 - Av.

(Av.+Av.)/2=(4+4)/2=4
(2+6+3+5+4)/5=4

I just can not understand why both answers are the same.

It is just for THAT set of numbers(Where average1 = average 2), where you find that result equal.

Here is an example,
(2+6)/2 = 4
(98+99+100+101+102)/5 = 100

(avg1 + avg1)/2 = (100+4)/2 = 52
sum of numbers = (98+99+100+101+102+2+6)/7 = #72.59 which is not equal to 52 !

In simple words, the average of averages may not always be equal to the average of all the numbers.

[lenagmat]

Two groups in the class have passed the test. If the average grade for the first group was 68.2, and the average grade for the second group was 73.5, what was the average grade in two groups.

1). The first group had 20 more students than the second one
2). The first group has 3 time more students than the second one


Like I already know that average grade in two groups = (68.2x + 73.5y)/(x + y)
1). =(68.2(y+20)+ 73.5y))/(y+20+y)
And I can find Y.

But why B is the answer?

[Anurag@Gurome]

Two groups in the class have passed the test. If the average grade for the first group was 68.2, and the average grade for the second group was 73.5, what was the average grade in two groups.

1). The first group had 20 more students than the second one
2). The first group has 3 time more students than the second one

Say, number of students in group 1 and group 2 are x and y respectively.
Hence, average grade of two groups = (68.2x + 73.5y)/(x + y)

Statement 1: x = y + 20
Hence, required average = (68.2(y + 20) + 73.5y))/(y + 20 + y) = (141.7y + 1364)/(2y + 40)
But we don't know y.

NOT sufficient

Statement 1: x = y + 3y = 4y
Hence, required average = (68.2*(4y) + 73.5y))/(4y + y) = (4*68.2 + 73.5)/5
We can calculate the value of the above expression.

SUFFICIENT

The correct answer is B.

Like I already know that average grade in two groups = (68.2x + 73.5y)/(x + y)
1). =(68.2(y+20)+ 73.5y))/(y+20+y)
And I can find Y. ----> How?

[lenagmat]

Thank you very much.
And just for the future to make it completle clear for me:
If we have "X" and it is said:

Y 3 times more than X - than Y=3X+X, not Y=3X? (Because I thought all the time that it is y=3x).

Statement 1: x = y + 3y = 4y

[Anurag@Gurome]

...Y 3 times more than X - than Y=3X+X, not Y=3X?

When we say Y is 2 more than X, it means Y = X + 2
Similarly, when Y is 3 times more than X, then it means Y = X + 3 times X = X + 3X = 4X

Hope that helps.