average

**kl050196** · March 20th 2009, 03:14 AM

In class P, there are 20 students and in class Q there are 28 students. Both classes sit for the same test. Th average of the student in class was 60% and the average of the students in class Q was 70%. It was decided to put all the marks together and find the common average. This average to the nearest % would be
a)64%
b)65%
c)66%
D)55%

**mr fantastic** · March 20th 2009, 03:42 AM

Originally Posted by kl050196

In class P, there are 20 students and in class Q there are 28 students. Both classes sit for the same test. Th average of the student in class was 60% and the average of the students in class Q was 70%. It was decided to put all the marks together and find the common average. This average to the nearest % would be
a)64%
b)65%
c)66%
D)55%

$60 = \frac{\sum_{i=1}^{20} x_i}{20} \Rightarrow 1200 = \sum_{i=1}^{20} x_i$ .

$70 = \frac{\sum_{i=1}^{28} y_i}{28} \Rightarrow 1960 = \sum_{i=1}^{28} y_i$ .

Therefore $\sum_{i=1}^{20} x_i + \sum_{i=1}^{28} y_i = 3160$ .

Therefore average for combined classes $= \frac{3160}{20 + 28} = \, ....$

**stapel** · March 20th 2009, 04:13 AM

Originally Posted by kl050196

In class P, there are 20 students and in class Q there are 28 students. Both classes sit for the same test. Th average of the student in class was 60% and the average of the students in class Q was 70%. It was decided to put all the marks together and find the common average. This average to the nearest % would be
a)64%
b)65%
c)66%
D)55%

In case you're not familiar with summation notation (displayed in the previous reply), just use the definition of "average", and work backwards:

You divided the sums of the scores by the numbers of students to get the averages. So multiply the averages by the numbers of students to get the sums.

Add the two sums to get the sum for all of the students together. Then divide by the total number of students.

**Soroban** · March 20th 2009, 04:20 AM

Hello, kl050196!

A simplified verstion of Mr. F's solution . . .

In class P, there are 20 students and in class Q there are 28 students.
Both classes sit for the same test.
The average of class P was 60% and the average of class Q was 70%.
It was decided to put all the marks together and find the common average.
This average, to the nearest %, would be:

. . $(a)\;64\% \qquad (b)\;65\% \qquad (c)\;66\% \qquad (d)\;55\%$

We are expected to know how to calculate an average.

. . $\text{average} \:=\:\frac{\text{total score}}{\text{number of scores}}$

Let $P$ be the total score of class P.
. . Then: . $\frac{P}{20} \:=\:0.60 \quad\Rightarrow\quad P \:=\:12$

Let $Q$ be the total score of class Q.
. . Then: . $\frac{Q}{28} \:=\:0.70 \quad\Rightarrow\quad Q \:=\:19.6$

Hence, the two classes had a total of: . $12 + 19.6 \:=\:31.6$ points
. . and a total of: . $20 + 28 \:=\:48$ scores.

Their combined average is: . $\frac{31.6}{48} \:=\:0.658333... \:=\:65\tfrac{5}{6}\%$ . . . answer (c)

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