Weighted Averages - Statistics

[shanice]

Hi all,

I was going through the explanation in the book about weighted averages.I could not understand what the book is trying to say about this topic.

Can anyone help me out by answering my below questions:-

1)What is weighted averages?What I must know about this topic? Please give an example.

2)Question : In a translation problem, 40% of a student's grade comes from exams, 30% from written
assignments, 20% from conversational practice, and 10% from interpretation. If a
student's grades are 94 for exams, 88 for written assignments, 98 for conversational
practice, and 85 for interpretation, what is the student's overall grade in the course?

Answer is 92.1


Thank you in advance.

P.S.I tried hiding the answer by using the spoiler but it's still not working.Please help.

[vk_vinayak]

Answer to the second question:

40% = 40/100 = 0.4,
similarly 30% = 30/100 = 0.3

(0.4)*(98) + (0.3)*(88) + (0.2)*(98) + (0.1)*(85)
=37.6 + 26.4 +19.6 + 8.5
=92.1

[shanice]

Thank you, Vk_vinayak. How do you apply the weighted average concept in this question? Can you explain?

[anuprajan5]

Shanice,

The effect/weightage of each section towards the final grade is:

40% of 94 on exams,
30% of 88 from written assignments,
20% of 98 for conversational practice,
10% of 85 from interpretation.

The total % add upto 100% (40+30+20+10)

When you calculate simple arithmetic mean, the weightage of each data point is equal towards the final average.

For example , arithmetic mean of 1,2,3,4 and 5 is 3. Each of these data points contribute evenly towards calculating the arithmetic mean. If you try to show it in weighted average terms, because there are 5 terms, the weightage for each data point is 20%.
Therefore, calculating by weighted average, 1*0.2 + 2*0.2 + 3* 0.2 + 4* 0.2 + 5*0.2 = 3.

In weighted averages some data points contribute more than others.

Regards
Anup

[Brent@GMATPrepNow]

1)What is weighted averages?What I must know about this topic? Please give an example.

We have a video that explains what weighted averages are and gives some examples: https://www.gmatprepnow.com/module/gmat- ... ics?id=805

Once you're more familiar with the concepts, you can tackle these questions:

https://www.beatthegmat.com/weighted-ave ... 14506.html
https://www.beatthegmat.com/weighted-ave ... 17237.html
https://www.beatthegmat.com/average-weig ... 57853.html
https://www.beatthegmat.com/averages-que ... 87118.html

Cheers,
Brent