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QOTD#9 Each of the people in three groups gave a rating of

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QOTD#9 Each of the people in three groups gave a rating of [#permalink] New post 12 Sep 2016, 11:22
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Question Stats:

100% (00:35) correct 0% (00:00) wrong based on 2 sessions
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Each of the people in three groups gave a rating of Product X on a scale from 1 through 5. For each of the groups, the table above shows the number of people in the group and the average (arithmetic mean) of their ratings. What is the average of the ratings of the product given by the 100 people in the three groups combined?

Give your answer to the nearest 0.1.



[Reveal] Spoiler: OA
4.1


[Reveal] Spoiler: Img
Attachment:
test.jpg
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Re: QOTD#9 Each of the people in three groups gave a rating of [#permalink] New post 18 Nov 2016, 06:38
Expert's post
sandy wrote:
Image

Each of the people in three groups gave a rating of Product X on a scale from 1 through 5. For each of the groups, the table above shows the number of people in the group and the average (arithmetic mean) of their ratings. What is the average of the ratings of the product given by the 100 people in the three groups combined?

Give your answer to the nearest 0.1.



[Reveal] Spoiler: OA
4.1


[Reveal] Spoiler: Img
Attachment:
test.jpg


We can use weighted averages to answer this question.

Weighted average of groups combined = (group A proportion)(group A average) + (group B proportion)(group B average) + (group C proportion)(group C average) + ...

Group A: 45/100 of the people are in this group. And their average rating is 3.8
Group B: 25/100 of the people are in this group. And their average rating is 4.6
Group C: 30/100 of the people are in this group. And their average rating is 4.2

Applying the above formula we get:
Weighted average of groups combined = (45/100)(3.8) + (25/100)(4.6) + (30/100)(4.2)
= 1.71 + 1.15 + 1.26
= 4.12

Answer: 4.1

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Re: QOTD#9 Each of the people in three groups gave a rating of   [#permalink] 18 Nov 2016, 06:38
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QOTD#9 Each of the people in three groups gave a rating of

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