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# The chart above shows the distribution of letter grades for three grou

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Math Expert
Joined: 02 Sep 2009
Posts: 58445
The chart above shows the distribution of letter grades for three grou  [#permalink]

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05 Jan 2015, 06:54
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4
00:00

Difficulty:

55% (hard)

Question Stats:

69% (02:17) correct 31% (02:46) wrong based on 162 sessions

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Tough and Tricky questions: Word Problems.

The chart above shows the distribution of letter grades for three groups of students on one test. Point values are assigned to the letter grades so that A = 4 points, B = 3 points, C = 2 points, and D = 1 point. Which of the following values is closest to the average (arithmetic mean) grade of students in group 3?

A. 2.2
B. 2.4
C. 2.9
D. 3.1
E. 3.7

Kudos for a correct solution.

Attachment:

2015-01-05_1753.png [ 4.2 KiB | Viewed 4216 times ]

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Re: The chart above shows the distribution of letter grades for three grou  [#permalink]

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05 Jan 2015, 09:04
1
For this one, we only need to calculate the weighted average of the students in group 3.

Two students got an A, 9 got a B, seven got a C and 4 got a D, so the total number of points is 2*4 + 9*2 + 7*2 + 4*1 = 53. With 22 students in total, we get a weighted average of just under 2.5. The Answer is B.
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Re: The chart above shows the distribution of letter grades for three grou  [#permalink]

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05 Jan 2015, 10:38
1
From the chart:

2*4+9*3+7*2+4*1 / 22 (total students in group 3)

= 53 / 22
= 2 9/22 = ~2.4-2.5

B - 2.4
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Re: The chart above shows the distribution of letter grades for three grou  [#permalink]

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05 Jan 2015, 17:12
Bunuel wrote:

Tough and Tricky questions: Word Problems.

The chart above shows the distribution of letter grades for three groups of students on one test. Point values are assigned to the letter grades so that A = 4 points, B = 3 points, C = 2 points, and D = 1 point. Which of the following values is closest to the average (arithmetic mean) grade of students in group 3?

A. 2.2
B. 2.4
C. 2.9
D. 3.1
E. 3.7

Kudos for a correct solution.

Attachment:
2015-01-05_1753.png

total of group 3 = 4*1 + 7*2 + 9*3 + 2*4 = 53
Total students 22

Mean = 53/22 = 2.4
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Re: The chart above shows the distribution of letter grades for three grou  [#permalink]

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06 Jan 2015, 00:44

Attachment:

2015-01-05_1753.png [ 5.71 KiB | Viewed 3794 times ]

Mean of Group 3 $$= \frac{4*1 + 7*2 + 9*3 + 2*4}{4+7+9+2} = \frac{53}{22} = 2.4$$
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Posts: 58445
Re: The chart above shows the distribution of letter grades for three grou  [#permalink]

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09 Jan 2015, 07:16
Bunuel wrote:

Tough and Tricky questions: Word Problems.

The chart above shows the distribution of letter grades for three groups of students on one test. Point values are assigned to the letter grades so that A = 4 points, B = 3 points, C = 2 points, and D = 1 point. Which of the following values is closest to the average (arithmetic mean) grade of students in group 3?

A. 2.2
B. 2.4
C. 2.9
D. 3.1
E. 3.7

Kudos for a correct solution.

Attachment:
2015-01-05_1753.png

OFFICIAL SOLUTION:

(B) There are 4 + 7 + 9 + 2 = 22 students in group 3.

The grade distribution in group 3 was:

Therefore, the sum of the grade points for group 3 is:
(4 × 1) + (7 × 2) + (9 × 3) + (2 × 4) =
4 + 14 + 27 + 8 = 53.

We can find the average grade in group 3 by dividing this sum by the number of students in group 3:
Average for group 3 = 53/22.

Performing the required division, we see that 2.4 is the closest answer choice.

The correct answer is choice (B).
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Re: The chart above shows the distribution of letter grades for three grou  [#permalink]

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20 Dec 2018, 04:12
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Re: The chart above shows the distribution of letter grades for three grou   [#permalink] 20 Dec 2018, 04:12
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