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# The incomplete table above shows a distribution of scores for a class

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Math Expert
Joined: 02 Sep 2009
Posts: 49858
The incomplete table above shows a distribution of scores for a class  [#permalink]

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28 Aug 2016, 10:54
00:00

Difficulty:

15% (low)

Question Stats:

88% (02:15) correct 13% (02:51) wrong based on 93 sessions

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The incomplete table above shows a distribution of scores for a class of 25 students. If the average (arithmetic mean) score for the class is 83, what score is missing from the table?

A. 75
B. 77
C. 81
D. 84
E. 86

Attachment:

2016-08-28_2152.png [ 5.7 KiB | Viewed 1831 times ]

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Re: The incomplete table above shows a distribution of scores for a class  [#permalink]

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28 Aug 2016, 17:08
5
msk0657 wrote:
Bunuel wrote:

The incomplete table above shows a distribution of scores for a class of 25 students. If the average (arithmetic mean) score for the class is 83, what score is missing from the table?

A. 75
B. 77
C. 81
D. 84
E. 86

Attachment:
2016-08-28_2152.png

92*4 + 91*6 + 3x+83*7+71*5 / 25 = 83

1850 + 3x = 2075
3x = 225 => x =75

Option A.

Is there any short cut method ?

Possible shortcut:

First, find the unit digit of the total sum.
Total sum = Avg * number of students
= 83 * 25 -> unit digit is 5.

Next, find the unit digit of each pair from the table and add them up.

92 * 4 -> xx8
91 * 6 -> xx6
83 * 7 -> xx1
71 * 5 -> xx5

8+6+1+5 -> 0

So, the remaining pair must end with 5. The number of student is 3 so the score must have 5 as the units digit. Only 75 from the given options satisfies.

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Re: The incomplete table above shows a distribution of scores for a class  [#permalink]

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28 Aug 2016, 11:36
Bunuel wrote:

The incomplete table above shows a distribution of scores for a class of 25 students. If the average (arithmetic mean) score for the class is 83, what score is missing from the table?

A. 75
B. 77
C. 81
D. 84
E. 86

Attachment:
2016-08-28_2152.png

Sum of all = Average * 25 = 83*25=2075. -- (1)

From the table we can say, sum of all numbers = 92*4 + 91 *6 +83*7 + 71*5 + 3*X [X is the Value of Unknown score) -- (2)

Equating (1) and -- (2), we will get X= 75.
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Re: The incomplete table above shows a distribution of scores for a class  [#permalink]

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28 Aug 2016, 11:43
Bunuel wrote:

The incomplete table above shows a distribution of scores for a class of 25 students. If the average (arithmetic mean) score for the class is 83, what score is missing from the table?

A. 75
B. 77
C. 81
D. 84
E. 86

Attachment:
2016-08-28_2152.png

92*4 + 91*6 + 3x+83*7+71*5 / 25 = 83

1850 + 3x = 2075
3x = 225 => x =75

Option A.

Is there any short cut method ?
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Joined: 07 Sep 2014
Posts: 383
Concentration: Finance, Marketing
Re: The incomplete table above shows a distribution of scores for a class  [#permalink]

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28 Aug 2016, 22:00
4
1
Bunuel wrote:

The incomplete table above shows a distribution of scores for a class of 25 students. If the average (arithmetic mean) score for the class is 83, what score is missing from the table?

A. 75
B. 77
C. 81
D. 84
E. 86

Attachment:
2016-08-28_2152.png

can ignore 83.

92-83 = 9 so +36
91-83 = 8 so +48

83-71 =12 so -60

total effect = 24
need to be distriubted in 3.
s0 83-8 =75
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Re: The incomplete table above shows a distribution of scores for a class  [#permalink]

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15 Nov 2017, 08:24
Bunuel wrote:

The incomplete table above shows a distribution of scores for a class of 25 students. If the average (arithmetic mean) score for the class is 83, what score is missing from the table?

A. 75
B. 77
C. 81
D. 84
E. 86

Attachment:
2016-08-28_2152.png

$$\frac{(92*4)+(91*6)+(x*3)+(83*7)+(71*5)}{25} = 83$$

Or, $$368 + 546 +3x + 581 + 355 = 2075$$

Or, $$3x = 225$$

Or, $$x = 75$$, answer will be (A) 75
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Re: The incomplete table above shows a distribution of scores for a class  [#permalink]

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28 Nov 2017, 06:58
1
Hi
I have a different approach to this question, Please confirm that this approach is right. See attachment.

Abhishek009 wrote:
Bunuel wrote:

The incomplete table above shows a distribution of scores for a class of 25 students. If the average (arithmetic mean) score for the class is 83, what score is missing from the table?

A. 75
B. 77
C. 81
D. 84
E. 86

Attachment:
The attachment 2016-08-28_2152.png is no longer available

$$\frac{(92*4)+(91*6)+(x*3)+(83*7)+(71*5)}{25} = 83$$

Or, $$368 + 546 +3x + 581 + 355 = 2075$$

Or, $$3x = 225$$

Or, $$x = 75$$, answer will be (A) 75

Attachments

24169342_10156971885658289_370232763_o.jpg [ 115.35 KiB | Viewed 542 times ]

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Joined: 30 Sep 2017
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Re: The incomplete table above shows a distribution of scores for a class  [#permalink]

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28 Nov 2017, 08:36
(1850+3x)/25=83
x=75

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Re: The incomplete table above shows a distribution of scores for a class  [#permalink]

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29 Nov 2017, 18:06
Bunuel wrote:

The incomplete table above shows a distribution of scores for a class of 25 students. If the average (arithmetic mean) score for the class is 83, what score is missing from the table?

A. 75
B. 77
C. 81
D. 84
E. 86

Attachment:
2016-08-28_2152.png

We are given that the average (arithmetic mean) score for the class is 83. Since we are given the average, we can find the difference between the average and each score and multiply their respective frequencies, and the sum of these products should be 0. That is, if we let n = the missing score, we can create the following equation:

(92 - 83) x 4 + (91 - 83) x 6 + (n - 83) x 3 + (83 - 83) x 7 + (71 - 83) x 5 = 0

36 + 48 + 3n - 249 + 0 - 60 = 0

3n - 225 = 0

3n = 225

n = 75

Alternate Solution:

We can calculate a weighted mean for the 25 scores, using the formula average = sum/number:

83 = [4(92) + 6(91) + 3x + 7(83) + 5(71)]/25

2075 = 368 + 546 + 3x + 581 +355

2075 = 1850 + 3x

225 = 3x

75 = x

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Re: The incomplete table above shows a distribution of scores for a class &nbs [#permalink] 29 Nov 2017, 18:06
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