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On a certain math exam, 10% of the students got 70 points, 25% got 80

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Bunuel
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On a certain math exam, 10% of the students got 70 points, 25% got 80 [#permalink] New post   24 Mar 2019, 23:48
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On a certain math exam, 10% of the students got 70 points, 25% got 80 points, 20% got 85 points, 15% got 90 points, and the rest got 95 points. What is the difference between the mean and the median score on this exam?

(A) 0
(B) 1
(C) 2
(D) 3
(E) 4
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B
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Archit3110
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Re: On a certain math exam, 10% of the students got 70 points, 25% got 80 [#permalink] New post   25 Mar 2019, 00:16
Bunuel wrote:
On a certain math exam, 10% of the students got 70 points, 25% got 80 points, 20% got 85 points, 15% got 90 points, and the rest got 95 points. What is the difference between the mean and the median score on this exam?

(A) 0
(B) 1
(C) 2
(D) 3
(E) 4


let total class = 20
so
10% ; 2*70 = 140
25%; 5*80=400
20%; 4*85= 340
15%; 3*90 = 270
rest ; 6*90 = 540
total score sum = 1720 ; mean = 1720/20 ; 86
and median = 85
difference = 1
IMO B
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Re: On a certain math exam, 10% of the students got 70 points, 25% got 80 [#permalink] New post   27 Mar 2019, 08:35
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Good solution Archit.

Removed a small typo...

Archit3110 wrote:
Bunuel wrote:
On a certain math exam, 10% of the students got 70 points, 25% got 80 points, 20% got 85 points, 15% got 90 points, and the rest got 95 points. What is the difference between the mean and the median score on this exam?

(A) 0
(B) 1
(C) 2
(D) 3
(E) 4


let total class = 20
so
10% ; 2*70 = 140
25%; 5*80=400
20%; 4*85= 340
15%; 3*90 = 270
rest ; 6*90 = 540 6*95=570
total score sum = 1720 ; mean = 1720/20 ; 86
and median = 85
difference = 1
IMO B
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Re: On a certain math exam, 10% of the students got 70 points, 25% got 80 [#permalink] New post   02 Apr 2019, 19:07
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Bunuel wrote:
On a certain math exam, 10% of the students got 70 points, 25% got 80 points, 20% got 85 points, 15% got 90 points, and the rest got 95 points. What is the difference between the mean and the median score on this exam?

(A) 0
(B) 1
(C) 2
(D) 3
(E) 4


We can let the number of students = 100, thus:

10 had a 70

25 had an 80

20 had an 85

15 had a 90

30 had a 95

The median position is (100 + 1)/2 = 50.5, i.e., the average of the 50th and 51st numbers. We see that they both are 85, so the median is also 85.

The mean is:

(10 x 70 + 25 x 80 + 20 x 85 + 15 x 90 + 30 x 95)/100

(700 + 2000 + 1700 + 1350 + 2850)/100

8600/100

86

So the difference between the mean and the median is 86 - 85 = 1.

Answer: B
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Re: On a certain math exam, 10% of the students got 70 points, 25% got 80 [#permalink]
02 Apr 2019, 19:07
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