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On last Wednesday, each of the 45 members of a certain task force team

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New post 30 Mar 2019, 12:31
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On last Wednesday, each of the 45 members of a certain task force team spent some time working on a project A. The above graph shows the number of hours and the number of members, who spent that number of hours working on the project A on last Wednesday. What was the median number of hours that the members of the task force team spent working on the project A on last Wednesday?

A. 3
B. 4
C. 5
D. 6
E. 7

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On last Wednesday, each of the 45 members of a certain task force team  [#permalink]

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New post 30 Mar 2019, 12:38
dabaobao wrote:
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On last Wednesday, each of the 45 members of a certain task force team spent some time working on a project A. The above graph shows the number of hours and the number of members, who spent that number of hours working on the project A on last Wednesday. What was the median number of hours that the members of the task force team spent working on the project A on last Wednesday?

A. 3
B. 4
C. 5
D. 6
E. 7


Solution:



We have set consisting of 45 terms (terms=number of members): 10+5+2+3+2+9+11+3=45. Median of a set, with odd number of terms, would be the middle term, so 23rd term. Values of terms: 10 terms=1, 5 terms=2, 2 terms=3, 3 terms=4 , 2 terms=5, 9 terms=6, 11 terms=7 and 3 terms=8 --> 23rd term is 6.

To illustrate:
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 3, 3, 4, 4, 4, 5, 5, 6, 6, 6, 6, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 8, 8, 8

Answer: D.

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On last Wednesday, each of the 45 members of a certain task force team  [#permalink]

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New post 18 Aug 2019, 08:55
I transformed the graph in the following table:

1 hr - 10
2 hr - 5
3 hr - 2
4 hr - 3
5 hr - 2
6 hr - 9
7 hr - 11
8 hr - 3

Then I figured out the position where the median is. The positions of the median in 45 numbers is the positions 23 (for which there are 22 to the left and 22 to the right):

Adding numbe of members up:

1hr 2hr 3hr 4hr 5hr
10 + 5 + 2 + 3 + 2 =22

So after the last member that has done the fifth hour comes the member that does 6 hours and this is the median (position 23)

OPTION D
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Re: On last Wednesday, each of the 45 members of a certain task force team  [#permalink]

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New post 18 Aug 2019, 10:37
dabaobao wrote:
Attachment:
Graph.png

On last Wednesday, each of the 45 members of a certain task force team spent some time working on a project A. The above graph shows the number of hours and the number of members, who spent that number of hours working on the project A on last Wednesday. What was the median number of hours that the members of the task force team spent working on the project A on last Wednesday?

A. 3
B. 4
C. 5
D. 6
E. 7


Number of hours = 1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,3,3,4,4,4,5,5,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,8,8,8
Number of terms = 45
Median = 23rd term = 6 hours

IMO D
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Re: On last Wednesday, each of the 45 members of a certain task force team   [#permalink] 18 Aug 2019, 10:37
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