Help with Statistics question

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debmalya_dutta: Master | Next Rank: 500 Posts; Posts: 385; Joined: Sun Jul 12, 2009 10:16 pmFollowed by: 2 members; Thanked: 29 times; GMAT Score:710

by debmalya_dutta » Sat Jul 17, 2010 7:54 am

Help!

"Each Senior in a College Course wrote a Thesis. The lengths, in page, of those seniors' theses re summarized in the graph above.

a. What is the least possible number of seniors whose theses were within six pages of the median length?

[/img]

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Source: Beat The GMAT — Problem Solving | Sat Jul 17, 2010 7:54 am

kvcpk: Legendary Member; Posts: 1893; Joined: Sun May 30, 2010 11:48 pmFollowed by: 7 members; Thanked: 215 times

by kvcpk » Sat Jul 17, 2010 8:03 am

debmalya_dutta wrote:Help!

"Each Senior in a College Course wrote a Thesis. The lengths, in page, of those seniors' theses re summarized in the graph above.

a. What is the least possible number of seniors whose theses were within six pages of the median length?

[/img]

Seniors between:
0-9 : 1
10-19: 4
20-29: 6
30-39: 7
40-49: 2

total 20 seniors are present. Therefore 22 entries for pagecounts will exist

We need to find out median length:
When arranged in ascending order, median will be the average of the Highestnumber of pages between 20-29 and the lowest number of pages between 30-39
(because, median of 20 elements is average of 10th and 11th elements)

Highest number of seniors whoes thesis is within 6 pages of median length would be :
all seniors between 10-19 and all seniors between 20-29
=6+4 = 10
(edited and corrected)
Whats the OA?

Last edited by kvcpk on Sat Jul 17, 2010 9:52 am, edited 2 times in total.

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selango: Legendary Member; Posts: 1460; Joined: Tue Dec 29, 2009 1:28 amFollowed by: 7 members; Thanked: 135 times

by selango » Sat Jul 17, 2010 8:17 am

Praveen,

Total number of seniors =20

Median =Highest-Lowest/20=49-9/20=2

Within 6 pages of the median length=8

1 people are with 8 pages[0-9]

Please correct me if i am wrong.

--Anand--

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singhpreet1: Senior | Next Rank: 100 Posts; Posts: 95; Joined: Tue Jun 08, 2010 11:27 am; Thanked: 7 times

by singhpreet1 » Sat Jul 17, 2010 9:40 am

debmalya_dutta wrote:Help!

"Each Senior in a College Course wrote a Thesis. The lengths, in page, of those seniors' theses re summarized in the graph above.

a. What is the least possible number of seniors whose theses were within six pages of the median length?

[/img]

Agreeing with Selango, median is 20. but students who are within 6 pages of 20 will include the students from 10-19 and 20-29, therefore i reached the answer of 4+6= 10

do we have the OA?

Preet

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debmalya_dutta: Master | Next Rank: 500 Posts; Posts: 385; Joined: Sun Jul 12, 2009 10:16 pmFollowed by: 2 members; Thanked: 29 times; GMAT Score:710

by debmalya_dutta » Sat Jul 17, 2010 12:29 pm

I picked this from a post in the Manhattan GMAT forum. The OA is 2 as per the post. No explanation has yet been posted

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