Median Problem

Expert replies

zagcollins: Master | Next Rank: 500 Posts; Posts: 167; Joined: Wed Jun 11, 2008 10:58 pmFollowed by: 1 member; Thanked: 2 times

by zagcollins » Sat Jul 19, 2008 6:32 am

Yesterday each of the 35 members of a certain task force spent some time working on project P. The graph shows the number of hours and the number of members who spent that number of hours working on project P yesterday. What was the median number of hours that the members of the task force spent working on project P yesterday?

A. 2
B. 3
C. 4
D. 5
E. 6

(Please find attached file to view the graph)

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Source: Beat The GMAT — Problem Solving | Sat Jul 19, 2008 6:32 am

pepeprepa: Legendary Member; Posts: 661; Joined: Tue Jul 08, 2008 12:58 pm; Location: France; Thanked: 48 times

by pepeprepa » Sat Jul 19, 2008 7:26 am

Sometimes it is better not to think too much about the utility of a question.

We know the number of the set is odd (35).
Thanks to the graph we have the number of hours work for each of the 35 workers
1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 3, 4, 4, 5, 6, 6, 6, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7

So take the middle one of the 35 numbers and you have your median, I mean 6.

--> E
Tell me if that's right but I think so.

zagcollins: Master | Next Rank: 500 Posts; Posts: 167; Joined: Wed Jun 11, 2008 10:58 pmFollowed by: 1 member; Thanked: 2 times

by zagcollins » Sun Jul 20, 2008 2:51 am

you're right, pepeprepa..good one...

ontherocks27: Junior | Next Rank: 30 Posts; Posts: 16; Joined: Mon Sep 01, 2008 8:13 pm; Thanked: 3 times; GMAT Score:700

by ontherocks27 » Tue May 12, 2009 7:31 pm

You can use the following approach as well:
Value Frequency Cumulative Frequency
1 9 9
2 4 13
3 1 14
4 2 16
5 1 17
6 8 25
7 10 35

So, the median will be the middle value which is 35/2 = 17.5 or which lies from 17th to 25th value if you arrange all in order.

Hence, median = 6
Ans: E

This approach can be used for all problem which require you to calculate median from a frequency distribution.

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