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Word Problem involving Stats

This topic has 2 expert replies and 0 member replies
MANIKAjo Newbie | Next Rank: 10 Posts Default Avatar
Joined
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Posted:
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Word Problem involving Stats

Post Mon Jul 10, 2017 4:02 am
Can anybody suggest the approach for attached question? TIA



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Matt@VeritasPrep GMAT Instructor
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Post Sun Aug 06, 2017 10:50 pm
Just reading this problem reminded me of the bad old days when I had to grade stacks of papers like these, and, well ...

‹’’›(Ͼ˳Ͽ)‹’’›

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Post Mon Jul 10, 2017 4:40 am
Quote:


Each senior in a college course wrote a thesis. The lengths, in pages, of those seniors' theses are summarized in the graph above.

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

b. What is the greatest possible number of seniors whose theses were within six pages of the median length ?
First determine the median thesis length. This seems a little tricky (since we have RANGES for the thesis lengths), but we could still list the ranges in ascending order.
We get: (0-9),(10-19),(10-19),(10-19),(10-19),(20-29),(20-29),(20-29),(20-29),(20-29),(20-29)...

Since there are 20 papers altogether (1 + 4 + 6 + 7 + 2 = 20), the median will be the mean (average) of the 10th and 11th terms.
So, the median can have several possible values.

a. What is the least possible number of seniors whose theses were within six pages of the median length?
Here's one way to minimize this value:
{2,11,11,11,11,20,20,20,20,29,29,39,39,39,39,39,39,39,49,49}
Here, the median = (29+29)/2 = 29.
So, there were only 2 theses within six pages of the median length

a. What is the greatest possible number of seniors whose theses were within six pages of the median length?
IMPORTANT: If we make the median length right in the middle of the 20-29 range, then the theses in the ranges on either side will both be within 6 pages.
Here's what I mean.
{2,19,19,19,19,20,20,20,20,20,29,30,30,30,30,30,30,30,49,49}
Here, the median = (20+29)/2 = 24.5
So, there were 17 theses within six pages of the median length

Cheers,
Brent

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