PS query

[prernamalhotra]

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

a) What is the least possible no. of seniors whose thesis were within 6 pages of the median length?
b) What is the greatest possible no. of seniors whose thesis were within 6 pages of the median length?


Regards,
Prerna

[Tushar14]

Hi Prerna,
So, total number of students = 20
The median length would be the average of 10th and 11th students writings, as they fall under 3rd group so median would be 20-29 pages.

1) Minimum which fall in the range median-6 and median+6 pages.Median here would be the mean values of 10th & 11...To minimize move the students away from the median.
0 10 10 10 10 20 20 20 20 29 29 39 39 39 39 39 39 39 49 49 So as the median is 10th & 11th which is 29 and range would be 23 - 35 so only 2 can satisfy statement 1. (Answer = 2)

2) Maximum which fall in the range median-6 and median+6 pages.Lets try to get everyone close to get the max numbers...
9 19 19 19 19 24 24 24 24 24 24 30 30 30 30 30 30 30 40 40 So median again would be 10th & 11th which is 24 and range would be 18 - 30 so max number which could satisfy statement 2 is 17. (Answer = 17)

I hope you got it...

Regards,
Tushar

[Tushar14]

Hi Prerna,
Just to add and simplify, the strength is 20 which is even so median would be (n + 1)/2 so 21/2 = 10.5 and 10th and 11th became the median.
1) Calculating least within the range try to set all apart from the median.
2) Calculating maximum within the range try to set all closer towards the median.

Regards,
Tushar

[Brent@GMATPrepNow]

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