anaik100 wrote:
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?
Attachment:
3zqfi.jpg
need help in solving this.
There are total of 20 students.
1 student wrote between 0-9 pages;
4 students wrote between 10-19 pages;
6 students wrote between 20-29 pages;
7 students wrote between 30-39 pages;
2 students wrote between 40-49 pages.
As there are 20 students, then the median length would be the average of 10th and 11th students writings. Both, 10th and 11th students are in the third group, so both these student wrote between 20 and 29 pages.
We want to minimize the # of writings which fall in the range median-6 and median+6 pages. Now, if all but 10th and 11th students from 3rd group wrote 20 pages (min possible for this group) and all student from 4th group wrote 39 pages (max possible for this group) and 10th and 11th students wrote 29 pages each, then \(median=\frac{29+29}{2}=29\) and only these 2 student fall in the range \(median-6=23\) and \(median+6=35\) pages. Note that less than 2 is not possible as even if we put as far apart as possible 10th and 11th students' writings, 20 pages for 10th and 29th pages for 11th, then \(median=\frac{20+29}{2}=24.5\) and still these 2 student (at least) fall in the range \(median-6=18.5\) and \(median+6=30.5\) pages.
Answer: 2.
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