DATA:
1 student --> 0-9 pages
4 students --> 10-19 pages
6 students --> 20-29 pages
7 students --> 30-39 pages
2 students --> 40-49 pages
There are a total of 20 students.
Thus, there are a total of 20 page lengths.
The median = average of the 10th and 11th page lengths.
The 10th and 11th page length fall within the RED RANGE above.
What is the LEAST possible number of pages lengths within 6 pages of the median length?
Strategy:
Put the 10th and 11th page lengths AS CLOSE TO EACH OTHER AS POSSIBLE, with the 18 remaining page lengths AS FAR AS POSSIBLE from the 10th and 11th page lengths.
The data points could be as follows:
0, 10, 10, 10, 10, 20, 20, 20, 20, 29, 29, 39, 39, 39, 39, 39, 39, 39, 49, 49.
Here:
Median = (29+29)/2 = 29.
Only the 2 values in green are within 6 pages of the median.
Final answer: 2
What is the GREATEST possible number of pages lengths within 6 pages of the median length?
Strategy:
Put the 10th and 11th page lengths AS FAR FROM EACH OTHER AS POSSIBLE, with the 18 remaining page lengths AS CLOSE AS POSSIBLE to the 10th and 11th page lengths.
The data points could be as follows:
9, 19, 19, 19, 19, 20, 20, 20, 20, 20, 29, 30, 30, 30, 30, 30, 30, 30, 40, 40.
Here:
Median = (20+29)/2 = 24.5.
All 17 values in green are within 6 pages of the median.
Final answer: 17
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