4th Strat guide, Page #148 - Minor Problem types, Q #10

[sumit_vicky]

I could not understand the solution for this questions.

The question is asking for the least possible # of seniors whose thesis were within six pages of the median length.

In the solution, we are calculating the mean of the number of students.

Can someone explain:
1. Why are we calculating the mean of the number of students?
2. Why are we not using (20 + 29)/2 = 24.5 as the median length of the number of pages?

[esledge]

The median of a set of terms is just the middle term. For example, in the set {2, 5, 6, 8, 10}, which has 5 terms, the median is 6 (3rd term: both 3rd smallest and 3rd largest).

But when the set has an even number of terms, there is not a single middle term. In that case, the median is the average of the two middle terms. For example, in the set {2, 5, 6, 8, 10, 10}, which has 6 terms, the median is 7 = (6+8)/2 (average of the 3rd smallest and 3rd largest).

In this problem, 20 students completed a thesis, so the median # of pages is the average of the number of pages the 10th student and 11th student wrote (when ranked by thesis length). Both of them are in the 20-29 pages range, but we don't know exactly how many pages each wrote. For example, the median could be (20+20)/2 = 20, or (29+29)/2 = 29, or (20+29)/2 = 24.5.

[viv09]

Hi.. I am not able to understand how there are 20 students? it os not given in the question that there are 20 students.

Can someone please explain the solution in simple terms.

Thanks!

[jnelson0612]

Look at the numbers on the left side of the chart. Those indicate the number of theses in each of the categories. Thus, 0-9 pages has one thesis, 10-19 has four theses, 20-29 has six theses, and so on.

[AlexandraWnyc]

I still don't understand why we are calculating the median of the # of students and not just picking the middle term of the page lengths...aka 10-19.

[StaceyKoprince]

We really are calculating based on the page lengths. The solution doesn't calculate the mean of the # of students - there are just 20 students, period. It calculates the mean of the page lengths of the two middle papers (which is how we calculate a median when we have an even number of terms).