Question

The scores of a group of students on a 10-point multiple choice placement test are shown below. The third quartile on the test is ____.

3, 3, 3, 3, 3, 4, 4, 4, 5, 5, 5, 5, 5, 6, 6, 7, 7, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8, 8, 9, 10

A: 7
B: 6.5
C: 8
D: 7.5
E: None

Answer 1

C: 8

The best way to do this is to first find the median of your data. In this case, you have 30 data points (it's even), so you split the upper and lower 15 of your points, and chose the arithmetic average of the two data points where you did the split (here you split your data at 6 and 7, so median = 6.5)

Now, to find the 3rd quartile is basically finding the mean of the upper portion of data points. So,
1) ignore the median from this set
2) find the new median of these points. Now you have 15 points (which is odd), so you select the middle value exactly. In this case, it's 8 (and there are 7 points above and below the 8)

Answer 2

8, I think. Look at calculator at
http://easycalculation.com/statistics/box-plot-grapher.php