Here is the data-set:
I understand that the cum per sums all the previous data up until that point. So 153 / 1655 = 19.8%, or if looking at the cum freq a total of 328 people scored 4 or less on the vocabulary test. But how does one determine if this is the 25th percentile? At what point in the range of cum per would one know it it's the 25th percentile, 50th percentile or 75th percentile?
Please help Thank you
The first quartile is the first where the cumulated percentage exceeds 25%. (In this case , 5). The logic behind this is that if those people are ranked by score, the last guy with a score of 4 is ranked 605 (19,8%), and the last guy with a score of 5 is ranked 1005 (36,6%). Thus any guy who has rank between 19,8% and 36,6% (i.e. number 606 to 1005) has a score of 5, and so does the first quartile.
The case of the two other quartiles is similar.