# What is the median in this gre question?

This is gre preparation question of data interpretation, Distribution of test score among students(Score range -> total % of students)

0-65 -> 16
65-69 -> 37
70-79 -> 25
80-89 -> 14
90-100 -> 8

Question is that

Which of the following point ranges includes the median reading test score for ninth grade students in School District X for 1993 ?

From my understanding, median is the middle value of the dataset

1,2,3,4,5 median=3
1,2,3,4,5,6 median=3.5

From this logic answers is 0-65 as 16 comes in middle (8,14,16,25,37), However that is not right, Correct answer is 65-69.

Can anyone explain to me what I am doing wrong?

You need to write down the cumulative frequencies and choose the class whose cumulative frequency just crosses $N/2$, where $N$ is the total number of observations.
$$\begin{array}{ccc} \text{Classes}&\text{Frequencies}&\text{Cumulative Frequencies}\\ 0-65 & 16 &16\\ 65-69 & 37 &16+37=53\\ 70-79 & 25 &53+25=78\\ 80-89 & 14 &78+14=92\\ 90-100 &8&92+8=100 \end{array}$$ Here $N/2=50$. That is the $50^th$ value is the median. The class $65-69$ has cumulative frequency $53>50$ and the class $0-65$ has cumulative frequency $16<50$. So the median, that is the $50^{th}$ observation lies in the class $65-69$.