Adata set has 24 data points. how many data points are above the median? how many data points are below the 1st quartile? how many data points are between the 1st and the 3rd quartiles, or in the interquartile range (iqr)?

Short Answers:

Question: How many points are above the median? 
12

Question: How many points are below the 1st quartile?
6

Question: How many points are between the first and third quartiles?
12



Explanations to how I got those answers:

We have 24 data points so half of them are below the median and the other half are above the median. Take half of 24 to get 24*(1/2) = 24*0.5 = 12
That's why there are 12 values above the median. 

Note: This trick only works if you have an even number of values. 



Q1 = first quartile
The first quartile is the median of set L, where L is the set of values lower than the median. We have 12 values in set L. Half of those values (6) are above Q1 and the other 6 values are below Q1. 



Q1 = first quartile
Q3 = third quartile
The interquartile range (IQR) spans from Q1 to Q3. This is exactly 50% of the distribution, or half of the values. We'll get the same answer as we did in the first part. So this is why there are 12 values between Q1 and Q3.

Are you trying to figure out the volume?