Question

A data set has 40 data points. Enter values to answer each of the questions below.

1. How many points are above the median?
2. How many points are below the first quartile?
3. How many points are in between the first and third quartiles, aka the IQR? (Interquartile range)

The reason I don't get this is because I heard that there can be an odd difference in how many points are above and below the median so I'm confused, can someone answer and provide a simple explanation??

Answer 1

20

10

20

Explanation:

Answer 2

When the number of data points is odd the formula to find the Ranking of the Median is (n+1)/2, When the number of data points is even the ranking of the Median will be the AVERAGE of n/2 + n/2 +1, where n is the number of data points.

In our case the ranking of the Median is the average (20+21)/2 = 20.5.

1- How many points are below the Median =20

Lower half = 20, Upper half = 20 & Median = 20.5 (Don't forget Median is the ranking of data points).

Again the 1st Quartile is at 10.5, so 10 data points are below the 1st Quartile

and 20 points are between Q1 & Q3