Question

Scores are 92, 68, 88, 96, 72, 88, 80, 64, 74, 92, 100, 84  
What is the IQR?

19

19.5

20.5

20

6

Answer 1

Answer: IQR = 19

Median:
The median is the middle number in a sorted data set and N is the total number of elements.
If N is odd then the median is a single middle number, and if N is even then the median is the average of the two middle numbers.

64,68,72,74,80,84,88,88,92,92,96,100

N=12 is even, so median is the average of the two middle numbers at position 6 and 7

We have (84 + 88) / 2 = 86

∴ Median = 86

First Quartile Q1:
Place parentheses around the numbers above and below the median.
{64,68,72,74,80,84},{88,88,92,92,96,100}

Q1 can be found by finding the median for lower half of data (left of the median)

64,68,72,74,80,84

N=6 is even, so median is the average of the two middle numbers at position 3 and 4

We have (72 + 74) / 2 = 73

∴Q1 = 73

Third Quartile Q3:
Q3 can be found by finding the median for upper half of data(right of the median)
88,88,92,92,96,100
N = 6 is even, so median is the average of the two middle numbers at position 3 and 4
We have ( 92 + 92) /2 = 92
∴Q3 = 92

Interquartile Range IQR:

IQR = Q3 – Q1 = 92 – 73 = 19