The interquartile range (IQR) is the range of the middle 50% scores in a distribution:
IQR= 75th percentile – 25th percentile
It is based on dividing a data set into quartiles. Quartiles are the values that divide scores into quarters. Q1 is the lower quartile and is the middle number between the smallest number and the median of a data set. Q2 is the middle quartile-or median. Q3 is the upper quartile and is the middle value between the median set and the highest value of a data set. The interquartile range formula is the first quartile subtracted from the third quartile
For Quiz 1, Q3 is 8 and Q1 is 6 . These are the scores:
5, 6, 7, 8, 9
If the median is 7, then Q1 is 6 (middle value between median and lowest value) and Q3 is 8 (middle value between median and highest value).
To calculate the IQR:
IQR= 8-6= 2
For Quiz 2, Q3 is 9 and Q1 is 5. These are the scores:
4, 5, 6, 7, 8, 9, 10
The median is 7. To find Q1, we’ll look at the lower half section of the distribution of scores: 4,5,6. Q 1 is the median of this section of the distribution: 5
To find Q2, we’ll look at the upper half section of the distribution of scores: 8, 9,10. Q3 is the median of this section of the distribution: 9.
To calculate the IQR, knowing Q1 and Q3:
IQR= 9-5= 4