A researcher records the number of individual instruments identified by students listening to a piece of classical music.He splits the data into quartiles and reports that students correctly identified 3 instruments at the 25th percentile,5 instruments at the 50th percentile,and 8 instruments at the 75th percentile.What are the IQR and SIQR for these data?
A)the IQR is 3;the SIQR is 1.5
B)the IQR is 2;the SIQR is 1.0
C)the IQR is 5;the SIQR is 2.5
D)There is not enough information to answer this question.

Question

Quizplus · Accepted Answer

The IQR (interquartile range) is the difference between the third quartile (Q3) and the first quartile (Q1). 
Here, Q1 = 3 and Q3 = 8. So, IQR = 8-3 = 5. 
The SIQR (semi-interquartile range) is half of the IQR. So, SIQR = IQR/2 = 5/2 = 2.5. 
Thus, the correct answer is C.

A Researcher Records the Number of Individual Instruments Identified by Students