Final answer:
The percentage of values between the first and third quartiles (Q1 and Q3) of the data set (3, 7, 8, 8, 14, 15, 20) is approximately 42.86%, considering Q1 as 7 and Q3 as 14.5 calculated from the given data.
Step-by-step explanation:
To answer the student's question regarding the percentage of values between the first and third quartiles (Q1 and Q3), we first need to identify these quartiles for the given data set (8, 7, 3, 8, 14, 15, 20). Upon arranging the data set in ascending order, it becomes (3, 7, 8, 8, 14, 15, 20). The median or Q2, which divides the data into two halves, is 8. To find Q1 (the median of the lower half), we look at the values less than the median: (3, 7, 8). Here, the median is 7. To find Q3 (the median of the upper half), we look at the values greater than the median: (8, 14, 15, 20). Here, Q3 is 14.5, which is the average of 14 and 15.
Since Q1 is 7 and Q3 is 14.5, the values between Q1 and Q3 are 8, 8, and 14. Out of the total seven data points, the percentage of values in this interquartile range is (3/7) * 100%, which equals approximately 42.86%. This portion of data represents the middle 50% of the data set in a distribution.