Solve the problem.
-The total distances (in miles) cycled by sixteen athletes in the week prior to a cycling race are shown below. Find the interquartile range.
787 644 820 676
475 603 525 663
568 693 875 501
590 460 562 490
A) 415 mi
B) 171.5 mi
C) 175 mi
D) 181.75 mi

Question

Quizplus · Accepted Answer

The interquartile range (IQR) is the difference between the third quartile (Q3) and the first quartile (Q1). First, we need to arrange the data in ascending order: 460, 475, 490, 501, 525, 562, 568, 590, 603, 644, 663, 676, 693, 787, 820, 875. With 16 data points, Q1 is the average of the 4th and 5th values (501 and 525), and Q3 is the average of the 12th and 13th values (676 and 693). Q1 = (501 + 525) / 2 = 513, Q3 = (676 + 693) / 2 = 684.5. The IQR = Q3 - Q1 = 684.5 - 513 = 171.5 mi.

Solve the Problem. -The Total Distances (In Miles) Cycled by Sixteen Athletes in Sixteen