jon, leroy, and simon are having a free - throw shooting contest. each boy takes six turns and records the…

jon, leroy, and simon are having a free - throw shooting contest. each boy takes six turns and records the number of free throws he makes out of 10 shots. which boys median is greatest?\njon: 4, 5, 6, 7, 8, 10\nleroy: 2, 4, 6, 8, 8, 9\nsimon: 3, 5, 5, 6, 9, 10\n\na. jon\nb. leroy\nc. simon\nd. none of the above

jon, leroy, and simon are having a free - throw shooting contest. each boy takes six turns and records the number of free throws he makes out of 10 shots. which boys median is greatest?\njon: 4, 5, 6, 7, 8, 10\nleroy: 2, 4, 6, 8, 8, 9\nsimon: 3, 5, 5, 6, 9, 10\n\na. jon\nb. leroy\nc. simon\nd. none of the above

Answer

Explanation:

Step1: Find Jon's median

Since there are 6 data - points (an even number of data - points), the median is the average of the 3rd and 4th ordered values. For Jon's data set (4,5,6,7,8,10), the 3rd value is 6 and the 4th value is 7. So, the median is (\frac{6 + 7}{2}=\frac{13}{2}=6.5).

Step2: Find Leroy's median

For Leroy's data set (2,4,6,8,8,9), with 6 data - points, the 3rd value is 6 and the 4th value is 8. So, the median is (\frac{6+8}{2}=\frac{14}{2} = 7).

Step3: Find Simon's median

For Simon's data set (3,5,5,6,9,10), with 6 data - points, the 3rd value is 5 and the 4th value is 6. So, the median is (\frac{5 + 6}{2}=\frac{11}{2}=5.5).

Step4: Compare medians

We have Jon's median (=6.5), Leroy's median (=7), and Simon's median (=5.5). Since (7>6.5>5.5), Leroy has the greatest median.

Answer:

B. Leroy