A cyclist won a bicycle race for seven consecutive years. His \"winning\" times
ID: 3196842 • Letter: A
Question
A cyclist won a bicycle race for seven consecutive years. His "winning" times and "victory" margins (time difference of the second place finisher) are given in the figure below.
Year Time (h:m:s) Margin (m:s)
1999 91:32:18 7:35
2000 92:33:05 6:01
2001 86:17:21 6:46
2002 82:05:11 7:13
2003 83:41:11 1:05
2004 83:36:07 6:16
2005 86:15:07 4:30
(a) Find the mean, median and mode of the cyclist's times. (If an answer does not exist, enter DNE.)
mean
median
Mode
Explanation / Answer
Mean is the average of the Cyclist's Winning times. Since the times are given in h:m:s, it'll be much easier to add up the total times in seconds, minutes and then hours first.
Total in seconds = 18+5+21+11+11+7+7 = 80 seconds
Total in minutes = 32 + 33 + 17 + 5 + 41 + 36 + 15 = 169 minutes
Total in hours = 91+92+86+82+83+93+86 = 603 hours
Therefore, the total time is 603h : 169m : 80s
Let's convert the total time in terms of seconds.
603h x 3600 = 2170800 s +
169m x 60 = 10140 s +
and 80s =
Total time = 2181020s
Mean time = 2181020/ No. of years = 2181020/7 = 311,574.28s
Converting the time back into h:m:s ---->
Ans : Mean cyclist's time = 86 hours, 32 minutes, 54.28 seconds
Median :
Arranging them in ascending order : 82:05:11 , 83:36:07 , 83:41:11 , 86:15:07 , 86:17:21 , 91:32:18 , 92:33:05
The median is the middle most value of data when sorted in ascending/descending order. Since the number of terms = 7, the middle term is (7+1)/2 = 4th term
Ans : Median time = 86:15:07
c)
Mode : Mode is that value which occurs the most number of times or has the highest frequency in the data. In our case, all the 7 values are distinct and each occurs once. Therefore, all the 7 times are the mode as they all occur 1 time each.
Ans : All 7 values.
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