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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.

Cheers!

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