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	91:32:19	7:35
2000	92:33:07	6:07
2001	86:17:27	6:41
2002	82:05:12	7:18
2003	83:41:12	1:05
2004	83:36:05	6:13
2005	86:15:05	4:20

(a) Find the mean, median and mode of the cyclist's times. (If an answer does not exist, enter DNE.)

mean	:  :  h:m:s
median	:  :  h:m:s
mode	:  :  h:m:s

(b) Find the mean, median and mode of the cyclist's margins. (If an answer does not exist, enter DNE.)

mean	:  m:s
median	:  m:s
mode	:  m:s

Answer 1

Solution:-

We have given data as follows.

Year	Time (H:M:S)	Margin (M:S)
1999	91:32:19	7:35
2000	92:33:07	6:07
2001	86:17:27	6:41
2002	82:05:12	7:18
2003	83:41:12	1:05
2004	83:36:05	6:13
2005	86:15:05	4:20

Now we have to convert data (H:M:S) in Only Hours

Ex: 34:30:00

Formula:-

Therefore,

34:30:00 = 34.5 hours

And

We have to convert data (M:S) in only minutes

Ex: 4:15

Formula:-

Therefore,

4:15 = 4.25 minutes

Therefore above data can be written as,

Year	Time (H)	Margin (M)
1999	91.5386	7.58
2000	92.5519	6.12
2001	86.2908	6.68
2002	82.0867	7.30
2003	83.6867	1.08
2004	83.6014	6.22
2005	86.2514	4.33
Total	606.0075	39.31

a) Find mean median and mode for cyclists time:-

----->

#)mean:-

Mean= Sum (time)/Total no.of observation(n)

Mean=606.0075/7

Mean=86.5725 hours.

Mean=86:34:21 .....in(H:M:S) units

#)Median:-

Median =[ (n+1)/2]th observation ..(after data in ascending order)

...............n=total no. of observation =7

Median=[(7+1)/2]th observation

Median= 4th observation

Here, 86.2514 is the 4 th observation after data in ascending order

Therefore,

Median= 86.2514 hours.

Median =86:15:05.....in(H:M:S) units

#mode:-

Mode= mode is the value in data set which occurs frequently (more than one times)

From above dataset, there is no observation which occurs frequently.

Therefore,

Mode Doesn't exist.

Mode=DNE

b)find mean median and mode for cyclists margin.

----->

#mean:-

Mean= Sum (margin)/Total no.of observation(n)

Mean=39.31/7

Mean=5.6157 minutes.

Mean=05:37 .....in(M:S) units

#)Median:-

Median =[ (n+1)/2]th observation ..(after data in ascending order)

...............n=total no. of observation =7

Median=[(7+1)/2]th observation

Median= 4th observation

Here, 6.12 is the 4 th observation after data in ascending order

Therefore,

Median= 6.12 minutes.

Median =06:07....in(M:S) units

#mode:-

Mode= mode is the value in data set which occurs frequently (more than one times)

From above dataset, there is no observation which occurs frequently.

Therefore,

Mode Doesn't exist.

Mode=DNE

Result:-

Result:-	Time(H:M:S)	Margin(M:S)
Mean	86:34:21	05:37
Median	86:15:05	06:07
Mode	DNE	DNE