The Kentucky Derby is held the first Saturday in May at Churchill Downs in Louis
ID: 3244881 • Letter: T
Question
The Kentucky Derby is held the first Saturday in May at Churchill Downs in Louisville, Kentucky. The race track is one and one-quarter miles. The following table shows the winners since 1990, their margin of victory, the winning time, and the payoff on a $2 bet.
Year Winner Winning Margin
(lengths) Winning Time
(minutes) Payoff on a
$2 Win Bet
1990 Unbridled 3.5 2.03333 10.80
1991 Strike the Gold 1.75 2.05000 4.80
1992 Lil E. Tee 1 2.05000 16.80
1993 Sea Hero 2.5 2.04000 12.90
1994 Go For Gin 2 2.06000 9.10
1995 Thunder Gulch 2.25 2.02000 24.50
1996 Grindstone nose 2.01667 5.90
1997 Silver Charm head 2.04000 4.00
1998 Real Quiet 0.5 2.03667 8.40
1999 Charismatic neck 2.05333 31.30
2000 Fusaichi Pegasus 1.5 2.02000 2.30
2001 Monarchos 4.75 1.99950 10.50
2002 War Emblem 4 2.01883 20.50
2003 Funny Cide 1.75 2.01983 12.80
2004 Smarty Jones 2.75 2.06767 4.10
2005 Giacomo 0.5 2.04583 50.30
2006 Barbaro 6.5 2.02267 6.10
2007 Street Sense 2.25 2.03617 4.90
2008 Big Brown 4.75 2.03033 6.80
2009 Mine That Bird 6.75 2.04433 103.20
2010 Super Saver 2.50 2.07417 18.00
2011 Animal Kingdom 2.75 2.034 43.80
Determine the mean and median for the variables winning time and payoff on a $2 bet. (Round your answers to 2 decimal places.)
Variables
winning time Payoff
Mean $ $
Median $ $
(b)
Determine the range and standard deviation of the variables time and payoff from the above sample data.(Round your answers to 2 decimal places.)
Variables
time Payoff
Range $ $
Standard deviation $ $
(c-1)
Refer to the variable winning margin. What is the level of measurement?
Ordinal
Ratio
Nominal
Interval
(c-2)
What measure of location would be most appropriate for Winning Margin?
Mode
Mean
Median
Explanation / Answer
A. Find mean:
To do this just find the average for each (winning time and payoff). add up all the winning times and divide by the total amount of times. Same for payoff
winning time mean : 38.66834/19 = 2.03517
payoff mean : 246.8/19 = 12.99
B. Find Range and Standard Deviation
Range is the difference between the highest and lowest values in the set
Winning time range : Highest=2.06667 Low=1.99667
2.06667 - 1.99667 = 0.07 <---Answer
Payoff time range : Highest=50.30 Low=2.30
50.30 - 2.30 = 48 <----Answer
Standard Deviation:
Variance and Standard Deviation: Step by Step
1. Calculate the mean, x. (Already done)
2. Write a table that subtracts the mean from each observed value.
3. Square each of the differences.
4. Add this column together to get the total.
5. Divide by n -1 where n is the number of items in the sample This is the variance.
(n=19, so you would divide by 18)
6. To get the standard deviation we take the square root of the variance.
Winning time Standard Deviation:
MEAN Time step 2 Squared
1990: 2.03517 - 2.03333 = 0.00184 = 3.3856 x 10^-6
1991 2.03517 - 2.05000 = -0.01483 = 2.19929 x 10^-4
1992 2.03517 - 2.05000 =-0.01483 = 2.19929 x 10^-4
1993 2.03517 - 2.04000 = -0.004 = 1.6 x 10^-5
1994 2.03517 - 2.06000 = -0.02483 = 6.165289 x 10^-4
1995 2.03517 - 2.02000 = 0.01517 = 2.301289 x 10^-4
1996 2.03517 - 2.01667 = 0.0185 = 3.4225 x 10^-4
1997 2.03517 - 2.04000 = -0.004 = 1.6 x 10^-5
1998 2.03517 - 2.03667 = -0.0015 = 2.25 x 10^-6
1999 2.03517 - 2.05333 = -0.01816 = 3.297856 x 10^-4
2000 2.03517 - 2.02000 = 0.01517 = 2.301289 x 10^-4
2001 2.03517 - 1.99667 = 0.0385 = 0.00148225
2002 2.03517 - 2.01667 = 0.0185 = 3.4225 x 10^-4
2003 2.03517 - 2.01667 = 0.0185 = 3.4225 x 10^-4
2004 2.03517 - 2.06667 = -0.0315 = 9.9225 x 10^-4
2005 2.03517 - 2.04583 = -0.01066 = 1.136356 x 10^-4
2006 2.03517 - 2.03933 = -0.00416 = 1.73056 x 10^-5
2007 2.03517 - 2.03617 = -0.001 = 1 x 10^-6
2008 2.03517 - 2.03033 = 0.00484 = 2.34256 x 10^-5
Step 4, add total of the squared column together = 0.0033143668
Step 5, divide step 4 by n-1 which is 19-1 = 1.841315 x 10^-4
Step 6 Take square root of step 5 = .0135695 <--ANSWER of winning time
Payoff Standard Deviation: (mean = 12.99)
Going to skip and give square value...
Squared
1990 10.80 = 4.7961
1991 4.80 = 67.0761
1992 16.80 = 14.5161
1993 12.90 = .0081
1994 9.10 = 15.1321
1995 24.50 =132.4801
1996 5.90 = 50.2681
1997 4.00 = 80.8201
1998 8.40 = 21.0681
1999 31.30 = 335.2561
2000 2.30 = 892.635129
2001 10.50 = 6.2001
2002 20.50 = 56.4001
2003 12.80 = .0361 f
2004 4.10 = 79.0321
2005 50.30 = 1392.0361
2006 6.10 = 47.4721
2007 4.90 = 65.4481
2008 6.80 = 38.3161
Step 4, add total of the squared column together = 3298.996929
Step 5, divide step 4 by n-1 which is 19-1 = 183.277607
Step 6 Take square root of step 5 = 13.538006 <--ANSWER of payout
c) level of measurement Ordinal,
most appropriate measure of location would be median
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