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HOMERUNNER
Math 120 – Elementray Statistics 1
Manju Poudel
Professor: Dr. Prabha Betne
Date: 05/22/05
Homerun
distances in
feet
McGwire (1), Sosa (2),
Bonds (3)
McGwire (1998)
Statistic
Mean
418.51
95% Confidence
Interval for Mean
Sosa (1998)
Bonds (2001)
Std. Error
Lower Bound
Upper Bound
5% Trimmed Mean
Median
Variance
Std. Deviation
Minimum
Maximum
Range
Interquartile Range
Skewness
Kurtosis
Mean
95% Confidence
Lower Bound
Interval for Mean
Upper Bound
5% Trimmed Mean
Median
Variance
Std. Deviation
Minimum
Maximum
Range
Interquartile Range
Skewness
Kurtosis
Mean
95% Confidence
Lower Bound
Interval for Mean
Upper Bound
5% Trimmed Mean
Median
Variance
Std. Deviation
Minimum
Maximum
Range
Interquartile Range
Skewness
Kurtosis
5.438
407.67
429.36
416.63
420.00
2069.732
45.494
340
550
210
70.00
.572
.146
404.85
.287
.566
4.394
396.07
413.62
403.62
410.00
1274.254
35.697
340
500
160
59.25
.361
-.123
403.67
.295
.582
3.586
396.52
410.82
404.48
410.00
938.696
30.638
320
488
168
40.00
-.408
.596
.281
.555
1. Quickly scanning the data given above, McGwire appears to be the best player
compared to the other two. But when we give deeper examination of the data, final
outcome can be completely different than what we judge roughly.
If we take mean value only, mean value of McGwire’s homerun is higher than
Sosa and Bonds. That means, he has made equal to or more than 50% runs
418.51 feet or higher. The difference between the mean distance covered by Sosa
and Bonds is minimal.
It is apparent that McGwire is ahead of the other two in average distance covered
in all of the homeruns he made. The median value of his homeruns (420) is
greater than the median values of the other two, which are exactly the same (410
each). While examining maximum distance covered in their homeruns, we find
that McGwire is far ahead of the other two. There is only a12 foot difference in
maximum distance covered by Sosa and Bonds. Compared to a 50-foot difference
between maximum distance covered by McGwire and Sosa. The difference
between distance covered by Sosa and Bonds is negligible.
When we compare minimum distance covered by all three players, McGwire and
Sosa have covered equal distance. Bonds have covered 20 foot less than the
other two.
Thus, while examining the figures given in above table, individually McGwire
appears to be strongest of three players and Bonds appears to be the weakest
one.
Nevertheless, keeping in mind that the calculation of average is very sensitive to
extreme values and noticing that McGwire’s maximum value (550) is 50 feet
higher than Sosa’s (500) and 62 feet higher than Bonds’ (488) we cannot rely on
this information alone. The median, on the other hand, being the same for Sosa
and Bonds (410) is only 10 ft less than McGwire’s, which tell us that the center of
the distances is not much different for all the players.
2. Examining all three histograms we can come to a conclusion that it is irrational to
say that player who hits farther hits more homeruns. In this scenario, Bonds (73),
who seems to be weaker in hitting farther than other two has made more
homeruns than other two (McGwire 70 and Sosa 66).
3. Standard deviation means deviation in numeric trends from mean and median or
average. When comparing standard deviation (McGwire: 45.494, Sosa: 35.697,
Bonds: 30.638) bonds seems to be more consistent in hitting homerun than other
two as standard deviation value in Bonds’ playing history is least (30.638) of all
three.
4. A quartile is one of the four divisions of observations, which have been grouped
into four equal-sized sets based on their statistical rank. So, Q1 should be mean
of all data above mean and Q2 should be mean of all data below mean. In this
problem, quartiles are not given but interruptible ranges (that could be calculated if
Q1 and Q2 were available) are given. Thus, instead of compare quartiles, we can
compare only IQR. The IQR is a measure of spread or dispersion. In our case,
IQR of Bonds (40) is much less than of the McGwire (70) and Sosa (59.25). This
also shows consistency in Bonds’ homerun hitting pattern. Sosa appears to be
more consistent than McGwire.
5. Looking at histogram of all three players, we can find that McGwire’s histogram is
more spread than other two. This shows that he hits long inconsistent long
distances most frequently whilst Sosa hit 420 to 430 feet most frequently than
others and Bonds hits 410 to 440 feet most frequently. It shows that Bonds makes
more calculated hits that help him to hit homeruns. We could conclude that
McGwire is a more unpredictable player, hit haphazard long distances capable of
hitting less homeruns (less than 15) in more variable distances. Although he hit
more long distances, he has less chances of hitting homeruns compared to
Bonds.
Histogram
For PLAYER= McGwire (1998)
20
15
Frequency
10
5
Std. Dev = 45.49
Mean = 418.5
N = 70.00
0
330.0
370.0
350.0
410.0
390.0
450.0
430.0
Homerun distances in feet
490.0
470.0
530.0
510.0
550.0
Histogram
For PLAYER= Sosa (1998)
20
Frequency
10
Std. Dev = 35.70
Mean = 404.8
N = 66.00
0
330.0
370.0
350.0
410.0
390.0
450.0
430.0
490.0
470.0
530.0
510.0
550.0
Homerun distances in feet
Histogram
For PLAYER= Bonds (2001)
30
Frequency
20
10
Std. Dev = 30.64
Mean = 403.7
N = 73.00
0
330.0
370.0
350.0
410.0
390.0
450.0
430.0
490.0
470.0
530.0
510.0
550.0
Homerun distances in feet
6. Comparing box plots we can concludes that standard deviation of Bonds’ hits is
less than other two. He has fixed range of distance of hitting. That may give room
for opponents for prediction that can case reduction of homeruns, though he is
highest home runner. McGwire appears unpredictable as his standard deviation is
high and Sosa remains between McGwire and Bonds in predictability of pattern of
hitting long distance.
7. Based on statistical data given, we can conclude that Bonds is more consistent,
predictable and capable of hitting more homeruns than others. McGwire is
versatile, unpredictable and relatively good homerun hitter. Sosa is relatively
consistent, predictable and above the average players. Looking at the number of
homeruns McGwire hit, we can say that his unpredictability is probably the
greatest strength of him whilst predictability and consistency are Bonds’ strength.
600
500
197
400
177
169
300
N=
70
66
73
McGw ire (1998)
Sosa (1998)
Bonds (2001)
McGwire (1), Sosa (2), Bonds (3)