Use Mathematics in A Range Of Contexts
Introduction
Nowadays, swimming as sport is known to everyone. Regardless of gender you have, swimming abilities of men and women are seem to be equal. Sexual differences or gender variations is not a matter of pre-existing categories with set contents, but is an interval or gap — a radical difference — between the sexes’ experiences and knowledge’s. It does not fit clearly into the dualism of nature and culture (Archer, S. 1989). Some may argue that gender have always been at the centre of various global discussions. The distinction between women and men is of great interest to researchers. Biologically speaking, women and men differ from each other. Each group has their own physical make up that is distinguishable from one another. Men are basically perceived as physically stronger and robust while women are more gentle and slender. The physical strength brought about by the anatomical characteristics of men typically becomes the basis for gender inequality. Since men are more muscular and stronger, women are put into a subordinate status. However, the essence of gender extends beyond biological evidence. Gender refers to the meanings that are attached to those differences within a culture. Sex is male and female; gender is masculinity and femininity or what it means to be a man or a woman. But in swimming, are they different? Who excel the most? Basically, this paper will be discussing the previous swimming records of both men and women from different years and location of competition. Comparison and prediction of future swimming records will be also shown in this paper.
Swimming Records of Women
In previous years, women are joining in different swimming events. These events are usually joined by different participants around the globe. As seen in figure 1, most of women participants in swimming event and considered in this paper are from DDR or the known German Democratic Republic (Deutsche Demokratische Republik). Basically from year 1966 up to year 2008, the overall women participants in swimming from DDR are 52.38%. This was also followed by participants from USA which is about 28.57%. As shown in the figure, women participants from China and Australia had only 9.52% of representatives for each.
In figure 2, the frequencies of participation of women with respect to year’s range are shown. As indicated in this figure, most women or 67% of the overall women participated in swimming competition occurred in year 1973 to 1981. There are also expressive numbers of women participants in years 1964-1972 i.e. 19%. Followed by 9% in year 1991-1999 and 5% in year 2000 up to 2008. However, in 1982 to 1990 the record shows that no women joined in any swimming event from the selected swimming records.
With regards to the swimming records of women, Figure 3 illustrates the average swimming speed of women. As the records shows, women shows expressive performance in year 1991-1999 with an average swimming speed of 120.135 seconds in 200 metres Individual Medley. As illustrated, the average swimming records of women in year 1964-1972 in 200 metres Individual Medley is 146.21, 137.028 seconds in year 1973-1981 and 128.92 for years 2000-2008. Since the selected records used in this paper indicates that no women joined in 1982-1990 swimming events, then their average swimming records for the said years is not recorded.
Men Swimming Records
Contrary to the swimming records of women, men participants in global swimming competition are usually from USA. As shown in figure, majority or 61% of the total men swimming participants are from USA. Followed by 16% from Canada. On the other hand, there are also quite good numbers of participants joined in global swimming competition from Hungary which was comprises of 10% of overall representatives around the globe. The record also shows that 7% of it are from Sweden, 3% from Finland, and another 3% from Great Britain.
Men participation in swimming competition throughout the years are expressive. As indicated from the records, 26% of overall men swimming representatives joined the competitions from years 1964-1972. Moreover, another 26% of them joined the competition in years 1973-1981. There were also 23% of men participants joined in 2000-2008 200 metres Individual Medley. 19% from 1982-1990 and 6 from 1991-1999.
As shown in figure 6, the average swimming speed of men throughout the years shows some consistency. As the year pass by, the average swimming speed of men increases. For the record, men average swimming speed for 1964-1972 was only 129.9 and now for 2000 to 2008, men speed increases to an average of 116.15 seconds in 200 metres Individual Medley.
Comparison and Prediction of Swimming Records
T-test
To determine if there are significant differences between the swimming performance of men and women throughout the years, the use of independent sample t-test was used.
Table 1. Descriptive
This table displays the number of cases, mean value, standard deviation, and standard error for the test variable(s) within categories defined by the grouping variable. Since the Independent Samples T Test procedure compares the two group means, it is useful to know what the mean values are. Basically, the mean and standard deviation results will be used in coefficient of variation analysis.
Table 2. Independent Sample T-test
Actually, the Independent-Samples T-Test procedure compares means for two groups of cases (Walpole,R.E., Myers,R.H., Myers,S.L.,& Ye. K. 2002). The mean values for the two groups are displayed in Table 1. Since the significance value for the Levene test is high (i.e. greater than 0.05), then we have to use the results that do not assume equal variances for both groups.
Basically, a low significance value for the t-test (typically less than 0.05) indicates that there is a significant difference between men and women means. Since the confidence interval for the mean difference does not contain zero, this also indicates that the difference is significant (Walpole, et al 2002). Since the computed sig. vale for gender variable with respect to their swimming speed in 200 metres Individual Medley is 0.000, then we may say that the swimming speed in 200 metres Individual Medley of men through the years is different to the speed of women.
From the series of statistical tests and analysis, it is found out that there is an existing gender-based difference in terms of swimming speed in 200 metres Individual Medley. To identify which gender dominates in terms of swimming speed, the use of coefficient of variation analysis will be considered.
Coefficient of Variation Analysis
To find if there is significant evidence that the swimming speed of men is lower than in the women, we have to compute the Coefficient of Variation of the two groups of data. Thus, , where s= sample standard deviation and is the sample mean. The details in table 1 such as mean and standard deviation was used (Walpole, et al 2002).
Computation:
Male: Female:
As shown in the computation, the male group is more variable in comparison to the female group, thus we may say that there is significant evidence that the swimming speed of men from previous years of performance is better than women. The results also show consistency which is an indication of possibilities of easy detection of the average speed of a swimmer if the competition year is given.
Linear Regression
Suppose we are trying to predict some continuous Y variable (competition years) from X (swimmers speed) and we obtain the scatter plot to the right. We wish to construct the “best fitting” prediction line which captures the linear relationship between X and Y and allows us to predict Y from a given X score (Walpole, et al 2002). We wish to form this prediction line such that we make as few prediction errors as possible. An error in prediction is defined as the difference between each subject’s actual score and the predicted Y score obtained from X via the prediction line (Walpole, et al 2002).
The regression line which minimizes errors of prediction for the whole sample will have the following formula, including a breakdown for the slope (b) and the intercept (a) (Walpole, et al 2002):
Note that the slope of the regression line is highly related to the correlation coefficient. Thus, we can obtain the prediction line from each X value via:
Furthermore, if X and Y are expressed as standard scores (i.e., we have converted raw scores for X and Y to z scores), then using a little algebraic massaging:
With this information and in order to compute the least regression line we have to use the following table and formula:
y
Years
y
Time in Seconds
xy
x2
y2
1997
129.72
259050.84
3988009
16827.2784
1992
131.35
261649.2
3968064
17252.8225
1981
131.73
260957.13
3924361
17352.7929
1980
133
263340
3920400
17689
1980
133.69
264706.2
3920400
17873.0161
1978
134.07
265190.46
3912484
17974.7649
1978
135.09
267208.02
3912484
18249.3081
1977
135.85
268575.45
3908529
18455.2225
1977
135.95
268773.15
3908529
18482.4025
1977
136.96
270769.92
3908529
18758.0416
1976
137.14
270988.64
3904576
18807.3796
1976
138.3
273280.8
3904576
19126.89
1975
138.83
274189.25
3900625
19273.7689
1974
138.97
274326.78
3896676
19312.6609
1973
140.51
277226.23
3892729
19743.0601
1973
143.01
282158.73
3892729
20451.8601
1972
143.07
282134.04
3888784
20469.0249
1967
146.1
287378.7
3869089
21345.21
1967
147.5
290132.5
3869089
21756.25
1966
147.8
290574.8
3865156
21844.84
2008
114.8
230518.4
4032064
13179.04
2007
114.98
230764.86
4028049
13220.4004
2006
115.84
232375.04
4024036
13418.9056
2003
115.94
232227.82
4012009
13442.0836
2003
116.04
232428.12
4012009
13465.2816
2003
117.52
235392.56
4012009
13810.9504
2003
117.94
236233.82
4012009
13909.8436
1994
118.16
235611.04
3976036
13961.7856
1991
119.36
237645.76
3964081
14246.8096
1989
120.11
238898.79
3956121
14426.4121
1988
120.17
238897.96
3952144
14440.8289
1987
120.56
239552.72
3948169
14534.7136
1984
121.42
240897.28
3936256
14742.8164
1986
121.42
241140.12
3944196
14742.8164
1982
122.25
242299.5
3928324
14945.0625
1981
122.78
243227.18
3924361
15074.9284
1980
123.24
244015.2
3920400
15188.0976
1979
123.29
243990.91
3916441
15200.4241
1978
125.24
247724.72
3912484
15685.0576
1977
125.31
247737.87
3908529
15702.5961
1975
126.32
249482
3900625
15956.7424
1974
126.32
249355.68
3896676
15956.7424
1974
126.8
250303.2
3896676
16078.24
1972
127.17
250779.24
3888784
16172.2089
1972
129.3
254979.6
3888784
16718.49
1970
129.3
254721
3880900
16718.49
1970
129.5
255115
3880900
16770.25
1969
129.6
255182.4
3876961
16796.16
1968
130.6
257020.8
3873024
17056.36
1967
131.3
258267.1
3869089
17239.69
1966
132.4
260298.4
3865156
17529.76
Σx=101042
Σy=6573.62
Σxy=13019694.93
Σx2=200193120
Σy2=851377.5818
The regression line formula: y= a+bx, and
Using the table and formula we have:
From the computed a and b, the regression line of the given data becomes: or simply
Let’s say, the predicted swimming speed of a swimmer in 2009 would be = 131.39 seconds in 200 metres Individual Medley.
Conclusion
From the results of analysis, we can conclude that men dominates women in 200 metres Individual Medley in terms of swimming speed throughout the years.
References:
Archer, S. (1989). Gender differences in identity development: Issues of process, domain, and timing. Journal of Adolescence, 12, 117-138.
Walpole,R.E., Myers,R.H., Myers,S.L.,and Ye. K. (2002) Probability and Statistics for Engineers and Scientists (Seventh edition), Prentice-Hall.
Credit:ivythesis.typepad.com
0 comments:
Post a Comment