R code for importing data and calculating its properties (R statistical Programming)
xdata= read.table("athletes.csv", header =T, sep = ",", row.names = 1);x=xdata[,1] # import
median(x); mean(x); sd(x); range(x); var(x); hist(x, col="blue") # Calculations
[1] 100, [1] 100, [1] 17.84985, [1] 70 130, [1] 318.6172 #Output
Frequency distribution R code
b.break=seq(70,130,2); x.cut = cut(x, b.break, right=F); x.freq = table(x.cut); x.freq
Figure 3: Frequency Distribution table
Since the number of sample observations is sufficiently large, we are going to assume that they are normally distributed and plot the data using the R code below.
x ; y=dnorm(x,100,10); plot(x, y, type="l", lwd=2,col="red");
Figure 4: A normal plot for the data
R code for evaluating the proportion of data within 1, 2 and 3 standard deviations of mean
pnorm(110,100,10)- pnorm(90,100,10); pnorm(120,100,10)-pnorm(80,100,10); pnorm(130,100,10) - pnorm(70, 100, 10)
[1] 0.6826895, [1] 0.9544997,[1] 0.9973002
Conclusion
The results of the analysis above indicates that the median duration of time taken to complete a race by athletes is 100 seconds, the sample mean is 100 seconds, the sample standard deviation is 17.84985 seconds, the range of the data is (70,130), and the sample variance is 318.6172 seconds.
The sample standard deviation is substantially large, hence indicating a larger discrepancy in the race performance index. Since the mean is same as the median, it is likely to have frequencies symmetrical to the mean. Furthermore, the histogram above suggests a normal distribution of the data.
Analytically, 68.3% of data is contained within one standard deviation of mean, 95% of data is contained within two standard deviations of the mean, and 99.7% of data is contained within three standard deviations of the mean. These results indicates that the histogram of the duration taken by athletes to complete the race is approximately bell shaped, since 68.3% of data is within the one standard deviation of mean and the rest 43.7% of data is spread away from the mean.
In general, the mean performance index for most 1500m athletes in Tshwane University which is 100 seconds doesn’t depict an excellent performance. Thus efforts should be made to improve the performance of athletics in Tshwane University. For instance, there should be more rigorous training especially in the regions of high altitude like the near the Cape Ranges Region. Consequently, Athletes’ strength and haemoglobin count will improve leading to a normal curve that is skewed to the left since more athletes shall complete their races quicker.
Reference
Tshwane University (2010). Athletics data: 1500 m race. South Africa, CA: Durban
