Between 21 July to 01 August the Fifth Micronesian Games 2002 will convene on Pohnpei. The games will include distance running such as the half-marathon. Distance runners have to pace themselves in order to win. If they run too fast they will tire and be unable to finish the race. If they run too slow they will not run the fastest race they could and will probably lose. They have to run exactly as fast as their maximum sustainable effort for the distance. As a result runners carefully track their running times and their pace. They also strive for consistency in pace. Below are the times for Lee Ling's most recent ten runs from the College to his home in Dolihner, a distance of about six miles. The times are in minutes.
Duration of run in minutes | |
---|---|
54.00 | 63.00 |
54.64 | 63.93 |
57.35 | 64.17 |
58.00 | 70.00 |
62.62 | 74.00 |
Bins | Frequency | Relative Frequency f/n |
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The table below is a distance versus time table for a single run from the College to Dolihner.
Location | Time in min | Distance in km |
---|---|---|
College | 0.0 | 0.0 |
Dolon pass | 18.2 | 3.3 |
West Bridge (Pent) | 24.9 | 4.6 |
East Bridge (SSC) | 30.0 | 5.6 |
Sokehs Island Jxn | 47.2 | 8.6 |
Dolihner | 54.o | 9.7 |
Basic Statistics | |||
---|---|---|---|
Statistic or Parameter | Symbol | Equations | Excel |
Square root | =SQRT(number) | ||
Sample size | n | =COUNT(data) | |
Sample mean | x | Sx/n | =AVERAGE(data) |
Sample standard deviation | sx or s | =STDEV(data) | |
Sample Coefficient of Variation | CV | 100(sx/x) | =100*STDEV(data)/AVERAGE(data) |
Linear Regression Statistics | |||
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Statistic or Parameter | Symbol | Equations | Excel |
Slope | b | =SLOPE(y data, x data) | |
Intercept | a | =INTERCEPT(y data, x data) | |
Correlation | r | =CORREL(y data, x data) | |
Coefficient of Determination | r^{2} | =(CORREL(y data, x data))^2 |
Statistic or Parameter | Symbol | Equations | Excel |
---|---|---|---|
Normal Statistics | |||
Calculate a z value from an x | z | ^{= } | =STANDARDIZE(x, µ, s) |
Calculate an x value from a z | x | = s z + µ | =s*z+µ |
Calculate a z-statistic from an x | z | =(x - µ)/(sx/SQRT(n)) | |
Calculate a t-statistic (t-stat) | t | =(x - µ)/(sx/SQRT(n)) | |
Calculate an x from a z | =µ + z_{c}*sx/sqrt(n) | ||
Find a probability p from a z value | =NORMSDIST(z) | ||
Find a z value from a probability p | =NORMSINV(p) | ||
Confidence interval statistics | |||
Degrees of freedom | df | = n-1 | =COUNT(data)-1 |
Find a z_{c} value from a confidence level c | z_{c} | =ABS(NORMSINV((1-c)/2)) | |
Find a t_{c} value from a confidence level c | t_{c} | =TINV(1-c,df) | |
Calculate an error tolerance E of a mean for n >= 30 using sx | E | =z_{c}*sx/SQRT(n) | |
Calculate an error tolerance E of a mean for n < 30 using sx. Can also be used for n >= 30. | E | =t_{c}*sx/SQRT(n) | |
Calculate a confidence interval for a population mean µ from a sample mean x and an error tolerance E | x-E<= µ <=x+E | ||
Hypothesis Testing | |||
Calculate t-critical for a two-tailed test | t_{c} | =TINV(a,df) | |
Calculate a p-value from a t-statistic | p | = TDIST(ABS(tstat),df,#tails) |