When I meet other runners a commonly asked question is "How many miles do you run a week?" This is a question I have not been able to answer, I have had no way to measure and track my weekly mileage. The number of miles a runner should run is often based on the distance for which they are training. Even given those guidelines, the optimal mileage for a runner will vary with the individual. While running has health and fitness benefits, some research has suggested that there is such a thing as too much mileage. While the threshold is still not determined, the threshold is currently thought to be somewhere around or above twenty miles per week.

In October 2014 I acquired my first GPS equipped cell phone. Using the Google My Tracks app I could, for the first time, run, juggle, and track my distance. Using the data recorded by My Tracks, I can calculate my outdoor running mileage for the first 16 weeks of 2015.

Basic statistics for a single variable table one

Basic statistics for paired, correlated variables table two

Open data exploration and data analysis table three

**I. Basic statistics for a single variable**

*Course student learning outcome one: Students will be able to perform basic statistical calculations for a single variable up to and including graphical analysis, confidence intervals, hypothesis testing against an expected value, and testing two samples for a difference of means.*

Weekly mileage for the first sixteen weeks of 2015

Table One |
---|

Mileage |

0 |

12 |

4 |

2 |

3.1 |

11.2 |

4.5 |

0 |

15 |

10.4 |

13.9 |

7.2 |

11.4 |

13 |

8.3 |

6.5 |

- What level of measurement is the mileage data?
- Calculate the sample size n:_
- Calculate the minimum:_
- Calculate the first quartile Q1:_
- Calculate the median:_
- Calculate the third quartile Q3:_
- Calculate the maximum:_
- Which is the correct box and whisker plot for the data?

- Calculate the range:_
- If the data is divided into
**five**classes, calculate the width of a single class:_ -
Determine the frequency and calculate the relative frequency for the data using five classes.

Class upper limits Frequency F Rel. Freq. **Sums:**

Which is the correct**frequency**histogram?

- What is the shape of the histogram?
- Calculate the mode:_
- Calculate the mean:_
- Calculate the sample standard deviation sx:_
- Calculate the standard error SE of the sample mean:_
- Calculate the degrees of freedom:_
- Calculate t-critical for a 95% confidence level:_
- Calculate the margin of error E of the sample mean:_
- Calculate the lower bound for the 95% confidence interval for the population mean μ:_
- Calculate the upper bound for the 95% confidence interval for the population mean μ:_
- For the paired data, calculate the sample size n:_
- Calculate the slope of the linear regression for the data:_
- Calculate the y-intercept of the linear regression for the data:_
- Is the relation positive, negative, or neutral?
- Calculate the correlation coefficient r for the data:_
- Is the correlation none, weak/low, moderate, strong/high, or perfect?
- Determine the coefficient of determination:_
- Use the slope and intercept to predict the distance that I could run in two hours:_
- Use the slope and intercept to predict the time to run seven miles:_

Paired data: time in hours versus distance in miles for eighteen recent runs.

Table Two | |
---|---|

Hours | Miles |

0.95 | 4.5 |

0.94 | 5 |

0.77 | 4.7 |

1.22 | 5.4 |

1.33 | 5.2 |

2.77 | 10.5 |

0.84 | 3.3 |

1.04 | 4.9 |

0.43 | 2.3 |

1.24 | 5.8 |

1.24 | 5.6 |

0.74 | 4.1 |

1.28 | 6.8 |

0.57 | 2.6 |

0.48 | 2.6 |

0.52 | 3.2 |

0.56 | 2.6 |

0.89 | 5.1 |

**III. Open data exploration and data analysis**

*Course student learning outcome three: Students will be able to engage in data exploration and analysis using appropriate statistical techniques including numeric calculations, graphical approaches, and tests.
*

In 2014 I was aware for the first time that my weekly mileage was low for a runner. I wanted to improve my weekly mileage in 2015. The following data compares the mileage for the last 16 weeks of 2014 to the first 16 weeks of 2015.

Table Three | |
---|---|

Weekly mileage 2014 | Weekly mileage 2015 |

2.9 | 0 |

8.8 | 12 |

5.2 | 4 |

5.7 | 2 |

0 | 3.1 |

6.9 | 11.2 |

3.9 | 4.5 |

8.5 | 0 |

5.1 | 15 |

7.8 | 10.4 |

3.7 | 13.9 |

7.4 | 7.2 |

8.2 | 11.4 |

4.1 | 13 |

9.2 | 8.3 |

7.7 | 6.5 |

**Provide numeric statistical support for the answers to the following questions.** Use the single blank to write up your answers to the questions including the statistical support for your answers.

- Has my weekly mileage increased from 2014 to 2015?
- Is that increase statistically significant?

*Do not simply write down any and all statistics you have ever learned. Answer the questions and then cite the specific statistic, statistics, or charts that support that answer. When citing a statistic or statistics, include both the name of the statistic and the numeric value. *