Throws |
---|

183 |

177 |

186 |

183 |

189 |

204 |

198 |

196 |

178 |

205 |

On Monday evening 27 September I joggled laps of the PICS track in lane four. Joggling is juggling while running. Each and every lap I counted the number of throws I made with my right hand. I also timed my laps. The first part of the midterm uses the number of right hand throws I made per lap for ten laps.

- _________ What level of measurement is the data?
- __________ Calculate the sample size n for the data.
- __________ Determine the minimum.
- __________ Determine the maximum.
- __________ Calculate the range.
- __________ Calculate the midrange.
- __________ Determine the mode.
- __________ Determine the median.
- __________ Calculate the sample mean x.
**10.27**Freebie: This is the standard deviation sx. If you obtain a different value, then you typed in the wrong data! Calculate the standard deviation sx and check for agreement. [10.2681 to four decimal places]- __________ Calculate the sample coefficient of variation CV.
- __________ If this data were to be divided into
**four**classes, what would be the width of a single class? -
Determine the frequency and calculate the relative frequency using
**four**classes. Record your results in the table provided.

Frequency table Riders CUL (cm) Frequency (f) Relative Frequency Sum: - Sketch a
**frequency**histogram chart of the data anywhere it fits, labeling your horizontal axis and vertical axis as appropriate. - ____________________ What is the shape of the distribution?
- __________ On the ninth lap I dropped my throw height down to 30 centimeters, which resulted in a 2:02 lap on which I made 178 throws from my right hand. Use the sample mean x and standard deviation sx calculated above to determine the z-score for 178 throws.
- ____________________ Is the z-score for 178 an ordinary or unusual z-score?
- __________ On the tenth lap I increased my throw height up to 50 centimeters, which resulted in a 2:54 lap on which I made 205 throws from my right hand. Use the sample mean x and standard deviation sx calculated above to determine the z-score for 205 throws.
- ____________________ Is the z-score for 205 an ordinary or unusual z-score?

For each and every lap I recorded the lap time for that lap. This section explores whether there is a relationship between my lap time and the number of throws I made from my right hand. I ran in lane four, which is 427 meters long. The times are the time for one lap. Smaller times are faster.

Time (min) | Throws |
---|---|

2.5 | 189 |

2.5 | 198 |

2.6 | 196 |

2.0 | 178 |

2.9 | 205 |

- __________ Calculate the slope of the linear regression for the data.
- __________ Calculate the y-intercept of the linear regression for the data.
- __________ Use the slope and intercept to predict the number of throws for a lap of 2.3 minutes.
- __________ Use the slope and intercept to predict the time for a lap with 185 throws.
- __________ Does the relationship appear to be linear, non-linear, or random?
- __________ Is the correlation positive, negative, or neutral?
- __________ Calculate the correlation coefficient r.
- __________ What is the strength of the correlation: strong, moderate, weak, or none?
- __________ Calculate the coefficient of determination r².
- __________ What percent of the variation in the lap time in minutes explains the variation in the number of throws?
- I can control the height I throw my tennis balls while running and juggling. The higher I throw the tennis ball, the longer the ball is in the air. I usually throw my tennis balls about 40 centimeters high. For example, when I threw the balls 50 centimeters high, I made 205 throws during a 2:54 lap (2.9 minutes). When I threw the balls lower, only 30 centimeters high, I made only 178 throws during a faster 2:02 lap (2.0 minutes). Does the correlation and coefficient of determination provide support for the theory that I can control my speed by how high I throw the tennis balls? Why or why not?