The data below represents the catch per unit effort for skipjack tuna caught by FSM owned purse seiners from 1992 to 2001. The catch per unit effort (CPUE) is the total tonnage of tuna caught divided by the total numbers of days fished and searched. In the table below 1992 is the "base year". 1992 is year 0, 1993 is year 1, 1994 is year 2, and so forth with 2001 being year 9. 2002 would be year 10 in this system.

Year | Skipjack CPUE |
---|---|

0 | 14.67 |

1 | 10.14 |

2 | 11.72 |

3 | 8.62 |

4 | 14.32 |

5 | 9.76 |

6 | 15.59 |

7 | 12.36 |

8 | 17.33 |

9 | 11.99 |

- _________ Determine the sample size
**n**for the skipjack CPUE. - _________ Calculate the sample mean for the skipjack CPUE
**x**. - _________ Determine the median for the skipjack CPUE.
- _________ Determine the mode for the skipjack CPUE.
- _________ Determine the minimum for the skipjack CPUE.
- _________ Determine the maximum for the skipjack CPUE.
- _________ Calculate the range for the skipjack CPUE.
- _________ Calculate the sample standard deviation
**sx**for the skipjack CPUE. - _________ Calculate the sample Coefficient of Variation for the skipjack CPUE.
- _________ Calculate the slope of the best fit (least squares) line for the data.
- _________ Calculate the y-intercept of the least squares line.
- _________ Is the correlation positive, negative, or neutral?
- _________ Use the equation of the best fit line to calculate the projected skipjack CPUE for 2003 (year 11 in the system used above).
- _________ Use the inverse of the best fit equation of the best fit line to calculate the expected year in which the CPUE might be expected to reach 18.
- _________ Calculate the linear correlation coefficient r for the data.
- _________ Is the correlation none, low, moderate, high, or perfect?
- _________ Calculate the coefficient of determination.
- _________ What percent of the variation in the year data explains the variation in the CPUE data?
- _________ Is there a relationship between the year and the CPUE?
- _________ The FSM purse seiner fleet is a "young" fleet. Based on the data above, are the boats and their crews becoming better purse seiners with the passing of the years?

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 | |||
---|---|---|---|

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 |