Grade: Physiotherapy

Date: April 01, 2016

## Question 1

The chart below shows the cumulative frequency distribution the maximum angle of knee deflection after a replacement of the knee cap in a group of patients.

- Calculate the quartiles and interpret them.
- Are there outliers in the sample?
- What percentage of patients have a maximum angle of knee deflection of 90 degrees?

## Question 2

The waiting times in a physiotherapy clinic of a sample of patiens are

- Calculate the mean. Is representative? Justify the answer.
- Calculate the coefficient of skewness and interpret it.
- Calculate the coefficient of kurtosis and interpret it.

Use the following sums for the calculations: $\sum x_i=385$ min, $\sum(x_i-\bar x)^2=983.75$ min$^2$, $\sum (x_i-\bar x)^3=-601.125$ min$^3$, $\sum (x_i-\bar x)^4=98369.1406$ min$^4$.

## Question 3

A study try to determine if there is relation between recovery time $Y$ (in days) of an injury and the age of the person $X$ (in years). For that purpose a sample of 15 persons with the injury was drawn with the following values:

Age (years) | Recovery time (days) |
---|---|

21 | 20 |

26 | 26 |

30 | 27 |

34 | 32 |

39 | 36 |

45 | 37 |

51 | 38 |

54 | 41 |

59 | 42 |

63 | 45 |

71 | 44 |

76 | 43 |

80 | 45 |

84 | 46 |

88 | 44 |

- Compute the regression line of the recovery time on the age. How much increase the recovery time for each year of age?
- Compute the logarithmic regression model of the recovery time on the age.
- Which of the previous models explains better the relation between the recovery time and the age? Justify the answer.
- Use the best of the previous models to predict the recovery time of a person 50 years old. Is reliable the prediction?

Use the following sums for the calculations: $\sum x_i=821$, $\sum \log(x_i)=58.7255$, $\sum y_j=566$, $\sum \log(y_j)=54.0702$, $\sum x_i^2=51703$, $\sum \log(x_i)^2=232.7697$, $\sum y_j^2=22270$, $\sum \log(y_j)^2=195.7633$, $\sum x_iy_j=33256$, $\sum x_i\log(y_j)=3026.6478$, $\sum \log(x_i)y_j=2265.458$, $\sum \log(x_i)\log(y_j)=213.1763$.