### Statistics Problem Set Aug-21-2012

1. Which of the following formulas measure symmetry of a sample data distribution?

(a)$(1/n) \sum (x-\overline{x})^2$ | (b) $ (1/n) \sum (x-\overline{x})^3$ | (c)$ (1/n) \sum (x-\overline{x})^4$ | (d.) Not listed |

2. The following were determined for a sample data: n = 10, min=-2, max= 10, sd = 3,

$\overline{x}=5$. The data is invalid since

$max > \overline{x} + (n-1) sd.$ | (b) $min < \overline{x} - (n-1) sd$ | (c) median is not specified | (d) None of the above. |

3. A sample has current mean mean 4.0 with sample size 10. If 5 is added to all sample values, the recomputed mean will :

stay the same! | (b) will increase by 5.0 | (c) will decrease by 5 | (d)will increase by 0.5 (e) None of the above |

4.A sample has current variance of 2.0 with sample size 10. If 5 is added to all sample values, the recomputed variance will :

stay the same! | (b) will increase by 5.0 | (c) will decrease by 5 | (d)will increase by 0.5 | (d) None of the above. |

5. The formula $e^{[(1/n)\sum_{i=1}^{i = n} \ln(x_i)}$ is another way of solving for the

(a) HM | (b) GM | (c) AM | (d) RMS. |

6. A new data value 2.5 is added to a sample with mean 3 and sample size 10. The recomputed mean will

increase | (b) decrease | (c) stay the same | (d) None of the above |

7. A sample has a sample size 10 and median 50, with all sample values unique. If the minimum value in the sample is removed,

the new median will

stay the same! | (b) increase | (c) decrease | (d) None of the above. |

8. Express (-1) + 2 + (-3) + 4 + (-5) + 6 in summation form with index k $ of summation varying from 1 to 6. You cannot use

a variable X as these are not stored in an a vector or array!.

9. If X = c( 4,5,6,7,8), what is the value of $\sum_{i=1}^4 (x_i)(x_{i-1})$?.

10.If X is the same above and Y= c(2,3,1,0,4) what is the value of $\sum_{i=1}^5 {(x_i -\overline{x}) (y_i-\overline{y})}$?

Solutions next week! Enjoy first solving.