Fox Module 3: Univariate displays HW


Fox Module 3: Univariate displays HW

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NEAS
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Module 3: Univariate displays

 

(The attached PDF file has better formatting.)

 

Homework assignment: stem and leaf display

 

A stem and leaf display for assault rates in the fifty U.S. states appears below. The assault rates range from 4.5% to 33.7%.

 

   4 | 568

   5 | 367

   6 |

   7 | 2

   8 | 136

   9 |

  10 | 2699

  11 | 035

  12 | 000

  13 |

  14 | 59

  15 | 1699

  16 | 1

  17 | 48

  18 | 8

  19 | 0

  20 | 14

  21 | 1

  22 |

  23 | 68

  24 | 99

  25 | 2459

  26 | 3

  27 | 69

  28 | 5

  29 | 4

  30 | 0

  31 |

  32 |

  33 | 57

 


A.   What is the median assault rate? There are 50 states, so average two points.

B.   What is the lower hinge (the 25th percentile)?

C.   What is the upper hinge (the 75th percentile)?

D.   What is the value of (HU – Median) / (Median – HL), where  HU is the upper hinge and HL is the lower hinge?

E.   This ratio indicates the skewness of the distribution. Is this distribution positively skewed or negatively skewed?

 


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jgorab17
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so the number of observations here is 50 right? so then we'd be using x(25) and x(26) but what are those numbers? i see that they both equal 15.9% but i'm not sure how you get those numbers and i think it's just because i don't know how to look at a stem and leaf plot...

 

also, how are we supposed to tell from the ratio whether this is positively or negatively skewed? i understand how we'd know that from looking at a graph but i can't find anything about a ratio...

[NEAS: The ratio uses the first and third quartiles.]

[NEAS: Positive and negative skew can sometimes be unclear. For this homework assignment, if the upper hinge minus the median is more than the median minus the lower hinge, the distribution is positively skewed; if the upper hinge minus the median is less than the median minus the lower hinge, the distribution is negatively skewed. The relevant ratio is (upper hinge - median) / (median - lower hinge). For exact analysis of skewness, we should evaluate the significance of this ratio, but that is not covered in the text.]


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