Statistics, Homework 2 Solutions

HOMEWORK 2 Solution 1. Create a stemplot for the heights of the students in your class using the class data sheet. I changed the measurements to inches: 2 pm class: 12pm class: 5'5" = 65” 5'0" = 60” 6'0" = 72” 5'5" = 65” 5'8" = 68” 5'8" = 68” 5'6" = 66” 5'2" =62” 6'0" =72” 6'0" =72” 5'9" = 69” 5'5" = 65” 5'11" =71” 5'7" = 67” 5'10" =70” 5'3" = 63” 5'6" = 66” 5'6" = 66” 5'8" = 68” 6'1" = 73” 6'2" = 74” 5'8" = 68” 5'10" = 70” 5'11" = 71” 5'8" = 68” 5'9" = 69” 6'0" = 72” 5'11" =71” 5'6" = 66” 5'6" = 66” 5'2" = 62” 5'10" = 70” 5'8" = 68” 5'10" = 70” 5'6" = 66” 23' --exlcude 5'7" = 67” 5'0" = 60” 5'3" = 63” 5'8" = 68” 5'11" = 71” 6 | 002233 6 | 55566666677888888899 7 | 00001111222234 5'4" = 64” 6'3" = 75” 5'7" = 67” 5'10" = 70” 5'0" = 60” 5'7" = 67” 5'3" = 63” 5'3" = 63” 5'3" = 63” 5'7" = 67” 5'11" = 71” 5'6" = 66” 5'2" = 62” 5'0" = 60” 5'11" = 71” 5'9" = 69” 5'5" = 65” 5'3" =63” 5'5" = 65” 5'7" = 67” 5'5" =65” 5'2" = 62” 5'4" = 64” 5'3" = 63” 5'2" = 62” 5'2" =62” 5'3" = 63” 5'4" = 64” 5'7" = 67” 5'7" =67” 5'6" =65” 5'3" =63” 6'2" = 74” 5'1" = 61” 5'7" = 67” 6'0" = 72” 5'10" = 70” 5'8" = 68” 5.67' = 5’ 8” = 68” 5'11" =71” 5'11" =71” 6 | 00122223333333444 6 | 555567777777889 7 | 00111124 7|5 2. The dotplot below shows the number of hurricanes that happened each year from 1944 through 2000 as reported by Science magazine. Describe the distribution. The distribution of the number of hurrican hurricanes is unimodal and right skewed. In most of the years between 1944 and 2000 there re were 3 or less hurricanes each year. There were only 9 years in this period when 4 or more hurricanes ricanes happened in a year. The most frequent number of hurricanes in a year was 2 in this time period. There are no outliers in the distribution. 3. Would you expect the distributions of these variables to be uniform, unimodal, unimodal or bimodal? Symmetric or skewed? a. Number of times each face of a die shows in 200 tosses Uniform. Each face ace of a die has the same chance to occur. b. Weights of newborn babies born in a particular hospital over the course of a year Unimodal, symmetric. I would expect a nice bell bell-shaped curve. c. The scores on a very easy statistics quiz Unimodal, and skewed to the left. If the quiz was very easy easy, I expect that most of the studentss did very well (high scores), and a few did not do very well (low scores). d. Number of siblings of the students in this class Unimodal, and skewed to the right. Most of you, I guess guess, have one or two siblings. Some of you have no sibling, and some of you have three siblings but only a few of you have four or more siblings.. Thus, we would see a “tail” on the right. 4. A class of students ents recorded the number of years their families had each lived in their town. Here are two graphs that the students drew to summarize the data. Which graph gives a more accurate representation of the data? Why? The second one. The first graph omits from the axis the values that not occur in the data set, which distorts the shape of the distribution. For example, a student whose family had lived in their town for 37 years has lived there much longer than one who has lived there 25 years; this is evident in Graph 2, but not in Graph 1. Graph 2 shows that the distribution is strongly right skewed, with at least one outlier. 5. For the graph below, of heights of singers in a large chorus, please write a complete description of the histogram. Be sure to comment on all the important features. The most striking feature is that the distribution is bimodal, with many singers around 65 to 66 inches tall and also quite a few near 62 to 63 inches. The heights vary between 60 and 69 inches, and there are no outliers.