MAT 328 -- 01 Probability and Statistics I Spring 2006 Exam 1 Date: 02/24/06
Name:_____________________________________ Code | | | |
Write your full name and class code clearly in the spaces above.
Work independently. Show all necessary steps and details of your work.
75 minutes. Total score is 100. Good luck!
Answer each question on a separate paper. Please do not write your solutions on the test.
Data A: “Record High Temperatures” for the 50 states of the United States (sorted order):
100 104 105 105 105 106 107 108 109 109
110 110 110 110 110 111 111 112 112 112
112 113 113 114 114 114 114 114 115 116
116 117 117 117 118 118 118 118 118 118
119 120 120 120 120 121 122 122 127 134
1. (35 pts, 5 pts each) Frequency analysis / exploratory data analysis:
Limits Boundaries Midpoint Frequency Cumulative Frequency
99.5-104.5 102 2
104.5-109.5 107 8
109.5-114.5 112 18
114.5-119.5 117 13
119.5-124.5 122 7
124.5-129.5 127 1
129.5-134.5 132 1
(1) The above frequency distribution for Data A is obtained by using 7 classes (equal width). Complete
the remaining columns: Limits and Cumulative Frequency;
(2) Draw the frequency histogram (use boundary points);
(3) Draw the frequency polygon (use Midpoints);
(4) Draw the Ogive (i.e., cumulative frequency graph; use boundary points);
(5) Compute the Five-number summary (min, max, quartiles) and draw the Box-and-whisker diagram;
(6) Explain the distribution of data (temperatures) based on (2), (3) and (5).
(7) If the Stem-and-Leaf Display is used for this data, a reasonable choice of stems should be the first
two digits of these data values (so the stems are 10, 11, 12, and 13). Explain why.
2. (4+4+2 = 10 pts) Find the (sample) mean, variance and standard deviation for the grouped data
obtained in part (1) of above question 1 (Give the formula and data only. Do not compute the final
results). Data A is considered as a sample.
3. None
4. (20 pts, 5 pts each) In how many different ways can 4 married couples attending a concert be seated in
a row of eight seats
(1) if there are no restrictions?
(2) if each married couple is seated together?
(3) if the members of each sex are seated together?
(4) Assume the eight people are seated randomly. Compute the probability P(“each married couple is
seated together or the members of each sex are seated together”).
