See: Notes on Statistics

1.    In each case, describe the population, the variable being studied and the type of survey:     a.    The Head Girl interviews students at Traf to find out what types of extracurricular activities             they would like to have.     b.    Safety officers want to check how many dogs in Montreal have rabies.     c.    A teacher asks all her students to fill out a questionnaire regarding the number of hours of sleep            each one gets each week.     d.    The principal of an elementary school wants to find out how many students come to school            without eating breakfast.

2.    In a class of 20 students, the results of a Math test are as follows:    53  57  60  66  69  70  70  75  78  80  80  83  84  86  87  87  87  93  95  97     a.    Which results are in the 4th quintile?     b.    In which quintile is the results 86?     c.    Construct the box-and-whiskers plot for this distribution.     d.    What is the area of concentration of this distribution?

3.    A total of 1500 contestants appeared on the Canadian Idols show.     a.    Francis finished 54th ; what is his percentile rank?     b.    What is the percentile rank of Alison who finished 28th ?     c.    Ricky placed 855th ; what is his percentile rank?     d.    In what place is Patricia if she finished in the 44th percentile?     e.    Lily is in the 10th percentile, what is her placement?

4.    Lisa and her friends sell special T-shirts as a project for their Economics class.         Below are the number of shirts sold by each of the 24 students:     2   3   5   6   7   7   7   7   8   8   9   10   16   16   19   20   20   25   28   30   30   33   34   36      a.    How many shirts were sold by the students in the 2nd quintile?     b.    How many shirts were sold by the student in the 66th percentile?     c.    What is the percentile rank of a student who sold 7 shirts?     d.    What are the quartiles of this distribution?

5.    The Junior and Senior Basketball teams compare their results using the box-and-whiskers plot shown below:     a.    Compare the minimum, maximum, median and quartiles of each team.     b.    What can be said about the results in each “box”?     c.    What percentage of each team had 3 or more baskets? 5 or more baskets?     d.   What can be said about these two teams?

Answers 1. a.  Sample survey b.   Study c.   Census d.   Sample survey 2. a. 69, 70, 70, 75 b.  R5 = 2 c.  Q1 = 70   M = 80        Q3 = 87 d. 3rd quarter 3. a.  97  b.  99 c.   44 d.  841st            e.  1351st 4. a.    112 shirts b.   19 shirts c.  34th d.   Q1 = 7    Md = 13           Q3 = 26.5 5. a.  Jr lower than Sr  b.   Sr [4, 5] baskets       Jr [1.5 , 3] baskets c.  3 or more:      Sr 100% / Jr 25%         5 or more:      Sr 25% / Jr 1