Exercises

1.

Consider the following eight variables in the Graduation Rate data of Section  1.3. Determine whether each variable is categorical or numerical. If the variable is categorical, state whether it is nominal or ordinal. If the variable is numerical, state whether it is an interval or ratio measurement.

(a)

Student

(b)

Major

(c)

Sex

(d)

Age upon entering the program

(e)

High school GPA

(f)

Did the student live in a dormitory during his/her first year in college?

(g)

College GPA after 2 years of college

(h)

Did the student graduate within 6 years of starting college?

2.

Identify the following types of data as numerical or categorical. If numerical, further classify into interval or ratio.

(a)

The scores on exam one for Stat 216 students this semester

(b)

Marital status

(c)

Annual income

(d)

Social Security Number

(e)

Cumulative GPA

3.

The following data presents the number of cases of tomato soup sold per week at a local supermarket over a period of 28 weeks:

Week	Sold	Week	Sold	Week	Sold
1	81	11	86	21	91
2	61	12	133	22	99
3	77	13	91	23	89
4	71	14	111	24	96
5	69	15	86	25	108
6	81	16	84	26	86
7	66	17	131	27	84
8	111	18	71	28	76
9	56	19	118
10	81	20	88

(a)

Construct a stem-and-leaf display of the number of cases of tomato soup sold per week. What values did you choose for your stems? How many stems do you have? Would the display look better if you had more stems? Fewer stems? How would you achieve this?

(b)

From the stem-and-leaf display, how many cases of tomato soup are most likely to be sold at any given week?

(c)

Construct a histogram of the number of cases of tomato soup sold per week. How many intervals would you choose? Write down the class boundaries for your chosen intervals.

4.

Using the Class Data of Section  1.1, consider the variable LEVEL.

(a)

Construct a bar chart for LEVEL.

(b)

Construct a pie chart for LEVEL.

5.

Consider the variable GPA in the Class Data of Section  1.1.

(a)

Compute the five-number summary.

(b)

Using the values from part (a), construct the box plot for GPA by hand.

(c)

Enter the data into your TI-83 and obtain a boxplot.

6.

The 6-year graduation rate for a random sample of 30 colleges and universities in the US is displayed in the following stem-and-leaf plot. Note that the stem unit is 10%, and the leaf unit is 1%. For example, the maximum value is 92%.

2
3	4
4	5 6 8 8 9
5	0 1 1 1 2 3 4 5 5 6 7 8 8 9
6	0 1 2 4 4 5 7
7	1 7
8
9	2

(a)

Obtain the five-number summary using 1-Var Stats on your TI-83.

(b)

Obtain a boxplot and histogram for 6-year graduation rate..

(c)

In your opinion, which of the three plots (stem-and-leaf, boxplot, histogram) best illustrates the data? Why?

7.

The following plots represent five different samples of data. For each, describe the shape.

(a)

(b)

(c)

4	5 8
5	0 1 1 2 4 5 5 6 9
6	2 4 4 5
7	1 7
8
9	2
10	5
11	0

(d)

(e)

0	4
1	8 8 9
2	1 1 1 4 6 7
3	4 5 7
4	7

8.

Consider the following (partial) Excel worksheet. Which of the columns contain categorical data?

9.

A manager of a car rental company took a random sample of 100 business days over the last fiscal year and recorded the number of cars rented per day. The frequency distribution for the data is given below.

Interval	Frequency	Relative Freq.
(20, 25]	4
(25, 30]	11
(30, 35]	23
(35, 40]	31
(40, 45]	15
(45, 50]	10
(50, 55]	6

(a)

Fill in the Relative Frequencies above.

(b)

Draw a histogram by hand, with either the frequencies or relative frequencies as the vertical axis.

(c)

What interval does the median number of car rentals per day fall into?

(d)

What percentage of business days had 30 or less car rentals?

(e)

How many business days had more than 45 car rentals?

(f)

Give an approximate value for the number of car rentals per day that would be the 95^th percentile.