Download Page | WORKSHEET: Basics of Statistics and Polling EXERCISES

Page |1
WORKSHEET: Basics of Statistics and Polling
EXERCISES: What do you know?
1.) Tell whether each of the following is a variable (V) or a constant (C):
a.) Scores obtained on a final examination by members of a statistics class.
b.) The cost of clothing purchased each year by secretaries.
c.) The number of days in the month of June.
d.) The time it takes to do grocery shopping.
e.) The age at which one may become a voter in the United States of America.
2.) Fill in the missing word to make a true statement.
a.) _____________________________________ are measurements obtained by observation.
b.) A __________________________________ is a complete set of items.
c.) ______________________________________takes data collected from a small group and
makes predictions about a wider sample.
d.) When every member of a set has an equal chance of being selected as part of a
sample, the sample is called a ___________________ _________________________.
e.) Characteristics that vary from one individual to another are _____________________.
f.) The study that deals with methods of collecting, organizing and analyzing data is
__________________________ ______________________________.
3.) Ten employees of a department store earn the following weekly wages:
$200, $150, $160, $125, $160, $150, $180, $130, $170 $150
a.) Find the average weekly income.
b.) What is the median wage?
c.) Find the mode.
4.) Write mean, median, or mode to complete the sentence.
a.) 7, 13, 8, 5, 9, 12.
b.) 6, 2, 4, 7, 6, 3.
c.) 18, 10, 21, 17, 12.
d.) 8, 3, 9, 4, 10, 14.
e.) 13, 11, 8, 15, 9, 10.
The __________________ is 9.
The __________________ is 6.
The __________________ is 17.
The __________________ is 8.
The _________________ is 10.5.
Page |2
5.) Find the mean, the median and the mode for each set of numbers.
a.) 72, 68, 56, 65, 72, 56, 68.
b.) 13, 19, 12, 18, 24, 10.
c.) 125, 132, 120, 118, 128, 126, 120.
d.) 8, 4, 6, 4, 10, 4, 10.
6.) Find the arithmetic mean of the following numbers:
Number Frequency
32
4
36
2
38
6
40
8
7.) The salaries of thirty people are listed below.
$12,500 $23,900 $18,750 $24,000 $$14,000
$18,750 $11,570 $25,000 $ 9,200
$15,000
$24,000 $22,000 $20,500 $12,500 $17,300
$10,980 $15,550 $18,750 $18,000 $16,200
$ 8,750
$12,500 $10 980 $13,000 $19,850
$32,000 $13,000 $22,000 $35,000 $21,000
a.) Arrange the salaries in intervals and make a frequency table for the set of data.
b.) What is the mode of the salaries?
c.) What is the median salary?
d.) What is the mean salary?
Page |3
8.) Compute the range and midpoint for the following sets of scores:
a.) 24, 15, 19, 29, 24, 22
b.) 113, 98, 107, 102, 123, 110
c.) 72.9, 75.6, 74.3, 86.1, 80, 82.7
d.) 56, 72, 98, 64, 87, 91, 22
9.) Compute the standard deviations for the following sets of scores:
a.) 26, 18, 19, 29, 20, 26
b.) 111, 98, 107, 103, 126
c.) 72.9, 75.6, 74.3, 86.1, 80, 82.7
10.) On an arithmetic test the mean was 78 and the standard deviation was 8. How many
standard deviations from the mean was each of the following scores?
86
74
94
80
98
70
62
11.) _____________________________ means the proportion of the population that holds a
particular opinion.
Intensity
Distribution
Latency
12.) Which of the following is not a requirement for scientific sampling?
A. Good questions have to be presented to be sure that the way a question if asked
does not bias how it is answered.
B. Every individual has an equal chance of being selected for a survey.
C. An equal number of Republicans and Democrats must be surveyed.
13.) An unscientific survey used to gauge public opinion on issues and policies is
called a
A. deliberative poll.
B. exit poll.
C. straw poll.
D. public opinion poll.
Page |4
DAILY APPLICATIONS OF STATISTICS
14.) Shakespeare’s plays. Figure 1 is a histogram of the lengths of words used in
Shakespeare’s plays. Because there are so many words in the plays, we use a histogram of
percents.
What is the overall shape of this distribution? What does this shape say about word lengths
in Shakespeare? Do you expect other authors to have word length distributions of the same
general shape? Why?
FIGURE 1 Histogram of the lengths of words used in Shakespeare’s plays.
15.) A medical study. Data from a medical study contain values of many variables
for each of the people who were the subjects of the study. Which of the following
variables are categorical and which are quantitative?
(a) Gender (female or male)
(b) Age (years)
(c) Race (Asian, black, white, or other)
(d) Smoker (yes or no)
(e) Systolic blood pressure (millimeters of mercury)
(f) Level of calcium in the blood (micrograms per milliliter)
16.) Barry Bonds. The Major League Baseball single-season home run record is
held by Barry Bonds of the San Francisco Giants, who hit 73 in 2001. Bonds played
only 14 games in 2005 because of injuries, so let's look at his home run totals from
1986 (his first year) to 2004:
16 25 24 19 33 25 34 46 37 33 42 40 37 34 49 73 46 45 45
Bonds's record year is a high outlier. How do his career mean and median number
Page |5
of home runs change when we drop the record 73? What general fact about the
mean and median does your result illustrate?
17.) Mean or median? Which measure of center, the mean or the median, should
you use in each of the following situations?
(a) Middletown is considering imposing an income tax on citizens. The city
government wants to know the average income of citizens so that it can estimate the
total tax base.
(b) In a study of the standard of living of typical families in Middletown, a sociologist
estimates the average family income in that city.
18.) How big are soldiers' heads? The army reports that the distribution of
head circumference among male soldiers is approximately Normal with mean 22.8
inches and standard deviation 1.1 inches.
Use the 68{95{99.7 rule to answer the following questions.
(a) What percent of soldiers have head circumference greater than 23.9 inches?
(b) What percent of soldiers have head circumference between 21.7 inches and 23.9
inches?
19.) Are the data Normal? Student loans. A government report looked at the
amount borrowed for college by students who graduated in 2000 and had taken out
student loans.
The mean amount was x = $17; 776 and the standard deviation was s = $12; 034.
The quartiles were Q1 = $9900, M = $15; 532, and Q3 = $22; 500.
(a) Compare the mean x and the median M. Also compare the distances of Q1 and
Q3 from the median. Explain why both comparisons suggest that the distribution
is right-skewed.
(b) The right skew pulls the standard deviation up. So a Normal distribution with
the same mean and standard deviation would have a third quartile larger than the
actual Q3. Find the third quartile of the Normal distribution with _ = $17; 776 and
_ = $12; 034 and compare it with Q3 = $22; 500.
Page |6
20.) Treating breast cancer. The most common treatment for breast cancer
was once removal of the breast. It is now usual to remove only the tumor and
nearby lymph nodes, followed by radiation. The change in policy was due to a
large medical experiment that compared the two treatments. Each treatment was
given to a separate group of breast cancer patients, chosen at random. The patients
were closely followed to see how long they lived following surgery.
a) What are the explanatory and response variables?
b) Are they categorical or quantitative variables?
21.) Time spent studying. Do women study more than men? We asked the students in a
large firstyear college class how many minutes they studied on a typical weeknight. Here
are the responses of random samples of 30 women and 30 men from the class:
(a) Examine the data. Why are you not surprised that most responses are multiples of 10
minutes?
We eliminated one student who claimed to study 30,000 minutes per night. Are there any
other responses you consider suspicious?
(b) Make a back-to-back stemplot of these data. Report the approximate midpoints of both
groups.
Does it appear that women study more than men (or at least claim that they do)?
Page |7
22. Web Exercise
The Current Population Survey (CPS) is a nationwide survey conducted by U.S. Census
Bureau for the Bureau of Labor Statistics. Through personal and telephone interviews, the
CPS gathers comprehensive data on the employment and unemployment experiences of the
nation’s population.
1. Go to the following website: www.bls.gov/cps/home.htm. From this website, gather the
latest numbers on the following:
SEASONALLY ADJUSTED
UNEMPLOYMENT
CHANGE IN UNEMPLOYMENT RATE
RATE
CHANGE IN EMPLOYMENT
CHANGE IN CIVILIAN LABOR
CIVILIAN LABOR FORCE
EMPLOYMENT-
LEVEL
FORCE LEVEL
PARTICIPATION RATE
POPULATION RATIO
ANNUAL AVERAGES
UNEMPLOYMENT RATE
UNEMPLOYMENT LEVEL
2. Search the website to identify and document how these numbers are used – that is,
what types of decisions are made based on these numbers? Document your findings
below:
____________________________________________________________________________________
____________________________________________________________________________________
____________________________________________________________________________________
____________________________________________________________________________________
____________________________________________________________________________________
____________________________________________________________________________________
____________________________________________________________________________________