Chapter 2 Test Review
In addition to this study guide, do P.82 #’s 1, 3, & 4 and P.83 #’s 1-10
Don’t forget that you will see a small amount of chapter 1 material on this test. You may
want to look at P.45 #1
If you run into any problems and need help, email me and I will do my best to get back to
you ASAP.
1. What is the difference between qualitative data and quantitative data?
Qualitative data is data that is classified categorically, whereas quantitative data is
data that can be classified numerically and has numerical significance. Although
qualitative data can contain numbers, it has no numerical significance (i.e.; two 2star rated movies are not equivalent to one 4-star movie).
2. Classify the following as either qualitative or quantitative.
a. The number of trees on a farm
Quantitative: this represents a count of trees; you could perform numerical
calculations that would be meaningful.
b. A students ID number
Qualitative: the numbers represent the student; it would be meaningless to
perform any calculations with those numbers.
c. The classification of a book as either fiction or non-fiction
Qualitative: this is simply a classification, no numerical significance.
3. Classify the following as continuous or discrete.
a. The time it takes a runner to complete the mile
Continuous: time can be measured using parts of a minute or second
b. The number of students in statistics class
Discrete: the number of people is a count; you can’t have part of a person
c. The temperature each day of the week
Continuous: temperature can be measured using parts of a degree
4. What are the four levels of measurement?
1. Nominal: qualitative; order does not matter
2. Ordinal: qualitative; order does matter
3. Interval: quantitative; no true zero
4. Ratio: quantitative; has a true zero
5. What is the difference between a nominal and ordinal levels of measurement?
Both levels of measurement are qualitative, but the data is classified as nominal if
there is no particular order and it is classified as ordinal when there is a particular
order.
Ex. ~ Nominal; the brand of shoes (one brand does not rate higher than
antoher)
Ordinal; pain scale rating (rating from low to high)
6. What is the difference between ratio and interval levels of measurement?
Both levels of measurement are quantitative, but the data is classified as interval
when there is no true zero and it is classified as ratio when there is a true zero.
Ex. ~ Interval; the temperatures each day for a week (temperature does not
have a true zero point since 0º does not represent a state of
no heat
Ratio; the time of swimmers at a meet (time does have a true zero)
7. Determine the level of measurement that is most appropriate.
a. Rating an item on a scale of 1 to 5, where 1 is the lowest rating and 5 is the
highest rating.
Ordinal
b. Nationalities of survey respondents
Nominal
c. The years of historic events
Interval (there is no true zero – year 0 doesn’t represent the beginning of
time)
d. The average weight of each player on the football team
Ratio (weight has a true zero)
8. Give an example in which a systematic error could occur.
**Answers will vary**
When a scale reads .03 lbs with nothing on it
9. Identify the potential error as random or systematic.
a. A student records the times at a track meet
Random; the student could record the wrong number
b. Recorded times throughout the day using a watch that was 3 minutes fast
Systematic; all time recorded would have been 3 minutes fast (this could
be easily fixed by going back and changing the times if the error is found)
10. Covert the following:
7
a. Express
as a decimal and as a percent.
8
7
 .875
.875  87.5%
8
b. Express .46 as a fraction and as a percent.
46 23
.46 

.46  46%
100 50
11. A camera costs $199. How much will you pay after applying 6% tax?
Not only will you be paying for 100% of the item, but you will be paying an
additional 6%, so essentially you are paying 106% of the camera.
1.06 199  210.94
The final cost will be $210.94
12. A $45 shirt is on sale for 30% off. What is the final cost of the shirt?
Since the item is discounted, you will not be paying for 100% of the item, but
instead, (100-30)% or 70%.
.70  45  31.50
The final cost will be $31.50
13. A survey of 1235 high school students revealed that 18% have tried smoking. How
many students have tried smoking?
.18 1235  222.3
222 students have tried smoking according to this statistic
14. If Joe weighs 65% more than Mary, then Mary’s weight is what percent of Joe’s?
To figure this out, you need to set up a proportion:
1
x

 1.65 x  100  x  60.6
1.65 100
So Mary’s weight is about 60.6% of Joe’s weight
**we did not really spend time on this in class, you will not see it on your test**
15. A golfer estimates that the distance to the hole for his next shot is 58 yards. The
actual distance is 50 yards exactly. What was the absolute error? What was the
relative error?
absolute error = measured value - actual value
absolute error = 58 - 50 = 8 ; the estimate of distance was 8 yards too high
relative error =
measured value - actual value
100
actual value
relative error =
58-50
100  16 ; the estimate of distance was 16% too high
50
16. A pharmacist puts 28 pills into a prescription order that calls for 30 pills. What is
the absolute error? What is the relative error?
absolute error = measured value - actual value
absolute error = 28 - 30 = -2 ; this prescription was 2 pills short
relative error =
relative error =
measured value - actual value
100
actual value
28-30
100  .06  .067 ; the prescription is about 6.7% less
30
than it should be
17. According to a specification, the nominal length of a particular manufactured part is
5.4523 cm. Quality control randomly selects one of the parts, and four different
technicians measure its length. Their measurements are 5.3234 cm, 5.11259 cm,
5.351 cm, and 5.45 cm. Which measurement is more precise? Which is more
accurate?
The measurement of 5.11259 cm is more precise because it measures to the
nearest hundred-thousandth
The measurement of 5.45 cm is more accurate because it is closest to the true
value of 5.4523 cm
18. Humanities majors spend an average of $115 per course on books. Math majors
spend an average of $70 per course. What is the percent difference between the two
amounts relative to the amount for math majors?
compared value - reference value
relative difference =
 100
reference value
relative difference =
115 - 70
100  64.3 ; Humanities majors spend 64.3% more
70
than the amount that math majors
spend on course books
19. Suppose that the average salary of an accountant starting off is $35,000 and after 5
years it goes up to $43,000. Find the relative change.
new value - reference value
relative change =
100
reference value
relative change =
43000 - 35000
100  22.9 ; the salary 5 years after the
35000
accountant started increased
22.9%
20. The number of people that attended a show in 1998 was 3,248. The number that
attended in 2008 was 2,563. What is the relative change?
new value - reference value
relative change =
100
reference value
relative change =
2563 - 3248
100  21.1 ; the number of people that attended
3248
the 2008 show was 21.1% lower than
the number that attended in 1998
21. Suppose that the cost for a gallon of milk in 1965 was $0.69 and the cost of a gallon
of milk today is $3.69. Find the index number using 1965 as the reference value.
value
index number =
 100
reference value
index number =
3.69
100  535
.69
22. If it cost $5 to fill your tank in 1955, how much did it cost to buy the same amount
of gas in 2005? (Refer to the price index table on P.75)
price in 2005 2.31

 7.9 ; this means that the price in 2005 is 7.9 times the price
price in 1955 .291
in 1955
5  7.9  39.5 ; the same amount of gas that cost $5 in 1955 cost $39.50 in 2005
23. Suppose an actuary’s salary was $46,000 in 1980. What would the salary have to be
in 1990 to keep up with inflation?
Year 1975 1980 1985 1990 1995
CPI 53.8 82.4 107.6 130.7 152.4
CPI in 1990 130.7

 1.59 ; the average rate of inflation increased at about
CPI in 1980 82.4
159%, so an actuary that made $46,000 in 1980 would have to make
( 46000 1.59 ) $73,140 to keep up with the average rate of inflation
24. The typical single family home rose from $115,900 in 1990 to $264,600 in 2004.
Calculate the percentage rise in cost of a home from 1990 to 2004, and compare it to
the rise of inflation as measured by the CPI. (Refer to P.77 for the table)
Find the percent rise in housing:
First find the amount of rise in housing: 264600 115900  148700
Calculate the percent rise by comparing it to the original amount:
148700
 100  128.3 ; the typical single family home rose about
115900
128.3% from 1990 to 2004
Find the percent rise in the average inflation rate:
First find the amount of rise in inflation: 188.9 130.7  58.2
Calculate the percent rise by comparing it to the original amount:
58.2
100  44.5 ; the average rate of inflation from 1990 to 2004
130.7
rose about 44.5%
The cost for a typical single family home rose much faster than the average
inflation rate.