§Chapter 1.
1. Identify the population and sample. Determine if the relavent numerical value is a parameter or
statistic.
A) Statistic. (The 10,000 alumni is a sample.)
B) Parameter. (All assembly-line workers are accounted for.)
C) Statistic. (360 card holders is a sample.)
2. Determine if the data are qualitative or quantitative.
A) Qualitative.
B) Qualitative (They are labels).
C) Quantitative.
D) Qualitative
E) Quantitative.
3. Identify the data set’s level of measurement (nominal, ordinal, interval, ratio.)
a) Nominal.
b) Nominal.
c) Ratio.
d) Interval. (Assume Fahrenheit or Celsius).
e) Ratio.
f) Ratio. Though if it was page numbers, this could be argued to be interval.
g) Nominal.
h) Nominal.
i) Ordinal.
j) Ordinal.
k) Ratio.
l) Nominal.
m) Nominal.
n) Ratio.
o) Ordinal.
4. Identify the method of data collection that you would use to collect data for the study. (Observational study, experiment, simulation, or survey.):
a) Observational.
b) Survey.
c) Simulation.
d) Experiment.
e) Experiment.
5. Identify the sampling technique uesd (random, cluster, stratified, convenience, systematic):
a) Systematic.
b) Cluster.
c) Random, and stratified. (The strata are sex.)
d) Convenience, and cluster.
e) Random, and convenience.
f) Convenience.
g) Random, stratified.
h) Cluster.
i) Convenience.
j) Random.
§2. Descriptive statistics and graphs
1. Construct a frequency distribution, frequency histogram, relative frequency histogram, frequency
polygon, and ogive using 6 classes for the following data on the midterm scores of 50 students in a
chemistry class:
Classes
21 - 34
35 - 48
49 - 62
63 - 76
77 - 90
91 - 104
Frequency f
2
3
5
10
18
12
Midpoints
27.5
41.5
55.5
69.5
83.5
97.5
Relative Frequency
0.04
0.06
0.10
0.20
0.36
0.24
Cumulative Frequency
2
5
10
20
38
50
2. Construct a stem-and-leaf plot for the following data on the weigth of carry-on luggage, in pounds,
for 40 passengers returing from a vacation:
0
1
2
3
4
5
|
|
|
|
|
|
03
22478889
11126677899
0112223355688
12357
1
3. Use a Pareto chart to organize the following data on most likely causes to be late to work:
Cause
snoozing after alarm goes off
car trouble
too long over breakfast
late night work shift
finding the right clothes
other
Frequency
20
3
15
18
12
4
4. Find the sample mean and median of the following data on the top speeds, in miles per hour, for
Pro-stock drag racing over the past two decades.
x̄ = 195.8 miles per hour, Q2 = 196.1 miles per hour.
5. Find the mean, median, and mode (if any), of the following scores of the top ten finishers in a recent
golf tournament.
x̄ = 71, Q2 = 72, and 72 points is the mode.
P
6. Using x̄ =
x · w where x is the score and w is the percentage weight,
x̄ = (85) · (0.15) + (78 + 81 + 92) · (0.15) + (85) · (0.10) + 89 · (0.30) = 85.6
7. Using
x̄ =
P
x·f
P
f
where x is the salary and f is the frequency,
x̄ =
8. Using s =
qP
1912.5
27, 000 · 10 + 35, 000 · 25 + 47, 000 · 10 + 59, 500 · 5
=
= $38.25.
50
50
(x−µ)2
n−1
x̄ = 26.77143
and
s = 7.029631
9. Construct a box plot as well.
70
10.
72
71
70
69
73
Min
68
Q1
69
Q1
70
Q1
71
Max
73
Min
37
Q1
64
Q1
78
Q1
88
Max
100
69
68
70
71
x̄ = 75.65. Since the median is not the same as the mean, we see that the data is skewed. Furthermore, since x̄ is smaller than Q2 , the data must be skewed left (toward the lower scores.)
11. a)
1) z =
2) z =
3) 0
b)
a) z =
b) z =
c) 0
59−56
4
45−56
4
= 0.75
= −2.75
97.4−98.6
= −1.5
0.8
100.6−98.6
= 2.5
0.8