Ch. 4
Which statement is TRUE if and only if events A and B are independent?
P(AB) = P(A) P(B)
Suppose the sample space S = cfw_E1, E2, E3, E4, E5, E6 and A = cfw_E1, E4.
cfw_E2, E3, E5, E6.
If a very large population consists of 40% males, what is the pr
1.
Travel and Transportation. A super-commuter is a person who
commutes to work from one large metro area to another by car, rail,
bus, or even air. Super-commuters are not necessarily elite business
travelers, but rather middle-income individuals who are
QUANTITATIVE DATA 1. 2. 3. Dot plots Stem-and-leaf displays Histograms
SAMPLE MEAN
SUMMATION NOTATION Data = cfw_ 1, 1, 2, 3, 5
x =x/n
REL. FREQ.
= freq. / N
MEDIAN Value of the middle number in an ordered set of quantitative data (or the mean of the two
Ch. 4
Which statement is TRUE if and only if events A and B are independent?
P(AB) = P(A) P(B)
Suppose the sample space S = cfw_E1, E2, E3, E4, E5, E6 and A = cfw_E1, E4.
cfw_E2, E3, E5, E6.
If a very large population consists of 40% males, what is the pr
Chapter 1
Statistics, Data, and Statistical Thinking data factual information (as measurements or statistics) used as a basis for reasoning, discussion, or calculation. statistics the science of data, involving collecting, classifying, summarizing, organi
26 Chapter 2 Tables and Graphs for Summarizing Data
Example 2.3.1 A random sample of city postal delivery routes was obtained. The number
of pieces of mail ready for delivery on each route was recorded and is given in the following
table.
669 713 715 668
30 Chapter 2 Tables and Graphs for Summarizing Data
Example 2.3.5 A random sample of four-wheeled gas-powered rotary mowers was obtained.
and the cutting width of each was measured (in cm). The data are given in the following table.
-_._._
43.8 44.6 44.8
Relative
L. siliquoidea 61 51/139 = 0.4388
P. alatus 37 0.2662
P. grandis 20 0.1439
L. complanata 7 0.0504
E. dilata 12 0.0863
Total 139 1.0000
Complete the frequency distribution, and construct a bar chart for this data.
Frequency
2.2 Bar Charts and Pie Charts 19
h as obtaincxl,
Example 2.2.2 A random samvle Of People W110 went to a Great Lakes beac w
and the destination of each is given in the following table.
M
Lake Shore Park Euclid Beach Euclid Beach Bay Beach
Ontario Beach Gla
2.3 Stem-andLeaf Plots 25
M
2.3 Stem-and-Leaf Plots
(c) Look for outliers: observations far away from the rest.
How to Create a Stem-and-Leaf Plot
To create a stem-and-leaf plot, each observation in the data set must have at least two
digits
I - . _ .I2IOI'I' ' cfw_113111312 TabIeISE-md GIraI'Phs fonI'ISuma-ierizing Data
(3100113111131 3Ifrec'11rency dlstnbutmn to Jdescrgib this data-1
-_(bJ Which brand' 15 moat ppeferred? Justify year answer. _. I . II
I_(cJ 1111131 11111511111311 of c
24 Chapter 2 Tables and Graphs for Summarizing Data
Example 2.2.8 A local bakery obtained a random sample of customers who purchased pier.
Complete the following table, and construct a pie chart for this data.
Relative
Class Hequency frequency Angle
App
13
Chapter 2 Tables and Graphs for Summarizing Data
\/_
2-2 Bar Charts and Pie Charts
. ' enc .
Tl'axurftl Surnmary measures for categorical data: frequency and relative frequ Y
- t a encies
The. followmg table summarizes the number of open contracts for
2.3 Stem-and-Leaf Plots 25
w
2-3 Stem-and-Leaf Plots
Graphical technique for describing numerical data-
Stemand-Leaf Plot h-
, - d ap lng.
1' RelatiVely new graphical precedure. Combination of sorting an gr
2. Actual data is used to create the graph-
3. C
2.3 Stem-and-Leaf Plots 29
ed or rounded.
. - be truncat
- - dlglts may
If there are two or more digits in each leaf. the lms. dollars) for police ofcers with 10
m
. d 25.74.
Example 2.3.4 A random sample of the 110le pay gbservations 25.16, 25-52: all
Ra
2.2 Bar Charts and Pie Charts 23
Pie chart: another graphical representation of a frequency distribution for categorical data.
Example 2.2.? The following pie chart shows the activities corresponding to serious injury
reports from a. hospital emergency ro
Type equation here .
A and B
Stacking three different ice-cream flavors on a
cone if there are 12 types 12 P 3 (12*11*10)
Order does
matter
A or B
Selecting three book from a stack of 10
10 C 3
A given that B has occurred
If A and B are independent
then P
Ch. 5
In a recent production of automobiles, 10% are found to have a minor engine defect. A
rental car company purchases 20 of these vehicles. What is the probability that exactly 3 of
the 20 purchased vehicles are defective?
0.1901
If a random variable (
Ch. 1
Nuclear power plants must discharge the excess heat generated in the nuclear process to
the environment. Some plants exhaust this heat to nearby water sources. There is concern
that this thermal pollution has an adverse effect on aquatic life near t
Ch. 1
Nuclear power plants must discharge the excess heat generated in the nuclear process to
the environment. Some plants exhaust this heat to nearby water sources. There is concern
that this thermal pollution has an adverse effect on aquatic life near t
Ch. 2
Class Frequency Relative Frequency
Strongly Disagree
10
0.172
Disagree
Agree 22
0.379
Strongly Agree
0.190
Total 58
1
The above frequency distribution table is a summary of responses to a customer survey.
Some of the values are purposely missing. Wh
International passengers on a commercial plane flying into Costa Rica are asked how many
days they intend to spend in the country. The pie chart above summarizes their responses.
What is the relative frequency of international passengers on this plane who
Ch. 1
Nuclear power plants must discharge the excess heat generated in the nuclear process to
the environment. Some plants exhaust this heat to nearby water sources. There is concern
that this thermal pollution has an adverse effect on aquatic life near t
Ch. 1
Nuclear power plants must discharge the excess heat generated in the nuclear process to
the environment. Some plants exhaust this heat to nearby water sources. There is concern
that this thermal pollution has an adverse effect on aquatic life near t
23 Chapter 2 Tables and Graphs for Summarizing Data
'Ixm data sets can be compared graphically using a backtoback stem-andleaf plot,
Example 2.3.3 A random sample of National Science Foundation grants made to chemists
and mathematicians was obtained. The
2.2 Bar Charts and Pie Charts 21
Bar chart: Graphical representation of a frequency distribution for categorical data.
How to Construct a Bar Chart
1. Draw a horizontal axis with equally spaced tick marks, one for each class.
2. Draw a vertical axis for t
2.3 Stem-a nd-Leaf Plots 27
Ramarks
- .- 0 stems.
1' Rule 0f thumb; try to construct a stemand-leaf 131 nth 5 2
Few than 5 too compact. More than 20.- too spread 0"
2- Ordered Stemandleaf plot: leaves in increasing 01119"
. rted.
3' Ailmtagesr each observ