v
v
4
2.10 IMPORTANT CONCEPTS AND TOOLS
2.11 KEY FORMULAS
n i
i n
i i
n n
i i
i i
3 1
1 2
2 1
2 2
2 2
1 1
X Z
Z X
Z a
bX a
b
X
Q Q
x x
n s
x x
n s
s x
x n
n X
Z 4
4 `
4 4
4 4
4 4
4
standardized variable.
93
2
2
2 2
2 2
2 2
2
m s
m s s
m s
CONCEPTS TOOLS
The variable
is called a A standardized variable
is a linear transformation of the variable
of the form with
and 1
. Using a table of standard normal curve areas and the symmetry of the normal density
function, we can determine areas under any normal curve.
Analytic study, 37 Ordinal data, 38
Boxplot, 65 Binary coding, 39
Percentiles, 61 Control chart, 90
Class boundary, 46 Qualitative variable, 38
Density histogram, 50 Class interval, 46
Quantitative variable, 38 Dot diagram, 42
Class limit, 46 Range, 63
Empirical rule, 64 Continuous variable, 40
Resistant summary measure, 59 Histogram, 46
Data, 38 Robust summary measure, 59
Modified boxplot, 67 Degrees of freedom, 63
Sample mean, 58 68 – 95 – 99.7 rule, 74
Discrete variable, 39 Sample median, 59
Stem-and-leaf diagram, 42 Enumerative study, 36
Sample quartiles, 61 Exploratory data analysis, 36
Sample variance, 63 Five-number summary, 65
Skewed data pattern, 48 Frame, 36
Standard normal distribution, 75 Frequency distribution, 41
Standardized observations, 76 Interquartile range, 64
Standardized variable, 75 Linear transformation, 75
Symmetric data pattern, 48 Lower control limit, 89
Trimmed mean, 59 Nominal data, 38
Upper control limit, 89 Normal density function, 72
Variable, 38 Normal distribution, 73
-bar chart, 91
IR Range
Max Min
1 Sample mean:
1 Sample variance:
1 1
1 Computing formula for
: 1
Standardized variable:
4 4
4 4
2.11 KEY FORMULAS
1 2
REVIEW EXERCISES
2.53
2.54
2.55
a, 2.56
2.57
2.58
2.59
, ,
, ,
,
4
Time min. Frequency
USA Today.
s x
x n
s
Minitab or similar program recommended
94
[ 0 10 8
[ 10 20 17
[ 20 30 14
[ 30 40 10
[ 40 60 11
CHAPTER 2 DESCRIBING PATTERNS IN DATA
Classify the following as enumerative or analytic studies. Justify your choice. a.
A postal employee wants to estimate the number of two-day letters, sent from the postal station, that arrive at their destination within 48 hours.
b. A manager wants to know the number of employees in her division who
were absent at least one-half day during the previous month. Refer to Exercise 2.53. For each of the studies, define the variable characteristic
of interest. If the variable is quantitative, indicate whether it is a discrete or continuous variable.
The following table gives the frequency distribution for the length of time in minutes of taxi rides originating at the local airport.
a. Complete this table by adding a relative frequency column and a density
column. b.
Using the results in part plot the density for time of ride. Comment on
the general appearance of the density histogram. Consider the statement, “The 238,544 figure for net worth is the mean, a figure
halfway between the highest and lowest amounts,” that appeared in an article in the February 19, 1996, issue of
What is wrong with this statement? Given the four observations
6 2
4 obtain the following:
a. The sample mean and median
b. using the definitional formula,
1 c.
using the computing formula see Exercise 2.28 The numbers of years of service for ten upper-level managers are
3 12
7 21
15 8
18 25
16 9
Calculate the following: a.
The sample mean b.
The sample quartiles c.
The range d.
The sample interquartile range Collect a set of data that interests
you. Try to collect 40 or more observations. The data set might be the start- ing salaries of undergraduate marketing, accounting, finance, or management
2 2
1 2
2 2
n i
i
2.60
b. 2.61
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