Overview of statistics

1. AN OVERVIEW OF BASIC STATISTICS
Statistics being a branch of mathematics is often associated with anxiety or unease
particularly among students who fear mathematics for one reason or another. Well, if you are
one of those students then sit, relax, and read this chapter first as it will take you through a
journey in which you will discover a world of fun, excitement, vision, and creativity. With
minimum mathematical details, this chapter introduces key concepts and universal terms that
are used among statisticians and briefly discusses common statistical tools, their underlying
principles and their practical merits.
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2. Why should you learn statistics?
In the general sense, statistics is the science of dealing with variability, uncertainty, and subjectivity
to produce objective and quantitative information that can assist in making reliable decisions about
numerous situations in life. Globally, statistics is a key tool in governments and organizations
activities.
The reason we need statistics is that we are living in a world of numbers, or more precisely a world of data.
• Numbers are called data, only when they reflect information
• Data, on the other hand, are called statistics when they reflect specific or descriptive measures
of the phenomenon or the event under study
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3. What is statistics?
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Definition Source
"The mathematics of the collection, organization, and
interpretation of numerical data, especially the analysis of
population characteristics by inference from sampling."
American Heritage Dictionary®
"A branch of mathematics dealing with the collection, analysis,
interpretation, and presentation of masses of numerical data."
The Merriam-Webster’s Collegiate
Dictionary®
“The scientific application of mathematical principles to the
collection, analysis, and presentation of numerical data.”
The American Statistical
Association (ASA,
http://www.amstat.org/)
Definitions of statistics
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4. What is statistics?
“The science and art of reading, describing, and manipulating data, which represents variables so that
practical observations about a population can be made from a sample drawn from the population, and
guidelines can be established to allow making precise and accurate conclusions about a certain
process or system”
Statistics: between science and art
• Science stems from the use of mathematical concepts
• Art stems from extrapolation, interpretation, and judgment
It is well-known, statistics does not provide causes and effects;
it only yields analysis outcome based on the data used.
It is then your job to provide causes and effects.
This is where the art of reading data and interpreting the
results of the statistical analysis comes into play.
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What is statistics?
“The science and art of reading, describing, and manipulating data, which represents variables so that
practical observations about a population can be made from a sample drawn from the population, and
guidelines can be established to allow making precise and accurate conclusions about a certain
process or system”
Numbers, data and statistics
100, 140, 213, 230, 180, 211, 120, 160, 200, 110, 260, 235, 280, 180, 300
NUMBERS
Human Weight (pound):
100, 140, 213, 230, 180, 211, 120, 160, 200, 110, 260, 235, 280, 180, 300
DATA
Statistics
Mean Value = 194.6 pound
Minimum = 100 pound
Maximum = 300 pound
Range = 200 pounds
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What is statistics?
“The science and art of reading, describing, and manipulating data, which represents variables so that
practical observations about a population can be made from a sample drawn from the population, and
guidelines can be established to allow making precise and accurate conclusions about a certain
process or system”
A Constant is a parameter that does not change:
- Your social security number will not change over time
- Your birth date will not change over time
A Constant may also refer to a controlled variable:
*** If you can maintain your grade at an “A” from course to course, it becomes
a controlled variable or a constant
A Variable is a parameter that is likely to change
- Grades of different students
- Your income from one year to another
- The heights of different students in your class
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What is statistics?
“The science and art of reading, describing, and manipulating data, which represents variables so that
practical observations about a population can be made from a sample drawn from the population, and
guidelines can be established to allow making precise and accurate conclusions about a certain
process or system”
Population Sample
A population implies a totality or a complete collection of things
(all students in a college, all people in a town, all machines in a
factory, and so on)
A sample is a sub-collection of units or components selected from
a population (few students from a college, few people from a town,
and few machines from a factory, and so on)
A census is a collection of data from every member of the
population (all students’ grades, all people ages, and all machines’
efficiencies, and so on).
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Example: In a survey conducted in a community college of 5000 students, 800 students were selected randomly
and asked if they would transfer to a four-year university. Five hundred and fifty of the students said yes. Identify
the population and the sample. Describe the data set.
What is statistics?
“The science and art of reading, describing, and manipulating data, which represents variables so that
practical observations about a population can be made from a sample drawn from the population, and
guidelines can be established to allow making precise and accurate conclusions about a certain
process or system”
Solution:
• The population consists of all students in the college (5000 students)
• The sample consists of all the students who were randomly selected (800 students)
• The actual data set consists of 550 yes’s and 250’s no’s.
• 68.75% said “Yes” & 31.25% said “No”

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Working Problem 1.1:
Major television networks constantly monitor the popularity of their programs via asking
some specialized organizations such as Nielsen company to sample the preferences of
TV viewers.
(a) Suppose 1000 TV prime-time viewers selected randomly were asked if they watched a new talk-show, and 450
indicated they watched the show. Identify the population and the sample. Describe the data set.
(b) In another survey, suppose 1100 TV prime-time viewers selected randomly were asked if they watched the 2009
Super Ball on TV, and 999 indicated they watched the game. Identify the population and the sample. Describe the
data set.
What is statistics?
“The science and art of reading, describing, and manipulating data, which represents variables so that
practical observations about a population can be made from a sample drawn from the population, and
guidelines can be established to allow making precise and accurate conclusions about a certain
process or system”
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What is statistics?
“The science and art of reading, describing, and manipulating data, which represents variables so that
practical observations about a population can be made from a sample drawn from the population, and
guidelines can be established to allow making precise and accurate conclusions about a certain
process or system”
Statistic and parameter
A statistic is any statistical measure of sample data
Examples: Sample Mean value and Sample Range
A parameter is any statistical measure of population data
It can either be calculated from an entire population data or estimated from
sample data taken from a population
Examples: Population Mean value and Population Range

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Example: Decide whether the numerical values given below describe a sample statistic or a population
parameter.
(a) A sample of community college professors in the U.S.A. revealed that the average starting salary of a college
professor is $52,000 and the range of salaries is $62,000.
(b) In a college survey of all freshmen students, it was revealed that 85% of the students were fresh out of the
high school and 15% were students who graduated from high schools more than 5 years ago
“The science and art of reading, describing, and manipulating data, which represents variables so that
practical observations about a population can be made from a sample drawn from the population, and
guidelines can be established to allow making precise and accurate conclusions about a certain
process or system”
What is statistics?
Solution:
(a) The average is a sample statistic and the range is a sample statistic
(b) The proportion or percent of students is a parameter describing the population of
freshmen students

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Working Problem 1.2:
Determine whether the numerical values given below describe a sample statistic or
a population parameter.
(a) Based on monitoring all units of a product prior to shipping, a company indicates that the
percent of second-quality units is 2%
(b) New residents of an apartment complex were asked if they like the landscaping surrounding the
complex. Eighty five percent indicated that they like it.
(c) The average salary of a group of 120 employees selected randomly from different divisions of a
company was found to be $65,000
“The science and art of reading, describing, and manipulating data, which represents variables so that
practical observations about a population can be made from a sample drawn from the population, and
guidelines can be established to allow making precise and accurate conclusions about a certain
process or system”
What is statistics?

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“The science and art of reading, describing, and manipulating data, which represents variables so that
practical observations about a population can be made from a sample drawn from the population, and
guidelines can be established to allow making precise and accurate conclusions about a certain
process or system”
What is statistics?
What is the difference between precision and accuracy?
Accuracy means: all data meet a target value
Precision means: all data are very close in values
Accurate measure: A measure is said to be accurate
when the measured values are very close to a target
or an actual value.
Precise measure: A measure is said to be precise
when the measured values are close to each other.
10 10
10 10
Inaccurate/Precise Accurate/Imprecise
Inaccurate/Imprecise Accurate/Precise

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“The science and art of reading, describing, and manipulating data, which represents variables so that
practical observations about a population can be made from a sample drawn from the population, and
guidelines can be established to allow making precise and accurate conclusions about a certain
process or system”
What is statistics?
Working Problem 1.3:
Suppose a lab refrigerator holds a constant temperature of 38.0 F. A temperature
sensor is tested 10 times in the refrigerator. The temperatures from the test yield
the following values of temperatures:
38.3 37.8 36.0 38.3 38.2 37.6 38.2 38.4 37.9 38.3 39.0
Describe these values in terms of precision and accuracy and explain your answer.

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“The science and art of reading, describing, and manipulating data, which represents variables so that
practical observations about a population can be made from a sample drawn from the population, and
guidelines can be established to allow making precise and accurate conclusions about a certain
process or system”
What is statistics?
• A process implies one or more of five basic elements: machine, material, methodology, people,
and environment.
• A system is an entity that has inputs and outputs

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Education
Process
Environment
(Classroom or
Laboratory)
Methodology
(Face-to-Face,
Distance
Learning)
Machine
(Projectors &
computers)
People
(Teachers &
Students)
Material
(Books &
Notes)

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System
(A)
(Weaving Machine)Yarns Fabric
Input Output
Examples of System Data:
Inputs: Outputs:
- Fiber type - Fabric width
- Yarn strength - Fabric thickness
- Yarn diameter - Fabric weight
Output-Input Relationships

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Descriptive statistics: how to describe data
Problem: The four sets of data shown below represent student grades of four consecutive
statistics quizzes given to a class of 10 students. Describe each set of data by closely
observing it and writing your comments.
1 2 3 4 5 6 7 8 9 10
Quiz 1 90 90 90 90 90 90 90 90 90 90
Quiz 2 82 86 78 30 88 82 79 77 81 99
Quiz 3 68 90 89 71 92 95 73 75 94 66
Quiz 4 82 76 85 88 95 86 84 87 96 78
• The starting point in any statistical analysis is to read data using the language of statistics
• This language uses the so called ‘descriptive statistics’ to establish an organized and
meaningful display of data with the goal being to reduce the flood of data presented down
to few statistics that can fully describe the data

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Simple Numerical descriptive statistics
Grades 82 76 85 88 95 86 84 87 96 78
Using statistics, we can provide two types of description:
76 78 82 84 85 86 87 88 9596
(1) Data Center (e.g. Mean Value)
(2) Data Spread (Variability)
(e.g. Range)
Example:
R = 96-76 = 20
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Working Problem 1.4:
Calculate the mean and the range for the following data set of people
income ($):
20,000, 22,000 ,28,000, 30,000, 27,000, 45,000, 50,000, 60,000
Simple Numerical descriptive statistics
Working Problem 1.5:
Calculate the mean and the range for the following data set of people weight (pound)
125, 145, 160, 155, 110, 95, 175, 158
Working Problem 1.6:
Calculate the mean and the range for the following data set of people temperature (Fo)
95.5, 98.0, 99.0, 96.5, 95.0, 97.0, 96.0, 98.0
Working Problem 1.7:
Calculate the mean and range for the following data set of property taxes ($)
8100, 3500, 7000, 4200, 3000, 5000, 5100, 4000, 7500, 4800

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Histogram and frequency distribution
Observation # 1 2 3 4 5 6 7 8 9 10
Grades 75 65 90 75 90 75 65 90 75 100
A histogram or a frequency distribution is a simple x-y graph in which the horizontal x-axis
represents the values (or classes of values) of the variable and the vertical y-axis represents
the number of observations corresponding to each value (or the frequency).
0
1
2
3
4
5
65 70 75 80 85 90 95 100
Frequency
Grade

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n
Weigh
t n
Weigh
t n Weight n Weight n Weight n Weight
1 146 11 145 21 144 31 153 41 127 51 146
2 145 12 157 22 267 32 162 42 145 52 159
3 147 13 148 23 151 33 144 43 137 53 157
4 120 14 155 24 143 34 160 44 160 54 144
5 187 15 158 25 161 35 110 45 141 55 159
6 157 16 195 26 148 36 142 46 154 56 162
7 143 17 142 27 240 37 155 47 152 57 157
8 117 18 154 28 128 38 145 48 149 58 149
9 170 19 160 29 136 39 150 49 125 59 283
10 138 20 160 30 110 40 136 50 139 60 154
Typical Example of a Histogram: Data of human weight (lb) of a random sample of 60 people
The Bulk of the Data
Extreme Values: Outliers
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Key Points about Descriptive Statistics:
• Any statistical analysis should begin by performing descriptive statistics
• Descriptive statistics represent a powerful tool of data description particularly
when a large amount of data must be analyzed
•The key elements of descriptive statistics are the measures of central tendency
and the measures of variability
• Using descriptive statistics, data abnormality or data errors can be detected
even for a large amount of data
• Frequency distributions and histograms represent graphical approaches of data
description
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What is probability?
Most people use terms such as chance, likelihood, or probability to reflect the level of uncertainty
about some issues or events. Some of the common examples of using these terms are as follows:
• As you watch the news every day, you hear forecasters saying that there is a 70% chance of rain
tomorrow.
• As you plan to enter a new business, an expert in the field tells you that the probability of making a
profit in this business is only 0.4, or there is a 40% chance that you will make a profit.
• As you take a new course, you may be wondering about the likelihood of passing or failing the
course.
• Your friend is undergoing a surgery and the physician is telling him that his chance of surviving the
surgery is 95%.
• You hear it on health news all the time that a smoker has a greater chance of getting lung cancer
than a nonsmoker.
These are all expressions of probability that we often hear or read about and they can affect
our planning or intention to do or not to do things in life.

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What is a probability Value?
The general definition of probability is that it is a value between zero and one, which reveals
the relative possibility an event will occur.
• A probability of zero or close to zero implies that an event is very improbable to occur
• A probability of one or close to one gives us higher assurance that an event will occur.
• Between these two extremes, different values of probability will be expressed as a decimal
such as 0.33, 0.7, or 0.50, as a fraction such as 1/3, 7/10, or 1/2, or as a percent such as
33.33%, 70%, or 50%.
Classically, probability is defined by the ratio of the number of particular target outcomes of an
event to the number of all possible equally likely and mutually exclusive outcomes. For example,
we know that in tossing a coin, the chance of head being the outcome is 50% or, in the context
of probability, we say that the probability of head occurrence is 0.5. This value is a direct
calculation from the classic definition of probability where the total number of possible
outcomes in tossing a coin is 2 (head or tail), and the chance of head being the outcome is 1/2.
H T

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Sampling and sampling techniques
Sampling:
•Selecting a number of representative samples (say, k samples, each of size n) from a
population using a technique suitable for the population under consideration and the
purpose of testing
•Testing the samples and listing sample data
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Why Sampling?
• Population can be too immense to test
• Test can be destructive

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What are the different types of sampling?
Random
Sampling
Population Sample
Stratified
Sampling
I II
III IV
I
II
IV
III
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What are the different sources of variability?
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Working Problem 1.9:
Identify the following sources of variability as inherent or induced:
(a) If one picks any boll of cotton from the field, one will not find two cotton
fibers in this boll that are similar in length, diameter, or maturity.
Inherent ( ) Induced ( )
b. You open a box of water bottles and you find that some bottles are completely filled and some are
half-empty
Inherent ( ) Induced ( )
c. At the workplace, you find some people performing better than other people of the same
experience and background
Inherent ( ) Induced ( )
d. In a sample of natural soil aggregates taken from a certain area you find no two soil particles that
are alike in size or texture.
Inherent ( ) Induced ( )

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What are the different types of variables?
Classification by data nature or measurement
levels:
•Continuous variables
•Discrete variables
•Special variables
Classification by Information Nature:
Quantitative Variables
Qualitative Variables
Two Ways to Classify variables:
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Working Problem 1.10:
Decide whether the following variables are discrete or continuous. Explain your reasoning.
1. The weights of football players in a team:
Discrete ( ) Continuous ( )
2. The number of defects in a shipment of cellular phones:
Discrete ( ) Continuous ( )
3. The number of passing students in a course:
Discrete ( ) Continuous ( )
4. Student grades in a course:
Discrete ( ) Continuous ( )
5. The speed at which different cars run on a highway:
Discrete ( ) Continuous ( )

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What are the levels of measurements?
Nominal Measures
The Pyramid of Data Levels of Measurements
Qualitative, no magnitude, no order
(e.g. colors, genders, country name, person name)
Ordinal Measures
Zero has no numerical meaning, and meaningful order
(e.g. ranking products as 1= superior, 2= very good, 3=
good, 4= fair, 5= poor)
Interval
Measures
Zero has no numerical meaning, meaningful
order but constant incremental difference (e.g.
temperature)
Ratio
Measures
Quantitative, meaningful magnitude, zero
has numerical meaning, ratio between
numbers is meaningful, and meaningful
order (e.g. weight, and length)
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In order to avoid any confusion about what level of measurement a variable belongs to, we
should begin by addressing the following key questions (Michael Sullivan III, 2010, Statistics-
Informed Decisions Using Data, Third Edition, Prentice Hall, Pearson Education, Inc.):
• Does the variable simply categorize each individual? If so, the variable is nominal (e.g.
gender)
• Does the variable categorize and allow ranking of each value of the variable? If so, the
variable is ordinal (letter grade in your calculus class)
• Do differences in values of the variable have meaning, but a value of zero does not mean
the absence of the quantity? If so, the variable is interval (e.g. temperature).
• Do ratios of values of the variable have meaning and there is a natural zero starting point?
If so, the variable is ratio (e.g. human weight and number of hours you study every week)
Key tips to figure out the level of measurement:
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Example: What is the level of measurement for each of the following variables?
a. Your score in the first Math quiz
b. People income in a given business
c. Classification of students by gender
d. Ranking of education by K-12, community college, and four-year University
e. The number of hours you spend watching TV every week
What are the levels of measurements?
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Working Problem 1.11:
What is the level of measurement reflected by the following data?
(a) The ages of a sample of students entering first year of college:
18, 21, 19, 17, 16, 22, 21, 22, 23, 18, 18, 17, 19
(b) In a survey of 500 luxury-house owners (above $2million price), 200 were from California, 150 from New York, and 150 from
Florida.
Working Problem 1.12:
What is the level of measurement for each of the following variables?
a. Student scores in the first stat test
b. Waiting time (minutes) waiting for a school bus
c. Classification of employee by gender
d. A ranking of students as freshman, sophomore, junior, and senior
e. The weight of football players

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What is a Normal Distribution?
The normal distribution is the key to numerous Statistical Concepts
A normal data set of a variable will typically have
the following basic characteristics:
• Relatively few components or elements will exhibit low values of the variable
• Relatively few components or elements will exhibit high values of the variable
•The majority of values will be in the middle
Frequency
Characteristic value
10 20 30 40 50 60 70 80
Examples:
• People Income
• Student Grades
• People Weight
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Center Values
High Values
Low Values
Frequency
Characteristic value
Measures of Central Tendency
Measures of Data Dispersion
Mean
Mode
Median
General Features of a Normal Distribution
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Comparison of the Distributions of Area of Ceramic Tiles of Two Different Types
Type A
Type B
Frequency
AreaMean
Mode
Median
High variability
Low variability
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Example: The Areas of Two Different Types of Ceramic Tiles

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Characteristic value
Frequency
Distributions associated with Different Categories of Variables
Larger-the-Better Variables
- Students grades
- Machine efficiency
- People income
Nominal-the-Best Variables
- Thickness of wood board
- Area of ceramic tiles
- Shoe size
Smaller-the-Better Variables
- Number of defects
- Number of failing students
- Number of car accidents
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Classifying Variables by the Nature of Values:

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Working Problem 1.13:
The frequency distributions below illustrate the grades of three quizzes for students taking a
biology class. The final frequency distribution combines all the grades of the three quizzes. Describe
the students’ performances in each quiz and the overall performance of the class.
0
5
10
15
20
25
30
35
40
45
50
Percent
Quiz 1
0
5
10
15
20
25
30
35
40
Percent
Quiz 2
0
5
10
15
20
25
30
35
40
45
50
Percent
Quiz 3
0
5
10
15
20
25
Percent
All Quizzes

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40 45 50 55 60 65 70 75 80 85 90 95
50
45
40
35
30
25
20
15
10
5.0
0.0
Quiz 1
Quiz 2
Quiz 3
All Quizzes
Grades
PercentFrequency
Working Problem 1.14:
The frequency distributions shown below are the same as those in Working Problem 1.13 but
superimposed. Describe the progressive students’ performances in each quiz and the overall
performance of the class.
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Working Problem 1.15:
The frequency distribution shown below represents the average grades of the three quizzes in
Working Problems 1.13 or 1.14. Describe this distribution.
0
5
10
15
20
25
30
35
Percent
Grade Averages
Frequency Distribution of Average Grades of the Three Quizzes

44. 44
Inferential statistics: how do you estimate population parameters from sample statistics?
Population
Sample
Population Parameters
Population mean (m)
Population Mode
Population Range
Population Standard Deviation (s)
Inferential Statistics
Notes:
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Descriptive Statistics: The analysis of determining sample statistics (e.g. mean and range)
Inferential Statistics: The analysis of estimating population parameters from sample
statistics
Descriptive Statistics
Sample Statistics
Sample mean (X-bar)
Sample Mode
Sample Range
Sample Standard Deviation (s)