SlideShare a Scribd company logo
1 of 68
Note: Most of the Slides were taken from
Elementary Statistics: A Handbook of Slide
Presentation prepared by Z.V.J. Albacea, C.E.
Reano, R.V. Collado, L.N. Comia and N.A.
Tandang in 2005 for the Institute of Statistics,
CAS, UP Los Banos
Training on Teaching
Basic Statistics for
Tertiary Level Teachers
Summer 2008
INTRODUCTION TO
STATISTICS AND
STATISTICAL
INFERENCE
Session 1.2
TEACHING BASIC STATISTICS ….
Florence Nightingale on Statistics
 “...the most important science in the whole
world: for upon it depends the practical
application of every other science and of every
art: the one science essential to all political
and social administration, all education, all
organization based on experience, for it only
gives results of our experience.”
 “To understand God's thoughts, we must study
statistics, for these are the measures of His
purpose.”
Session 1.3
TEACHING BASIC STATISTICS ….
Realities about Statistics
 The man in the street distrusts statistics and
despises [his image of] statisticians, those who
diligently collect irrelevant facts and figures and
use them to manipulate society.
“There are three kinds of lies: lies, damned lies, and
statistics” – Mark Twaine
 One can not go about without statistics.
“Statistics are like bikinis. What they reveal is suggestive,
but what they conceal is vital.” – Aaron Levenstein
Session 1.4
TEACHING BASIC STATISTICS ….
Definition of Statistics
plural sense: numerical facts, e.g. CPI,
peso-dollar exchange rate
singular sense: scientific discipline
consisting of theory and methods for
processing numerical information
that one can use when making
decisions in the face of uncertainty.
Session 1.5
TEACHING BASIC STATISTICS ….
History of Statistics
 The term statistics came from the Latin phrase
“ratio status” which means study of practical
politics or the statesman’s art.
 In the middle of 18th
century, the term statistik
(a term due to Achenwall) was used, a German
term defined as “the political science of several
countries”
 From statistik it became statistics defined as a
statement in figures and facts of the present
condition of a state.
Session 1.6
TEACHING BASIC STATISTICS ….
Application of Statistics
 Diverse applications
“During the 20th Century statistical thinking
and methodology have become the
scientific framework for literally dozens of
fields including education, agriculture,
economics, biology, and medicine, and with
increasing influence recently on the hard
sciences such as astronomy, geology, and
physics. In other words, we have grown
from a small obscure field into a big obscure
field.” – Brad Efron
Session 1.7
TEACHING BASIC STATISTICS ….
Application of Statistics
 Comparing the effects of five kinds of
fertilizers on the yield of a particular
variety of corn
 Determining the income distribution of
Filipino families
 Comparing the effectiveness of two diet
programs
 Prediction of daily temperatures
 Evaluation of student performance
Session 1.8
TEACHING BASIC STATISTICS ….
Two Aims of Statistics
Statistics aims to uncover
structure in data, to explain
variation…
 Descriptive
 Inferential
Session 1.9
TEACHING BASIC STATISTICS ….
Areas of Statistics
Descriptive statistics
 methods concerned w/
collecting, describing, and
analyzing a set of data
without drawing
conclusions (or inferences)
about a large group
Inferential statistics
 methods concerned
with the analysis of a
subset of data leading
to predictions or
inferences about the
entire set of data
Session 1.10
TEACHING BASIC STATISTICS ….
Example of Descriptive Statistics
Present the Philippine population by constructing a
graph indicating the total number of Filipinos counted
during the last census by age group and sex
Session 1.11
TEACHING BASIC STATISTICS ….
Example of Inferential Statistics
A new milk formulation designed to improve the psychomotor
development of infants was tested on randomly selected infants.
Based on the results, it was concluded that the new milk formulation is
effective in improving the psychomotor development of infants.
Session 1.12
TEACHING BASIC STATISTICS ….
Inferential Statistics
Larger Set
(N units/observations) Smaller Set
(n units/observations)
Inferences and
Generalizations
Session 1.13
TEACHING BASIC STATISTICS ….
Key Definitions
 The universe/physical population is the collection of
things or observational units under consideration.
 A variable is a characteristic observed or measured on
every unit of the universe.
 The statistical population is the set of all possible values
of the variable.
 Measurement is the process of determining the value or
label of the variable based on what has been observed.
 An observation is the realized value of the variable.
 Data is the collection of all observations.
Session 1.14
TEACHING BASIC STATISTICS ….
Key Definitions
 Parameters are numerical measures
that describe the population or universe
of interest. Usually donated by Greek
letters; µ (mu), σ (sigma), ρ (rho), λ
(lambda), τ (tau), θ (theta), α (alpha) and
β (beta).
 Statistics are numerical measures of a
sample
Session 1.15
TEACHING BASIC STATISTICS ….
VARIABLES
Qualitative Quantitative
ContinuousDiscrete
Types of Variables
Qualitative variable
 Describes the quality or
character of something
Quantitative variable
 Describes the amount or
number of something
a. Discrete
 countable
a. Continuous
 Measurable (measured
using a continuous scale
such as kilos, cms, grams)
a. Constant
Session 1.16
TEACHING BASIC STATISTICS ….
Levels of Measurement
1. Nominal
 Numbers or symbols used to classify units
into distinct categories
1. Ordinal scale
 Accounts for order; no indication of distance
between positions
1. Interval scale
 Equal intervals (fixed unit of measurement);
no absolute zero
1. Ratio scale
 Has absolute zero
Session 1.17
TEACHING BASIC STATISTICS ….
Methods of Collecting Data
 Objective Method
 Subjective Method
 Use of Existing Records
Session 1.18
TEACHING BASIC STATISTICS ….
Methods of Presenting Data
Textual
Tabular
Graphical
Session 1.19
TEACHING BASIC STATISTICS ….
Mean Median Mode
Summary Measures
Variation
Variance
Standard Deviation
Coefficient of
Variation
Range
Location
Maximum
Minimum
Percentile
Quartile
Decile
Median
Interquartile
Range
Skewness
Kurtosis
Central
Tendency
Session 1.20
TEACHING BASIC STATISTICS ….
 A single value that is used to identify
the “center” of the data
it is thought of as a typical value of
the distribution
precise yet simple
most representative value of the
data
Measures of Central Tendency
Session 1.21
TEACHING BASIC STATISTICS ….
Mean
 Most common measure of the center
 Also known as arithmetic average
1 1 2
N
i
i N
X
X X X
N N
µ = + + +
= =
∑ K
1 21
n
i
ni
x
x x x
x
n n
= + + +
= =
∑ K
Population Mean:
Sample Mean:
Session 1.22
TEACHING BASIC STATISTICS ….
Properties of the Mean
 may not be an actual
observation in the data set
 can be applied in at least
interval level
 easy to compute
 every observation contributes to
the value of the mean
Session 1.23
TEACHING BASIC STATISTICS ….
Properties of the Mean
 subgroup means can be combined to come up
with a group mean (use weighted mean)
 easily affected by extreme values
0 1 2 3 4 5 6 7 8 9 10 0 1 2 3 4 5 6 7 8 9 10 12 14
Mean = 5
Mean = 6
Session 1.24
TEACHING BASIC STATISTICS ….
Median
 Divides the observations into two equal
parts
 If the number of observations is odd, the
median is the middle number.
 If the number of observations is even, the
median is the average of the 2 middle
numbers.
 Sample median denoted as
while population median is denoted as
x~
µ~
Session 1.25
TEACHING BASIC STATISTICS ….
Properties of a Median
 may not be an actual observation in
the data set
 can be applied in at least ordinal level
 a positional measure; not affected by
extreme values
0 1 2 3 4 5 6 7 8 9 10 0 1 2 3 4 5 6 7 8 9 10 12 14
Median = 5
Session 1.26
TEACHING BASIC STATISTICS ….
Mode
 occurs most frequently
 nominal average
 may or may not exist
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14
Mode = 9
0 1 2 3 4 5 6
No Mode
Session 1.27
TEACHING BASIC STATISTICS ….
Properties of a Mode
 can be used for qualitative as
well as quantitative data
 may not be unique
 not affected by extreme values
 can be computed for
ungrouped and grouped data
Session 1.28
TEACHING BASIC STATISTICS ….
Mean, Median & Mode
Use the mean when:
 sampling stability is desired
 other measures are to be
computed
Session 1.29
TEACHING BASIC STATISTICS ….
Mean, Median & Mode
Use the median when:
 the exact midpoint of the
distribution is desired
 there are extreme
observations
Session 1.30
TEACHING BASIC STATISTICS ….
Mean, Median & Mode
Use the mode when:
 when the "typical" value is
desired
 when the dataset is measured
on a nominal scale
Session 1.31
TEACHING BASIC STATISTICS ….
Measures of Location
 A Measure of Location summarizes a
data set by giving a value within the
range of the data values that describes
its location relative to the entire data set
arranged according to magnitude
(called an array).
Some Common Measures:
 Minimum, Maximum
 Percentiles, Deciles, Quartiles
Session 1.32
TEACHING BASIC STATISTICS ….
Maximum and Minimum
 Minimum is the smallest value in the
data set, denoted as MIN.
 Maximum is the largest value in the
data set, denoted as MAX.
Session 1.33
TEACHING BASIC STATISTICS ….
Percentiles
 Numerical measures that give the
relative position of a data value
relative to the entire data set.
 Divide an array (raw data arranged
in increasing or decreasing order of
magnitude) into 100 equal parts.
 The jth
percentile, denoted as Pj, is
the data value in the the data set
that separates the bottom j% of the
data from the top (100-j)%.
Session 1.34
TEACHING BASIC STATISTICS ….
EXAMPLE
Suppose LJ was told that relative
to the other scores on a certain
test, his score was the 95th
percentile.
 This means that (at least) 95%
of those who took the test had
scores less than or equal to LJ’s
score, while (at least) 5% had
scores higher than LJ’s.
Session 1.35
TEACHING BASIC STATISTICS ….
Deciles
 Divide an array into ten equal
parts, each part having ten
percent of the distribution of
the data values, denoted by Dj.
 The 1st
decile is the 10th
percentile; the 2nd
decile is the
20th
percentile…..
Session 1.36
TEACHING BASIC STATISTICS ….
Quartiles
 Divide an array into four equal
parts, each part having 25% of
the distribution of the data
values, denoted by Qj.
 The 1st
quartile is the 25th
percentile; the 2nd
quartile is the
50th
percentile, also the median
and the 3rd
quartile is the 75th
percentile.
Session 1.37
TEACHING BASIC STATISTICS ….
Measures of Variation
 A measure of variation is a
single value that is used to
describe the spread of the
distribution
A measure of central tendency
alone does not uniquely
describe a distribution
Session 1.38
TEACHING BASIC STATISTICS ….
Mean = 15.5
s = 3.33811 12 13 14 15 16 17 18 19 20 21
11 12 13 14 15 16 17 18 19 20 21
Data B
Data A
Mean = 15.5
s = .9258
11 12 13 14 15 16 17 18 19 20 21
Mean = 15.5
s = 4.57
Data C
A look at dispersion…
Session 1.39
TEACHING BASIC STATISTICS ….
Two Types of Measures of
Dispersion
Absolute Measures of Dispersion:
 Range
 Inter-quartile Range
 Variance
 Standard Deviation
Relative Measure of Dispersion:
 Coefficient of Variation
Session 1.40
TEACHING BASIC STATISTICS ….
Range (R)
The difference between the maximum and
minimum value in a data set, i.e.
R = MAX – MIN
Example: Pulse rates of 15 male residents of a
certain village
54 58 58 60 62 65 66 71
74 75 77 78 80 82 85
R = 85 - 54 = 31
Session 1.41
TEACHING BASIC STATISTICS ….
Some Properties of the Range
 The larger the value of the
range, the more dispersed
the observations are.
 It is quick and easy to
understand.
 A rough measure of
dispersion.
Session 1.42
TEACHING BASIC STATISTICS ….
Inter-Quartile Range (IQR)
The difference between the third quartile and
first quartile, i.e.
IQR = Q3 – Q1
Example: Pulse rates of 15 residents of a
certain village
54 58 58 60 62 65 66 71
74 75 77 78 80 82 85
IQR = 78 - 60 = 18
Session 1.43
TEACHING BASIC STATISTICS ….
Some Properties of IQR
 Reduces the influence of
extreme values.
 Not as easy to calculate
as the Range.
Session 1.44
TEACHING BASIC STATISTICS ….
Variance
 important measure of variation
 shows variation about the mean
Population variance
Sample variance
N
X
N
i
i∑=
−
= 1
2
2
)( µ
σ
1
)(
1
2
2
−
−
=
∑=
n
xx
s
n
i
i
Session 1.45
TEACHING BASIC STATISTICS ….
Standard Deviation (SD)
 most important measure of variation
 square root of Variance
 has the same units as the original data
Population SD
Sample SD
N
X
N
i
i∑=
−
= 1
2
)( µ
σ
1
)(
1
2
−
−
=
∑=
n
xx
s
n
i
i
Session 1.46
TEACHING BASIC STATISTICS ….
(Sample) Data: 10 12 14 15 17 18 18
24
n = 8 Mean =16
309.4
7
2)1624(2)1618(2)1617(2)1615(2)1614(2)1612(2)1610(
=
−+−+−+−+−+−+−
=s
Computation of Standard Deviation
Session 1.47
TEACHING BASIC STATISTICS ….
Remarks on Standard Deviation
 If there is a large amount of variation,
then on average, the data values will be
far from the mean. Hence, the SD will be
large.
 If there is only a small amount of
variation, then on average, the data
values will be close to the mean. Hence,
the SD will be small.
Session 1.48
TEACHING BASIC STATISTICS ….
Mean = 15.5
s = 3.33811 12 13 14 15 16 17 18 19 20 21
11 12 13 14 15 16 17 18 19 20 21
Data B
Data A
Mean = 15.5
s = .9258
11 12 13 14 15 16 17 18 19 20 21
Mean = 15.5
s = 4.57
Data C
Comparing Standard Deviations
(comparable only when units of measure are the same and
the means are not too different from each other)
Session 1.49
TEACHING BASIC STATISTICS ….
Example: Team A - Heights of five marathon players in inches
5”
65 “ 65 “ 65 “ 65 “ 65 “
Mean = 65
S = 0
Comparing Standard Deviations
Session 1.50
TEACHING BASIC STATISTICS ….
Example: Team B - Heights of five marathon players in inches
62 “ 67 “ 66 “ 70 “ 60 “
Mean = 65”
s = 4.0”
Comparing Standard Deviation
Session 1.51
TEACHING BASIC STATISTICS ….
Properties of Standard Deviation
 It is the most widely used measure of
dispersion. (Chebychev’s Inequality)
 It is based on all the items and is rigidly
defined.
 It is used to test the reliability of measures
calculated from samples.
 The standard deviation is sensitive to the
presence of extreme values.
 It is not easy to calculate by hand (unlike the
range).
Session 1.52
TEACHING BASIC STATISTICS ….
Chebyshev’s Rule
It permits us to make statements about
the percentage of observations that
must be within a specified number of
standard deviation from the mean
The proportion of any distribution that
lies within k standard deviations of the
mean is at least 1-(1/k2
) where k is any
positive number larger than 1.
This rule applies to any distribution.
Session 1.53
TEACHING BASIC STATISTICS ….
For any data set with mean (µ) and
standard deviation (SD), the following
statements apply:
At least 75% of the observations are
within 2SD of its mean.
At least 88.9% of the observations are
within 3SD of its mean.
Chebyshev’s Rule
Session 1.54
TEACHING BASIC STATISTICS ….
Illustration
At least 75%
At least 75% of the observations
are within 2SD of its mean.
Session 1.55
TEACHING BASIC STATISTICS ….
Example
The midterm exam scores of 100 STAT 1 students
last semester had a mean of 65 and a standard
deviation of 8 points.
Applying the Chebyshev’s Rule, we can say that:
1. At least 75% of the students had scores
between 49 and 81.
2. At least 88.9% of the students had scores
between 41 and 89.
Session 1.56
TEACHING BASIC STATISTICS ….
Coefficient of Variation (CV)
 measure of relative variation
 usually expressed in percent
 shows variation relative to mean
 used to compare 2 or more groups
 Formula :
100%×





=
Mean
SD
CV
Session 1.57
TEACHING BASIC STATISTICS ….
Comparing CVs
 Stock A: Average Price = P50
SD = P5
CV = 10%
 Stock B: Average Price = P100
SD = P5
CV = 5%
Session 1.58
TEACHING BASIC STATISTICS ….
Measure of Skewness
 Describes the degree of departures of the
distribution of the data from symmetry.
 The degree of skewness is measured by
the coefficient of skewness, denoted as SK
and computed as,
( )
SD
MedianMean
K
−
=
3
S
Session 1.59
TEACHING BASIC STATISTICS ….
What is Symmetry?
A distribution is said to be
symmetric about the mean,
if the distribution to the left
of mean is the “mirror
image” of the distribution to
the right of the mean.
Likewise, a symmetric
distribution has SK=0 since
its mean is equal to its
median and its mode.
Session 1.60
TEACHING BASIC STATISTICS ….
SK > 0
positively
skewed
Measure of Skewness
SK < 0
negatively skewed
Session 1.61
TEACHING BASIC STATISTICS ….
Measure of Kurtosis
 Describes the extent of peakedness or
flatness of the distribution of the data.
 Measured by coefficient of kurtosis (K)
computed as,
( )4
1
4
3
N
i
i
X
K
N
µ
σ
=
−
= −
∑
Session 1.62
TEACHING BASIC STATISTICS ….
K = 0
mesokurtic
K > 0
leptokurtic
K < 0
platykurtic
Measure of Kurtosis
Session 1.63
TEACHING BASIC STATISTICS ….
Box-and-Whiskers Plot
 Concerned with the symmetry of the
distribution and incorporates
measures of location in order to study
the variability of the observations.
 Also called as box plot or 5-number
summary (represented by Min, Max,
Q1, Q2, and Q3).
 Suitable for identifying outliers.
Session 1.64
TEACHING BASIC STATISTICS ….
The diagram is made up of a box which
lies between the first and third
quartiles.
The whiskers are the straight lines
extending from the ends of the box to
the smallest and largest values that
are not outliers.
Box-and-Whiskers Plot
Session 1.65
TEACHING BASIC STATISTICS ….
Steps to Construct a Box-and-Whiskers plot
Step 1: Draw a rectangular box whose left edge is at the
Q1
and whose right edge is at the Q3
so the box width
is the IQR. Then draw a vertical line segment inside
the box where the median is found.
Q1 Q3Md
75 78 85
Session 1.66
TEACHING BASIC STATISTICS ….
Step 2: Place marks at distances 1.5 IQR from
either end of the box. (1.5 IQR =15)
100
Q1 Q3Md
75 78 8560
1.5 IQR 1.5 IQR
Steps to Construct a Box-and-Whiskers plot
Session 1.67
TEACHING BASIC STATISTICS ….
Step 3:Draw the horizontal line
segments known as the “whiskers”
from each of the end box to the
largest and smallest values in the
data set that are not outliers.
(An observation beyond ±1.5 IQR is
an outlier.)
Steps to Construct a Box-and-Whiskers
plot
Session 1.68
TEACHING BASIC STATISTICS ….
Step 4: For every outlier, draw a dot. If two or more dots
have the same values, draw the dots side by side.
Q1 Q3
Md
75 78 8560 100
1.5 IQR 1.5 IQR
9855
.
.
Steps to Construct a Box-and-Whiskers
plot

More Related Content

What's hot

Basic Descriptive Statistics
Basic Descriptive StatisticsBasic Descriptive Statistics
Basic Descriptive Statisticssikojp
 
Introduction to Statistics - Basic concepts
Introduction to Statistics - Basic conceptsIntroduction to Statistics - Basic concepts
Introduction to Statistics - Basic conceptsDocIbrahimAbdelmonaem
 
Descriptive statistics
Descriptive statisticsDescriptive statistics
Descriptive statisticsAileen Balbido
 
Descriptive statistics
Descriptive statisticsDescriptive statistics
Descriptive statisticsAiden Yeh
 
Meaning and Importance of Statistics
Meaning and Importance of StatisticsMeaning and Importance of Statistics
Meaning and Importance of StatisticsFlipped Channel
 
Introduction to Statistics
Introduction to StatisticsIntroduction to Statistics
Introduction to StatisticsRobert Tinaro
 
Types of Statistics
Types of StatisticsTypes of Statistics
Types of Statisticsloranel
 
descriptive and inferential statistics
descriptive and inferential statisticsdescriptive and inferential statistics
descriptive and inferential statisticsMona Sajid
 
Descriptive statistics
Descriptive statisticsDescriptive statistics
Descriptive statisticsRajesh Gunesh
 
Descriptive statistics
Descriptive statisticsDescriptive statistics
Descriptive statisticsAnand Thokal
 

What's hot (20)

statistic
statisticstatistic
statistic
 
Math 102- Statistics
Math 102- StatisticsMath 102- Statistics
Math 102- Statistics
 
Descriptive statistics
Descriptive statisticsDescriptive statistics
Descriptive statistics
 
Basic Descriptive Statistics
Basic Descriptive StatisticsBasic Descriptive Statistics
Basic Descriptive Statistics
 
Introduction to Statistics - Basic concepts
Introduction to Statistics - Basic conceptsIntroduction to Statistics - Basic concepts
Introduction to Statistics - Basic concepts
 
Descriptive statistics
Descriptive statisticsDescriptive statistics
Descriptive statistics
 
Descriptive statistics
Descriptive statisticsDescriptive statistics
Descriptive statistics
 
Statistics
StatisticsStatistics
Statistics
 
Measures of Variability
Measures of VariabilityMeasures of Variability
Measures of Variability
 
Meaning and Importance of Statistics
Meaning and Importance of StatisticsMeaning and Importance of Statistics
Meaning and Importance of Statistics
 
Introduction to Statistics
Introduction to StatisticsIntroduction to Statistics
Introduction to Statistics
 
Advanced statistics
Advanced statisticsAdvanced statistics
Advanced statistics
 
Types of Statistics
Types of StatisticsTypes of Statistics
Types of Statistics
 
descriptive and inferential statistics
descriptive and inferential statisticsdescriptive and inferential statistics
descriptive and inferential statistics
 
Probability and statistics
Probability and statisticsProbability and statistics
Probability and statistics
 
Descriptive statistics
Descriptive statisticsDescriptive statistics
Descriptive statistics
 
STATISTICS
STATISTICSSTATISTICS
STATISTICS
 
Chapter 1 what is statistics
Chapter 1 what is statisticsChapter 1 what is statistics
Chapter 1 what is statistics
 
Understanding statistics in research
Understanding statistics in researchUnderstanding statistics in research
Understanding statistics in research
 
Descriptive statistics
Descriptive statisticsDescriptive statistics
Descriptive statistics
 

Similar to Introduction to Statistics and Statistical Inference

1_INTRODUCTION TO STATISTICS AND STATISTICAL INFERENCE.ppt
1_INTRODUCTION TO STATISTICS AND STATISTICAL INFERENCE.ppt1_INTRODUCTION TO STATISTICS AND STATISTICAL INFERENCE.ppt
1_INTRODUCTION TO STATISTICS AND STATISTICAL INFERENCE.pptJhuveLhynn
 
Introduction to Business Statistics
Introduction to Business StatisticsIntroduction to Business Statistics
Introduction to Business StatisticsSOMASUNDARAM T
 
Biostatistical methods
Biostatistical methodsBiostatistical methods
Biostatistical methodsPrakkan Hillol
 
Statistics text book higher secondary
Statistics text book higher secondaryStatistics text book higher secondary
Statistics text book higher secondaryChethan Kumar M
 
Paktia university lecture prepare by hameed gul ahmadzai
Paktia university lecture prepare by hameed gul ahmadzaiPaktia university lecture prepare by hameed gul ahmadzai
Paktia university lecture prepare by hameed gul ahmadzaiHameedgul Ahmadzai
 
Texto estudiante etad01
Texto estudiante etad01Texto estudiante etad01
Texto estudiante etad01leoscarmillan
 
Machine learning pre requisite
Machine learning pre requisiteMachine learning pre requisite
Machine learning pre requisiteRam Singh
 
Statistics and probability
Statistics and probability   Statistics and probability
Statistics and probability Muhammad Mayo
 
Statistics and probability lecture 01
Statistics and probability  lecture 01Statistics and probability  lecture 01
Statistics and probability lecture 01MuhammadTufailKaran
 
Bahir dar institute of technology.pdf
Bahir dar institute of technology.pdfBahir dar institute of technology.pdf
Bahir dar institute of technology.pdfHailsh
 
Basics of Research Types of Data Classification
Basics of Research Types of Data ClassificationBasics of Research Types of Data Classification
Basics of Research Types of Data ClassificationHarshit Pandey
 
Meaning and uses of statistics
Meaning and uses of statisticsMeaning and uses of statistics
Meaning and uses of statisticsRekhaChoudhary24
 
Statistics-Chapter-1.pptxheheheueuehehehehehe
Statistics-Chapter-1.pptxheheheueueheheheheheStatistics-Chapter-1.pptxheheheueuehehehehehe
Statistics-Chapter-1.pptxheheheueueheheheheheraulskie17
 
Biostatistics Lecture 1 8th Sem B.Pharm AKTU
Biostatistics Lecture 1 8th Sem B.Pharm AKTUBiostatistics Lecture 1 8th Sem B.Pharm AKTU
Biostatistics Lecture 1 8th Sem B.Pharm AKTUWebTech16
 
Unit 1 - Mean Median Mode - 18MAB303T - PPT - Part 1.pdf
Unit 1 - Mean Median Mode - 18MAB303T - PPT - Part 1.pdfUnit 1 - Mean Median Mode - 18MAB303T - PPT - Part 1.pdf
Unit 1 - Mean Median Mode - 18MAB303T - PPT - Part 1.pdfAravindS199
 

Similar to Introduction to Statistics and Statistical Inference (20)

1_INTRODUCTION TO STATISTICS AND STATISTICAL INFERENCE.ppt
1_INTRODUCTION TO STATISTICS AND STATISTICAL INFERENCE.ppt1_INTRODUCTION TO STATISTICS AND STATISTICAL INFERENCE.ppt
1_INTRODUCTION TO STATISTICS AND STATISTICAL INFERENCE.ppt
 
Introduction to Business Statistics
Introduction to Business StatisticsIntroduction to Business Statistics
Introduction to Business Statistics
 
Statistics
StatisticsStatistics
Statistics
 
Biostatistical methods
Biostatistical methodsBiostatistical methods
Biostatistical methods
 
Statistics text book higher secondary
Statistics text book higher secondaryStatistics text book higher secondary
Statistics text book higher secondary
 
Paktia university lecture prepare by hameed gul ahmadzai
Paktia university lecture prepare by hameed gul ahmadzaiPaktia university lecture prepare by hameed gul ahmadzai
Paktia university lecture prepare by hameed gul ahmadzai
 
Texto estudiante etad01
Texto estudiante etad01Texto estudiante etad01
Texto estudiante etad01
 
Machine learning pre requisite
Machine learning pre requisiteMachine learning pre requisite
Machine learning pre requisite
 
chapter 1.pptx
chapter 1.pptxchapter 1.pptx
chapter 1.pptx
 
Statistics and probability
Statistics and probability   Statistics and probability
Statistics and probability
 
Statistics and probability lecture 01
Statistics and probability  lecture 01Statistics and probability  lecture 01
Statistics and probability lecture 01
 
Bahir dar institute of technology.pdf
Bahir dar institute of technology.pdfBahir dar institute of technology.pdf
Bahir dar institute of technology.pdf
 
Basics of Research Types of Data Classification
Basics of Research Types of Data ClassificationBasics of Research Types of Data Classification
Basics of Research Types of Data Classification
 
Meaning and uses of statistics
Meaning and uses of statisticsMeaning and uses of statistics
Meaning and uses of statistics
 
Statistics-Chapter-1.pptxheheheueuehehehehehe
Statistics-Chapter-1.pptxheheheueueheheheheheStatistics-Chapter-1.pptxheheheueuehehehehehe
Statistics-Chapter-1.pptxheheheueuehehehehehe
 
Biostatistics Lecture 1 8th Sem B.Pharm AKTU
Biostatistics Lecture 1 8th Sem B.Pharm AKTUBiostatistics Lecture 1 8th Sem B.Pharm AKTU
Biostatistics Lecture 1 8th Sem B.Pharm AKTU
 
Unit 1 - Mean Median Mode - 18MAB303T - PPT - Part 1.pdf
Unit 1 - Mean Median Mode - 18MAB303T - PPT - Part 1.pdfUnit 1 - Mean Median Mode - 18MAB303T - PPT - Part 1.pdf
Unit 1 - Mean Median Mode - 18MAB303T - PPT - Part 1.pdf
 
Akhiesh maurya
Akhiesh mauryaAkhiesh maurya
Akhiesh maurya
 
Biostats in ortho
Biostats in orthoBiostats in ortho
Biostats in ortho
 
Sta301 lec01
Sta301 lec01Sta301 lec01
Sta301 lec01
 

More from Jezhabeth Villegas

Myths and Theories of Entrepreneurship _ Villegas, J..pptx
Myths and Theories of Entrepreneurship _ Villegas, J..pptxMyths and Theories of Entrepreneurship _ Villegas, J..pptx
Myths and Theories of Entrepreneurship _ Villegas, J..pptxJezhabeth Villegas
 
Introduction to basic concept in sampling and sampling techniques
Introduction to basic concept in sampling and sampling techniquesIntroduction to basic concept in sampling and sampling techniques
Introduction to basic concept in sampling and sampling techniquesJezhabeth Villegas
 
Introduction to Probability and Probability Distributions
Introduction to Probability and Probability DistributionsIntroduction to Probability and Probability Distributions
Introduction to Probability and Probability DistributionsJezhabeth Villegas
 

More from Jezhabeth Villegas (6)

Myths and Theories of Entrepreneurship _ Villegas, J..pptx
Myths and Theories of Entrepreneurship _ Villegas, J..pptxMyths and Theories of Entrepreneurship _ Villegas, J..pptx
Myths and Theories of Entrepreneurship _ Villegas, J..pptx
 
Introduction to basic concept in sampling and sampling techniques
Introduction to basic concept in sampling and sampling techniquesIntroduction to basic concept in sampling and sampling techniques
Introduction to basic concept in sampling and sampling techniques
 
Introduction to Probability and Probability Distributions
Introduction to Probability and Probability DistributionsIntroduction to Probability and Probability Distributions
Introduction to Probability and Probability Distributions
 
10 keys to career success
10 keys to career success10 keys to career success
10 keys to career success
 
Grade 4 MTAP Reviewer
Grade 4 MTAP ReviewerGrade 4 MTAP Reviewer
Grade 4 MTAP Reviewer
 
Grade 3 MTAP Reviewer
Grade 3 MTAP ReviewerGrade 3 MTAP Reviewer
Grade 3 MTAP Reviewer
 

Recently uploaded

Bios of leading Astrologers & Researchers
Bios of leading Astrologers & ResearchersBios of leading Astrologers & Researchers
Bios of leading Astrologers & Researchersdarmandersingh4580
 
如何办理(UCLA毕业证书)加州大学洛杉矶分校毕业证成绩单学位证留信学历认证原件一样
如何办理(UCLA毕业证书)加州大学洛杉矶分校毕业证成绩单学位证留信学历认证原件一样如何办理(UCLA毕业证书)加州大学洛杉矶分校毕业证成绩单学位证留信学历认证原件一样
如何办理(UCLA毕业证书)加州大学洛杉矶分校毕业证成绩单学位证留信学历认证原件一样jk0tkvfv
 
Go paperless and transform your procurement process with the Hive Collaborati...
Go paperless and transform your procurement process with the Hive Collaborati...Go paperless and transform your procurement process with the Hive Collaborati...
Go paperless and transform your procurement process with the Hive Collaborati...LitoGarin1
 
SCI8-Q4-MOD11.pdfwrwujrrjfaajerjrajrrarj
SCI8-Q4-MOD11.pdfwrwujrrjfaajerjrajrrarjSCI8-Q4-MOD11.pdfwrwujrrjfaajerjrajrrarj
SCI8-Q4-MOD11.pdfwrwujrrjfaajerjrajrrarjadimosmejiaslendon
 
sourabh vyas1222222222222222222244444444
sourabh vyas1222222222222222222244444444sourabh vyas1222222222222222222244444444
sourabh vyas1222222222222222222244444444saurabvyas476
 
Identify Rules that Predict Patient’s Heart Disease - An Application of Decis...
Identify Rules that Predict Patient’s Heart Disease - An Application of Decis...Identify Rules that Predict Patient’s Heart Disease - An Application of Decis...
Identify Rules that Predict Patient’s Heart Disease - An Application of Decis...ThinkInnovation
 
1:1原版定制利物浦大学毕业证(Liverpool毕业证)成绩单学位证书留信学历认证
1:1原版定制利物浦大学毕业证(Liverpool毕业证)成绩单学位证书留信学历认证1:1原版定制利物浦大学毕业证(Liverpool毕业证)成绩单学位证书留信学历认证
1:1原版定制利物浦大学毕业证(Liverpool毕业证)成绩单学位证书留信学历认证ppy8zfkfm
 
Credit Card Fraud Detection: Safeguarding Transactions in the Digital Age
Credit Card Fraud Detection: Safeguarding Transactions in the Digital AgeCredit Card Fraud Detection: Safeguarding Transactions in the Digital Age
Credit Card Fraud Detection: Safeguarding Transactions in the Digital AgeBoston Institute of Analytics
 
Northern New England Tableau User Group (TUG) May 2024
Northern New England Tableau User Group (TUG) May 2024Northern New England Tableau User Group (TUG) May 2024
Northern New England Tableau User Group (TUG) May 2024patrickdtherriault
 
Data Analytics for Digital Marketing Lecture for Advanced Digital & Social Me...
Data Analytics for Digital Marketing Lecture for Advanced Digital & Social Me...Data Analytics for Digital Marketing Lecture for Advanced Digital & Social Me...
Data Analytics for Digital Marketing Lecture for Advanced Digital & Social Me...Valters Lauzums
 
What is Insertion Sort. Its basic information
What is Insertion Sort. Its basic informationWhat is Insertion Sort. Its basic information
What is Insertion Sort. Its basic informationmuqadasqasim10
 
Displacement, Velocity, Acceleration, and Second Derivatives
Displacement, Velocity, Acceleration, and Second DerivativesDisplacement, Velocity, Acceleration, and Second Derivatives
Displacement, Velocity, Acceleration, and Second Derivatives23050636
 
Statistics Informed Decisions Using Data 5th edition by Michael Sullivan solu...
Statistics Informed Decisions Using Data 5th edition by Michael Sullivan solu...Statistics Informed Decisions Using Data 5th edition by Michael Sullivan solu...
Statistics Informed Decisions Using Data 5th edition by Michael Sullivan solu...ssuserf63bd7
 
Predictive Precipitation: Advanced Rain Forecasting Techniques
Predictive Precipitation: Advanced Rain Forecasting TechniquesPredictive Precipitation: Advanced Rain Forecasting Techniques
Predictive Precipitation: Advanced Rain Forecasting TechniquesBoston Institute of Analytics
 
MATERI MANAJEMEN OF PENYAKIT TETANUS.ppt
MATERI  MANAJEMEN OF PENYAKIT TETANUS.pptMATERI  MANAJEMEN OF PENYAKIT TETANUS.ppt
MATERI MANAJEMEN OF PENYAKIT TETANUS.pptRachmaGhifari
 
社内勉強会資料_Object Recognition as Next Token Prediction
社内勉強会資料_Object Recognition as Next Token Prediction社内勉強会資料_Object Recognition as Next Token Prediction
社内勉強会資料_Object Recognition as Next Token PredictionNABLAS株式会社
 
obat aborsi Banjarmasin wa 082135199655 jual obat aborsi cytotec asli di Ban...
obat aborsi Banjarmasin wa 082135199655 jual obat aborsi cytotec asli di  Ban...obat aborsi Banjarmasin wa 082135199655 jual obat aborsi cytotec asli di  Ban...
obat aborsi Banjarmasin wa 082135199655 jual obat aborsi cytotec asli di Ban...siskavia95
 
一比一原版(ucla文凭证书)加州大学洛杉矶分校毕业证学历认证官方成绩单
一比一原版(ucla文凭证书)加州大学洛杉矶分校毕业证学历认证官方成绩单一比一原版(ucla文凭证书)加州大学洛杉矶分校毕业证学历认证官方成绩单
一比一原版(ucla文凭证书)加州大学洛杉矶分校毕业证学历认证官方成绩单aqpto5bt
 
1:1原版定制伦敦政治经济学院毕业证(LSE毕业证)成绩单学位证书留信学历认证
1:1原版定制伦敦政治经济学院毕业证(LSE毕业证)成绩单学位证书留信学历认证1:1原版定制伦敦政治经济学院毕业证(LSE毕业证)成绩单学位证书留信学历认证
1:1原版定制伦敦政治经济学院毕业证(LSE毕业证)成绩单学位证书留信学历认证dq9vz1isj
 

Recently uploaded (20)

Bios of leading Astrologers & Researchers
Bios of leading Astrologers & ResearchersBios of leading Astrologers & Researchers
Bios of leading Astrologers & Researchers
 
如何办理(UCLA毕业证书)加州大学洛杉矶分校毕业证成绩单学位证留信学历认证原件一样
如何办理(UCLA毕业证书)加州大学洛杉矶分校毕业证成绩单学位证留信学历认证原件一样如何办理(UCLA毕业证书)加州大学洛杉矶分校毕业证成绩单学位证留信学历认证原件一样
如何办理(UCLA毕业证书)加州大学洛杉矶分校毕业证成绩单学位证留信学历认证原件一样
 
Go paperless and transform your procurement process with the Hive Collaborati...
Go paperless and transform your procurement process with the Hive Collaborati...Go paperless and transform your procurement process with the Hive Collaborati...
Go paperless and transform your procurement process with the Hive Collaborati...
 
SCI8-Q4-MOD11.pdfwrwujrrjfaajerjrajrrarj
SCI8-Q4-MOD11.pdfwrwujrrjfaajerjrajrrarjSCI8-Q4-MOD11.pdfwrwujrrjfaajerjrajrrarj
SCI8-Q4-MOD11.pdfwrwujrrjfaajerjrajrrarj
 
sourabh vyas1222222222222222222244444444
sourabh vyas1222222222222222222244444444sourabh vyas1222222222222222222244444444
sourabh vyas1222222222222222222244444444
 
Identify Rules that Predict Patient’s Heart Disease - An Application of Decis...
Identify Rules that Predict Patient’s Heart Disease - An Application of Decis...Identify Rules that Predict Patient’s Heart Disease - An Application of Decis...
Identify Rules that Predict Patient’s Heart Disease - An Application of Decis...
 
1:1原版定制利物浦大学毕业证(Liverpool毕业证)成绩单学位证书留信学历认证
1:1原版定制利物浦大学毕业证(Liverpool毕业证)成绩单学位证书留信学历认证1:1原版定制利物浦大学毕业证(Liverpool毕业证)成绩单学位证书留信学历认证
1:1原版定制利物浦大学毕业证(Liverpool毕业证)成绩单学位证书留信学历认证
 
Credit Card Fraud Detection: Safeguarding Transactions in the Digital Age
Credit Card Fraud Detection: Safeguarding Transactions in the Digital AgeCredit Card Fraud Detection: Safeguarding Transactions in the Digital Age
Credit Card Fraud Detection: Safeguarding Transactions in the Digital Age
 
Northern New England Tableau User Group (TUG) May 2024
Northern New England Tableau User Group (TUG) May 2024Northern New England Tableau User Group (TUG) May 2024
Northern New England Tableau User Group (TUG) May 2024
 
Data Analytics for Digital Marketing Lecture for Advanced Digital & Social Me...
Data Analytics for Digital Marketing Lecture for Advanced Digital & Social Me...Data Analytics for Digital Marketing Lecture for Advanced Digital & Social Me...
Data Analytics for Digital Marketing Lecture for Advanced Digital & Social Me...
 
What is Insertion Sort. Its basic information
What is Insertion Sort. Its basic informationWhat is Insertion Sort. Its basic information
What is Insertion Sort. Its basic information
 
Displacement, Velocity, Acceleration, and Second Derivatives
Displacement, Velocity, Acceleration, and Second DerivativesDisplacement, Velocity, Acceleration, and Second Derivatives
Displacement, Velocity, Acceleration, and Second Derivatives
 
Statistics Informed Decisions Using Data 5th edition by Michael Sullivan solu...
Statistics Informed Decisions Using Data 5th edition by Michael Sullivan solu...Statistics Informed Decisions Using Data 5th edition by Michael Sullivan solu...
Statistics Informed Decisions Using Data 5th edition by Michael Sullivan solu...
 
Abortion pills in Riyadh Saudi Arabia (+966572737505 buy cytotec
Abortion pills in Riyadh Saudi Arabia (+966572737505 buy cytotecAbortion pills in Riyadh Saudi Arabia (+966572737505 buy cytotec
Abortion pills in Riyadh Saudi Arabia (+966572737505 buy cytotec
 
Predictive Precipitation: Advanced Rain Forecasting Techniques
Predictive Precipitation: Advanced Rain Forecasting TechniquesPredictive Precipitation: Advanced Rain Forecasting Techniques
Predictive Precipitation: Advanced Rain Forecasting Techniques
 
MATERI MANAJEMEN OF PENYAKIT TETANUS.ppt
MATERI  MANAJEMEN OF PENYAKIT TETANUS.pptMATERI  MANAJEMEN OF PENYAKIT TETANUS.ppt
MATERI MANAJEMEN OF PENYAKIT TETANUS.ppt
 
社内勉強会資料_Object Recognition as Next Token Prediction
社内勉強会資料_Object Recognition as Next Token Prediction社内勉強会資料_Object Recognition as Next Token Prediction
社内勉強会資料_Object Recognition as Next Token Prediction
 
obat aborsi Banjarmasin wa 082135199655 jual obat aborsi cytotec asli di Ban...
obat aborsi Banjarmasin wa 082135199655 jual obat aborsi cytotec asli di  Ban...obat aborsi Banjarmasin wa 082135199655 jual obat aborsi cytotec asli di  Ban...
obat aborsi Banjarmasin wa 082135199655 jual obat aborsi cytotec asli di Ban...
 
一比一原版(ucla文凭证书)加州大学洛杉矶分校毕业证学历认证官方成绩单
一比一原版(ucla文凭证书)加州大学洛杉矶分校毕业证学历认证官方成绩单一比一原版(ucla文凭证书)加州大学洛杉矶分校毕业证学历认证官方成绩单
一比一原版(ucla文凭证书)加州大学洛杉矶分校毕业证学历认证官方成绩单
 
1:1原版定制伦敦政治经济学院毕业证(LSE毕业证)成绩单学位证书留信学历认证
1:1原版定制伦敦政治经济学院毕业证(LSE毕业证)成绩单学位证书留信学历认证1:1原版定制伦敦政治经济学院毕业证(LSE毕业证)成绩单学位证书留信学历认证
1:1原版定制伦敦政治经济学院毕业证(LSE毕业证)成绩单学位证书留信学历认证
 

Introduction to Statistics and Statistical Inference

  • 1. Note: Most of the Slides were taken from Elementary Statistics: A Handbook of Slide Presentation prepared by Z.V.J. Albacea, C.E. Reano, R.V. Collado, L.N. Comia and N.A. Tandang in 2005 for the Institute of Statistics, CAS, UP Los Banos Training on Teaching Basic Statistics for Tertiary Level Teachers Summer 2008 INTRODUCTION TO STATISTICS AND STATISTICAL INFERENCE
  • 2. Session 1.2 TEACHING BASIC STATISTICS …. Florence Nightingale on Statistics  “...the most important science in the whole world: for upon it depends the practical application of every other science and of every art: the one science essential to all political and social administration, all education, all organization based on experience, for it only gives results of our experience.”  “To understand God's thoughts, we must study statistics, for these are the measures of His purpose.”
  • 3. Session 1.3 TEACHING BASIC STATISTICS …. Realities about Statistics  The man in the street distrusts statistics and despises [his image of] statisticians, those who diligently collect irrelevant facts and figures and use them to manipulate society. “There are three kinds of lies: lies, damned lies, and statistics” – Mark Twaine  One can not go about without statistics. “Statistics are like bikinis. What they reveal is suggestive, but what they conceal is vital.” – Aaron Levenstein
  • 4. Session 1.4 TEACHING BASIC STATISTICS …. Definition of Statistics plural sense: numerical facts, e.g. CPI, peso-dollar exchange rate singular sense: scientific discipline consisting of theory and methods for processing numerical information that one can use when making decisions in the face of uncertainty.
  • 5. Session 1.5 TEACHING BASIC STATISTICS …. History of Statistics  The term statistics came from the Latin phrase “ratio status” which means study of practical politics or the statesman’s art.  In the middle of 18th century, the term statistik (a term due to Achenwall) was used, a German term defined as “the political science of several countries”  From statistik it became statistics defined as a statement in figures and facts of the present condition of a state.
  • 6. Session 1.6 TEACHING BASIC STATISTICS …. Application of Statistics  Diverse applications “During the 20th Century statistical thinking and methodology have become the scientific framework for literally dozens of fields including education, agriculture, economics, biology, and medicine, and with increasing influence recently on the hard sciences such as astronomy, geology, and physics. In other words, we have grown from a small obscure field into a big obscure field.” – Brad Efron
  • 7. Session 1.7 TEACHING BASIC STATISTICS …. Application of Statistics  Comparing the effects of five kinds of fertilizers on the yield of a particular variety of corn  Determining the income distribution of Filipino families  Comparing the effectiveness of two diet programs  Prediction of daily temperatures  Evaluation of student performance
  • 8. Session 1.8 TEACHING BASIC STATISTICS …. Two Aims of Statistics Statistics aims to uncover structure in data, to explain variation…  Descriptive  Inferential
  • 9. Session 1.9 TEACHING BASIC STATISTICS …. Areas of Statistics Descriptive statistics  methods concerned w/ collecting, describing, and analyzing a set of data without drawing conclusions (or inferences) about a large group Inferential statistics  methods concerned with the analysis of a subset of data leading to predictions or inferences about the entire set of data
  • 10. Session 1.10 TEACHING BASIC STATISTICS …. Example of Descriptive Statistics Present the Philippine population by constructing a graph indicating the total number of Filipinos counted during the last census by age group and sex
  • 11. Session 1.11 TEACHING BASIC STATISTICS …. Example of Inferential Statistics A new milk formulation designed to improve the psychomotor development of infants was tested on randomly selected infants. Based on the results, it was concluded that the new milk formulation is effective in improving the psychomotor development of infants.
  • 12. Session 1.12 TEACHING BASIC STATISTICS …. Inferential Statistics Larger Set (N units/observations) Smaller Set (n units/observations) Inferences and Generalizations
  • 13. Session 1.13 TEACHING BASIC STATISTICS …. Key Definitions  The universe/physical population is the collection of things or observational units under consideration.  A variable is a characteristic observed or measured on every unit of the universe.  The statistical population is the set of all possible values of the variable.  Measurement is the process of determining the value or label of the variable based on what has been observed.  An observation is the realized value of the variable.  Data is the collection of all observations.
  • 14. Session 1.14 TEACHING BASIC STATISTICS …. Key Definitions  Parameters are numerical measures that describe the population or universe of interest. Usually donated by Greek letters; µ (mu), σ (sigma), ρ (rho), λ (lambda), τ (tau), θ (theta), α (alpha) and β (beta).  Statistics are numerical measures of a sample
  • 15. Session 1.15 TEACHING BASIC STATISTICS …. VARIABLES Qualitative Quantitative ContinuousDiscrete Types of Variables Qualitative variable  Describes the quality or character of something Quantitative variable  Describes the amount or number of something a. Discrete  countable a. Continuous  Measurable (measured using a continuous scale such as kilos, cms, grams) a. Constant
  • 16. Session 1.16 TEACHING BASIC STATISTICS …. Levels of Measurement 1. Nominal  Numbers or symbols used to classify units into distinct categories 1. Ordinal scale  Accounts for order; no indication of distance between positions 1. Interval scale  Equal intervals (fixed unit of measurement); no absolute zero 1. Ratio scale  Has absolute zero
  • 17. Session 1.17 TEACHING BASIC STATISTICS …. Methods of Collecting Data  Objective Method  Subjective Method  Use of Existing Records
  • 18. Session 1.18 TEACHING BASIC STATISTICS …. Methods of Presenting Data Textual Tabular Graphical
  • 19. Session 1.19 TEACHING BASIC STATISTICS …. Mean Median Mode Summary Measures Variation Variance Standard Deviation Coefficient of Variation Range Location Maximum Minimum Percentile Quartile Decile Median Interquartile Range Skewness Kurtosis Central Tendency
  • 20. Session 1.20 TEACHING BASIC STATISTICS ….  A single value that is used to identify the “center” of the data it is thought of as a typical value of the distribution precise yet simple most representative value of the data Measures of Central Tendency
  • 21. Session 1.21 TEACHING BASIC STATISTICS …. Mean  Most common measure of the center  Also known as arithmetic average 1 1 2 N i i N X X X X N N µ = + + + = = ∑ K 1 21 n i ni x x x x x n n = + + + = = ∑ K Population Mean: Sample Mean:
  • 22. Session 1.22 TEACHING BASIC STATISTICS …. Properties of the Mean  may not be an actual observation in the data set  can be applied in at least interval level  easy to compute  every observation contributes to the value of the mean
  • 23. Session 1.23 TEACHING BASIC STATISTICS …. Properties of the Mean  subgroup means can be combined to come up with a group mean (use weighted mean)  easily affected by extreme values 0 1 2 3 4 5 6 7 8 9 10 0 1 2 3 4 5 6 7 8 9 10 12 14 Mean = 5 Mean = 6
  • 24. Session 1.24 TEACHING BASIC STATISTICS …. Median  Divides the observations into two equal parts  If the number of observations is odd, the median is the middle number.  If the number of observations is even, the median is the average of the 2 middle numbers.  Sample median denoted as while population median is denoted as x~ µ~
  • 25. Session 1.25 TEACHING BASIC STATISTICS …. Properties of a Median  may not be an actual observation in the data set  can be applied in at least ordinal level  a positional measure; not affected by extreme values 0 1 2 3 4 5 6 7 8 9 10 0 1 2 3 4 5 6 7 8 9 10 12 14 Median = 5
  • 26. Session 1.26 TEACHING BASIC STATISTICS …. Mode  occurs most frequently  nominal average  may or may not exist 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 Mode = 9 0 1 2 3 4 5 6 No Mode
  • 27. Session 1.27 TEACHING BASIC STATISTICS …. Properties of a Mode  can be used for qualitative as well as quantitative data  may not be unique  not affected by extreme values  can be computed for ungrouped and grouped data
  • 28. Session 1.28 TEACHING BASIC STATISTICS …. Mean, Median & Mode Use the mean when:  sampling stability is desired  other measures are to be computed
  • 29. Session 1.29 TEACHING BASIC STATISTICS …. Mean, Median & Mode Use the median when:  the exact midpoint of the distribution is desired  there are extreme observations
  • 30. Session 1.30 TEACHING BASIC STATISTICS …. Mean, Median & Mode Use the mode when:  when the "typical" value is desired  when the dataset is measured on a nominal scale
  • 31. Session 1.31 TEACHING BASIC STATISTICS …. Measures of Location  A Measure of Location summarizes a data set by giving a value within the range of the data values that describes its location relative to the entire data set arranged according to magnitude (called an array). Some Common Measures:  Minimum, Maximum  Percentiles, Deciles, Quartiles
  • 32. Session 1.32 TEACHING BASIC STATISTICS …. Maximum and Minimum  Minimum is the smallest value in the data set, denoted as MIN.  Maximum is the largest value in the data set, denoted as MAX.
  • 33. Session 1.33 TEACHING BASIC STATISTICS …. Percentiles  Numerical measures that give the relative position of a data value relative to the entire data set.  Divide an array (raw data arranged in increasing or decreasing order of magnitude) into 100 equal parts.  The jth percentile, denoted as Pj, is the data value in the the data set that separates the bottom j% of the data from the top (100-j)%.
  • 34. Session 1.34 TEACHING BASIC STATISTICS …. EXAMPLE Suppose LJ was told that relative to the other scores on a certain test, his score was the 95th percentile.  This means that (at least) 95% of those who took the test had scores less than or equal to LJ’s score, while (at least) 5% had scores higher than LJ’s.
  • 35. Session 1.35 TEACHING BASIC STATISTICS …. Deciles  Divide an array into ten equal parts, each part having ten percent of the distribution of the data values, denoted by Dj.  The 1st decile is the 10th percentile; the 2nd decile is the 20th percentile…..
  • 36. Session 1.36 TEACHING BASIC STATISTICS …. Quartiles  Divide an array into four equal parts, each part having 25% of the distribution of the data values, denoted by Qj.  The 1st quartile is the 25th percentile; the 2nd quartile is the 50th percentile, also the median and the 3rd quartile is the 75th percentile.
  • 37. Session 1.37 TEACHING BASIC STATISTICS …. Measures of Variation  A measure of variation is a single value that is used to describe the spread of the distribution A measure of central tendency alone does not uniquely describe a distribution
  • 38. Session 1.38 TEACHING BASIC STATISTICS …. Mean = 15.5 s = 3.33811 12 13 14 15 16 17 18 19 20 21 11 12 13 14 15 16 17 18 19 20 21 Data B Data A Mean = 15.5 s = .9258 11 12 13 14 15 16 17 18 19 20 21 Mean = 15.5 s = 4.57 Data C A look at dispersion…
  • 39. Session 1.39 TEACHING BASIC STATISTICS …. Two Types of Measures of Dispersion Absolute Measures of Dispersion:  Range  Inter-quartile Range  Variance  Standard Deviation Relative Measure of Dispersion:  Coefficient of Variation
  • 40. Session 1.40 TEACHING BASIC STATISTICS …. Range (R) The difference between the maximum and minimum value in a data set, i.e. R = MAX – MIN Example: Pulse rates of 15 male residents of a certain village 54 58 58 60 62 65 66 71 74 75 77 78 80 82 85 R = 85 - 54 = 31
  • 41. Session 1.41 TEACHING BASIC STATISTICS …. Some Properties of the Range  The larger the value of the range, the more dispersed the observations are.  It is quick and easy to understand.  A rough measure of dispersion.
  • 42. Session 1.42 TEACHING BASIC STATISTICS …. Inter-Quartile Range (IQR) The difference between the third quartile and first quartile, i.e. IQR = Q3 – Q1 Example: Pulse rates of 15 residents of a certain village 54 58 58 60 62 65 66 71 74 75 77 78 80 82 85 IQR = 78 - 60 = 18
  • 43. Session 1.43 TEACHING BASIC STATISTICS …. Some Properties of IQR  Reduces the influence of extreme values.  Not as easy to calculate as the Range.
  • 44. Session 1.44 TEACHING BASIC STATISTICS …. Variance  important measure of variation  shows variation about the mean Population variance Sample variance N X N i i∑= − = 1 2 2 )( µ σ 1 )( 1 2 2 − − = ∑= n xx s n i i
  • 45. Session 1.45 TEACHING BASIC STATISTICS …. Standard Deviation (SD)  most important measure of variation  square root of Variance  has the same units as the original data Population SD Sample SD N X N i i∑= − = 1 2 )( µ σ 1 )( 1 2 − − = ∑= n xx s n i i
  • 46. Session 1.46 TEACHING BASIC STATISTICS …. (Sample) Data: 10 12 14 15 17 18 18 24 n = 8 Mean =16 309.4 7 2)1624(2)1618(2)1617(2)1615(2)1614(2)1612(2)1610( = −+−+−+−+−+−+− =s Computation of Standard Deviation
  • 47. Session 1.47 TEACHING BASIC STATISTICS …. Remarks on Standard Deviation  If there is a large amount of variation, then on average, the data values will be far from the mean. Hence, the SD will be large.  If there is only a small amount of variation, then on average, the data values will be close to the mean. Hence, the SD will be small.
  • 48. Session 1.48 TEACHING BASIC STATISTICS …. Mean = 15.5 s = 3.33811 12 13 14 15 16 17 18 19 20 21 11 12 13 14 15 16 17 18 19 20 21 Data B Data A Mean = 15.5 s = .9258 11 12 13 14 15 16 17 18 19 20 21 Mean = 15.5 s = 4.57 Data C Comparing Standard Deviations (comparable only when units of measure are the same and the means are not too different from each other)
  • 49. Session 1.49 TEACHING BASIC STATISTICS …. Example: Team A - Heights of five marathon players in inches 5” 65 “ 65 “ 65 “ 65 “ 65 “ Mean = 65 S = 0 Comparing Standard Deviations
  • 50. Session 1.50 TEACHING BASIC STATISTICS …. Example: Team B - Heights of five marathon players in inches 62 “ 67 “ 66 “ 70 “ 60 “ Mean = 65” s = 4.0” Comparing Standard Deviation
  • 51. Session 1.51 TEACHING BASIC STATISTICS …. Properties of Standard Deviation  It is the most widely used measure of dispersion. (Chebychev’s Inequality)  It is based on all the items and is rigidly defined.  It is used to test the reliability of measures calculated from samples.  The standard deviation is sensitive to the presence of extreme values.  It is not easy to calculate by hand (unlike the range).
  • 52. Session 1.52 TEACHING BASIC STATISTICS …. Chebyshev’s Rule It permits us to make statements about the percentage of observations that must be within a specified number of standard deviation from the mean The proportion of any distribution that lies within k standard deviations of the mean is at least 1-(1/k2 ) where k is any positive number larger than 1. This rule applies to any distribution.
  • 53. Session 1.53 TEACHING BASIC STATISTICS …. For any data set with mean (µ) and standard deviation (SD), the following statements apply: At least 75% of the observations are within 2SD of its mean. At least 88.9% of the observations are within 3SD of its mean. Chebyshev’s Rule
  • 54. Session 1.54 TEACHING BASIC STATISTICS …. Illustration At least 75% At least 75% of the observations are within 2SD of its mean.
  • 55. Session 1.55 TEACHING BASIC STATISTICS …. Example The midterm exam scores of 100 STAT 1 students last semester had a mean of 65 and a standard deviation of 8 points. Applying the Chebyshev’s Rule, we can say that: 1. At least 75% of the students had scores between 49 and 81. 2. At least 88.9% of the students had scores between 41 and 89.
  • 56. Session 1.56 TEACHING BASIC STATISTICS …. Coefficient of Variation (CV)  measure of relative variation  usually expressed in percent  shows variation relative to mean  used to compare 2 or more groups  Formula : 100%×      = Mean SD CV
  • 57. Session 1.57 TEACHING BASIC STATISTICS …. Comparing CVs  Stock A: Average Price = P50 SD = P5 CV = 10%  Stock B: Average Price = P100 SD = P5 CV = 5%
  • 58. Session 1.58 TEACHING BASIC STATISTICS …. Measure of Skewness  Describes the degree of departures of the distribution of the data from symmetry.  The degree of skewness is measured by the coefficient of skewness, denoted as SK and computed as, ( ) SD MedianMean K − = 3 S
  • 59. Session 1.59 TEACHING BASIC STATISTICS …. What is Symmetry? A distribution is said to be symmetric about the mean, if the distribution to the left of mean is the “mirror image” of the distribution to the right of the mean. Likewise, a symmetric distribution has SK=0 since its mean is equal to its median and its mode.
  • 60. Session 1.60 TEACHING BASIC STATISTICS …. SK > 0 positively skewed Measure of Skewness SK < 0 negatively skewed
  • 61. Session 1.61 TEACHING BASIC STATISTICS …. Measure of Kurtosis  Describes the extent of peakedness or flatness of the distribution of the data.  Measured by coefficient of kurtosis (K) computed as, ( )4 1 4 3 N i i X K N µ σ = − = − ∑
  • 62. Session 1.62 TEACHING BASIC STATISTICS …. K = 0 mesokurtic K > 0 leptokurtic K < 0 platykurtic Measure of Kurtosis
  • 63. Session 1.63 TEACHING BASIC STATISTICS …. Box-and-Whiskers Plot  Concerned with the symmetry of the distribution and incorporates measures of location in order to study the variability of the observations.  Also called as box plot or 5-number summary (represented by Min, Max, Q1, Q2, and Q3).  Suitable for identifying outliers.
  • 64. Session 1.64 TEACHING BASIC STATISTICS …. The diagram is made up of a box which lies between the first and third quartiles. The whiskers are the straight lines extending from the ends of the box to the smallest and largest values that are not outliers. Box-and-Whiskers Plot
  • 65. Session 1.65 TEACHING BASIC STATISTICS …. Steps to Construct a Box-and-Whiskers plot Step 1: Draw a rectangular box whose left edge is at the Q1 and whose right edge is at the Q3 so the box width is the IQR. Then draw a vertical line segment inside the box where the median is found. Q1 Q3Md 75 78 85
  • 66. Session 1.66 TEACHING BASIC STATISTICS …. Step 2: Place marks at distances 1.5 IQR from either end of the box. (1.5 IQR =15) 100 Q1 Q3Md 75 78 8560 1.5 IQR 1.5 IQR Steps to Construct a Box-and-Whiskers plot
  • 67. Session 1.67 TEACHING BASIC STATISTICS …. Step 3:Draw the horizontal line segments known as the “whiskers” from each of the end box to the largest and smallest values in the data set that are not outliers. (An observation beyond ±1.5 IQR is an outlier.) Steps to Construct a Box-and-Whiskers plot
  • 68. Session 1.68 TEACHING BASIC STATISTICS …. Step 4: For every outlier, draw a dot. If two or more dots have the same values, draw the dots side by side. Q1 Q3 Md 75 78 8560 100 1.5 IQR 1.5 IQR 9855 . . Steps to Construct a Box-and-Whiskers plot