Introduction To Statistics.ppt

 Gestor:
prof. Ing. Zlata Sojková, CSc.
zlata.sojkova@uniag.sk
 Lecturer
Ing. Jozef Palkovič, PhD.
jozef.palkovic@uniag.sk

Conditions for successful course
completion
 Method of evaluation and completion:
- credit
- exam (with a sufficient number of points, there's an
opportunity to get the grade "free of charge")
 Continuous assessment:
- two tests during the semester (mid-term test and end-
term test)
 You should get at least 50% of total points to get credit
Final evaluation:
- exam (written and verbal part)
- presenting a project
 Precondition for successful course completion: Basic
knowledge of MS Excel

Recommended literature:
 Hanke E. J, Reitsch A. G: Understanding Business
Statistics
 Anderson, D.R. - Sweeney, D.J. - Williams, T.A.: Statistics
for Business and Economics. South-Western Pub., 2005,
320 p., ISBN 978-032-422-486-3
 Jaisingh, L.R.: Statistics for the Utterly Confused. McGraw
Hill, 2005, 352 p., ISBN 978-007-146-193-1
 Everitt, B. S.: The Cambridge (explanatory) dictionary of
statistics. Cambridge University Press, 2006, 442 p., ISBN
978-052-169-027-0
 Illowsky, B. - Dean, S. (2009, August 5). Collaborative
Statistics. Retrieved from the Connexions Web site:
http://cnx.org/content/col10522/1.36
Moodle course by Martina Majorova at:
http://moodle.uniag.sk/fem/course/view.php?id=211

„There are three kinds of lies: lies,
damned lies, and statistics.“ (B.Disraeli)
Introduction To Statistics

Why study statistics?
1. Data are everywhere
2. Statistical techniques are used to make many
decisions that affect our lives
3. No matter what your career, you will make
professional decisions that involve data. An
understanding of statistical methods will help
you make these decisions efectively

Applications of statistical concepts in
the business world
 Finance – correlation and regression, index
numbers, time series analysis
 Marketing – hypothesis testing, chi-square tests,
nonparametric statistics
 Personel – hypothesis testing, chi-square tests,
nonparametric tests
 Operating management – hypothesis testing,
estimation, analysis of variance, time series
analysis

Statistics
 The science of collectiong, organizing,
presenting, analyzing, and interpreting data to
assist in making more effective decisions
 Statistical analysis – used to manipulate
summarize, and investigate data, so that useful
decision-making information results.

Introduction To Statistics.ppt

Types of statistics
 Descriptive statistics – Methods of organizing,
summarizing, and presenting data in an
informative way
 Inferential statistics – The methods used to
determine something about a population on the
basis of a sample
 Population –The entire set of individuals or objects
of interest or the measurements obtained from all
individuals or objects of interest
 Sample – A portion, or part, of the population of
interest

Inferential Statistics
 Estimation
 e.g., Estimate the population
mean weight using the sample
mean weight
 Hypothesis testing
 e.g., Test the claim that the
population mean weight is 70 kg
Inference is the process of drawing conclusions or making decisions
about a population based on sample results

Sampling
a sample should have the same characteristics
as the population it is representing.
Sampling can be:
 with replacement: a member of the population
may be chosen more than once (picking the
candy from the bowl)
 without replacement: a member of the
population may be chosen only once (lottery
ticket)

Sampling methods
Sampling methods can be:
 random (each member of the population has an equal
chance of being selected)
 nonrandom
The actual process of sampling causes sampling
errors. For example, the sample may not be large
enough or representative of the population. Factors not
related to the sampling process cause nonsampling
errors. A defective counting device can cause a
nonsampling error.

Random sampling methods
 simple random sample (each sample of the same
size has an equal chance of being selected)
 stratified sample (divide the population into groups
called strata and then take a sample from each
stratum)
 cluster sample (divide the population into strata and
then randomly select some of the strata. All the
members from these strata are in the cluster sample.)
 systematic sample (randomly select a starting point
and take every n-th piece of data from a listing of the
population)

Descriptive Statistics
 Collect data
 e.g., Survey
 Present data
 e.g., Tables and graphs
 Summarize data
 e.g., Sample mean = i
X
n


Statistical data
 The collection of data that are relevant to the
problem being studied is commonly the most
difficult, expensive, and time-consuming part of
the entire research project.
 Statistical data are usually obtained by counting
or measuring items.
 Primary data are collected specifically for the
analysis desired
 Secondary data have already been compiled and
are available for statistical analysis
 A variable is an item of interest that can take on
many different numerical values.
 A constant has a fixed numerical value.

Data
Statistical data are usually obtained by counting or
measuring items. Most data can be put into the
following categories:
 Qualitative - data are measurements that each
fail into one of several categories. (hair color,
ethnic groups and other attributes of the
population)
 quantitative - data are observations that are
measured on a numerical scale (distance traveled
to college, number of children in a family, etc.)

Qualitative data
Qualitative data are generally described by words or
letters. They are not as widely used as quantitative data
because many numerical techniques do not apply to the
qualitative data. For example, it does not make sense to
find an average hair color or blood type.
Qualitative data can be separated into two subgroups:
 dichotomic (if it takes the form of a word with two
options (gender - male or female)
 polynomic (if it takes the form of a word with more
than two options (education - primary school,
secondary school and university).

Quantitative data
Quantitative data are always numbers and are the
result of counting or measuring attributes of a
population.
Quantitative data can be separated into two
subgroups:
 discrete (if it is the result of counting (the number of
students of a given ethnic group in a class, the
number of books on a shelf, ...)
 continuous (if it is the result of measuring (distance
traveled, weight of luggage, …)

Types of variables
Variables
Quantitative
Qualitative
Dichotomic Polynomic Discrete Continuous
Gender, marital
status
Brand of Pc, hair
color
Children in family,
Strokes on a golf
hole
Amount of income
tax paid, weight of
a student

Numerical scale of measurement:
 Nominal – consist of categories in each of which the number of
respective observations is recorded. The categories are in no logical
order and have no particular relationship. The categories are said to
be mutually exclusive since an individual, object, or measurement
can be included in only one of them.
 Ordinal – contain more information. Consists of distinct categories in
which order is implied. Values in one category are larger or smaller
than values in other categories (e.g. rating-excelent, good, fair, poor)
 Interval – is a set of numerical measurements in which the distance
between numbers is of a known, sonstant size.
 Ratio – consists of numerical measurements where the distance
between numbers is of a known, constant size, in addition, there is a
nonarbitrary zero point.

Data presentation
„ The question is“ said Alice, „whether you can
make words mean so many different things.“
„The question is,“ said Humpty Dumpty, „which
is to be master-that´s all.“ (Lewis Carroll)

Numerical presentation of qualitative
data
 pivot table (qualitative dichotomic statistical
attributes)
 contingency table (qualitative statistical
attributes from which at least one of them is
polynomic)
You should know how to convert absolute
values to relative ones (%).

Frequency distributions – numerical
presentation of quantitative data
 Frequency distribution – shows the frequency, or
number of occurences, in each of several
categories. Frequency distributions are used to
summarize large volumes of data values.
 When the raw data are measured on a
qunatitative scale, either interval or ration,
categories or classes must be designed for the
data values before a frequency distribution can
be formulated.

Steps for constructing a frequency
distribution
1. Determine the number of classes
2. Determine the size of each class
3. Determine the starting point for the first class
4. Tally the number of values that occur in each
class
5. Prepare a table of the distribution using actual
counts and/ or percentages (relative
frequencies)
m n

 
max min
h
m



Frequency table
 absolute frequency “ni” (Data TabData
AnalysisHistogram)
 relative frequency “fi”
Cumulative frequency distribution shows the
total number of occurrences that lie above or
below certain key values.
 cumulative frequency “Ni”
 cumulative relative frequency “Fi”

Charts and graphs
 Frequency distributions are good ways to present
the essential aspects of data collections in
concise and understable terms
 Pictures are always more effective in displaying
large data collections

Histogram
 Frequently used to graphically present interval
and ratio data
 Is often used for interval and ratio data
 The adjacent bars indicate that a numerical range
is being summarized by indicating the frequencies
in arbitrarily chosen classes

Frequency polygon
 Another common method for graphically
presenting interval and ratio data
 To construct a frequency polygon mark the
frequencies on the vertical axis and the values of
the variable being measured on the horizontal
axis, as with the histogram.
 If the purpose of presenting is comparation with
other distributions, the frequency polygon
provides a good summary of the data

Ogive
 A graph of a cumulative frequency distribution
 Ogive is used when one wants to determine how
many observations lie above or below a certain
value in a distribution.
 First cumulative frequency distribution is
constructed
 Cumulative frequencies are plotted at the upper
class limit of each category
 Ogive can also be constructed for a relative
frequency distribution.

Pie Chart
 The pie chart is an effective way of displaying the
percentage breakdown of data by category.
 Useful if the relative sizes of the data components
are to be emphasized
 Pie charts also provide an effective way of
presenting ratio- or interval-scaled data after they
have been organized into categories

Bar chart
 Another common method for graphically
presenting nominal and ordinal scaled data
 One bar is used to represent the frequency for
each category
 The bars are usually positioned vertically with
their bases located on the horizontal axis of the
graph
 The bars are separated, and this is why such a
graph is frequently used for nominal and ordinal
data – the separation emphasize the plotting of
frequencies for distinct categories

Time Series Graph
The time series graph is a graph of
data that have been measured over
time.
The horizontal axis of this graph
represents time periods and the
vertical axis shows the numerical
values corresponding to these time
periods

Introduction To Statistics.ppt

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