Introduction to statistics

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.

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 = iX
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
QuantitativeQualitative
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

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