Introduction to statistics

Introduction to Statistics
Course Instructor : Mr.
Utkarsh Sharma

TOPICS TO BE DISCUSSED
1. Statistics in Business
 Basic statistics concept
 Types of Statistics
 Variables and data
2. Data Measurement
 Levels of data
 Comparison of the levels of data
04-05-2022 QUANTITATIVE TECHNIQUES 2

PRE-REQUISITE
The course is pitched at a beginning business school student. A prior understanding of college level algebra
would be useful.
A working knowledge of spreadsheets will help you get through the material with ease.
Bridge course for statistics
Elementary mathematics and logical reasoning

HISTORY
In early 18th
Century these got
popular
Statistics, Statistik
Statista Italian word, Meaning
“Statesman”

WHAT IS STATISTICS?
All about numbers and their
understanding to make some
actionable information.
The field of business statistics is
about collecting, analyzing and
making decisions using data for the
success of the business.
Is it that simple?
Source :Medium
Marriages made with data

WHY STATISTICS?

HOW TO USE STATISTICS?
Collect
The Data
Preprocess
The Data
Analyze The
Data
Based on the analysis, the manager will decide the
plan of action but the efforts in analysis make the
decision Good or Bad.

TYPES OF STATISTICS
Statistics
Descriptive Inferential
Descriptive – using data gathered on a
group to describe or reach conclusions
about the group.
Inferential – data gathered from a sample
and used to reach conclusions about the
population from which the data was
gathered
Used to draw conclusions about the group
or similar groups.

DESCRIPTIVE STATISTICS
Most of the statistical information reports,
magazines and in any other publications
consists of data that are summarized and
presented in a form that is easy for the
reader to understand.
Such summaries of data, may be in tabular,
graphical or numerical format are
considered as descriptive statistics as they
describe the properties of data.
Top 5 S&P 500 Companies

INFERENTIAL STATISTICS
Many situations require information about a large group of elements(
individuals, companies, voters, products, customers, and so on). But,
because of time, cost, and other considerations, data can be collected
from only a small portion of group.
The larger group of elements in a particular study is called
Population, and the smaller group is called the sample.
Using data from a sample to make estimates about the characteristics
of a population is referred to as inferential statistics.
Example:- Covid-19 vaccine efficiency calculation.

POPULATION VERSUS SAMPLE
Population — the whole
 a collection of persons, objects, or items under study
Census — gathering data from the entire population
Sample — a portion of the whole/population
 a subset of the population; must be large enough to represent the whole

PARAMETER VS. STATISTIC
Parameter — descriptive measure of the population
 Usually represented by Greek letters
Statistic — descriptive measure of a sample
 Usually represented by Roman letters

POPULATION

POPULATION AND CENSUS DATA
Identifier Color MPG
RD1 Red 12
RD2 Red 10
RD3 Red 13
RD4 Red 10
RD5 Red 13
BL1 Blue 27
BL2 Blue 24
GR1 Green 35
GR2 Green 35
GY1 Gray 15
GY2 Gray 18
GY3 Gray 17

SAMPLE AND SAMPLE DATA
Identifier Color MPG
RD2 Red 10
RD5 Red 13
GR1 Green 35
GY2 Gray 18

SYMBOLS FOR POPULATION
PARAMETERS
parameter
population
denotes

2
 denotes population variance
 denotes population standard deviation

SYMBOLS FOR SAMPLE STATISTICS
mean
sample
denotes
x
2
S denotes sam
ple variance
S denotes sample standard deviation

PROCESS OF INFERENTIAL
STATISTICS
)
(parameter
Population
1.

)
(statistic
x
Sample
3.

estimate
to
x
Calculate
4.
sample
random
a
Select
2.

TYPES OF SAMPLING
Simple Random Sampling
 There is an equal probability of selecting any particular item
Sampling without replacement
 As each item is selected, it is removed from the population
Sampling with replacement
 Objects are not removed from the population as they are selected for the sample.
 In sampling with replacement, the same object can be picked up more than once
Stratified sampling
 Split the data into several partitions; then draw random samples from each partition

STATISTICS IN BUSINESS
Inferences about parameters made under conditions of uncertainty
(which are always present in statistics)
 Uncertainty can be caused by
Randomness in selection of a sample
lack of knowledge about the source of the inferences
change in conditions not accounted for

STATISTICS IN BUSINESS
Probability is used in statistics
To estimate the level of confidence in a confidence interval
To calculate the p-value in hypothesis testing

INTRODUCTION TO DATA

WHAT IS DATA?
Collection of data objects and their
attributes
An attribute is a property or characteristic of
an object
Examples: eye color of a person,
temperature, etc.
Attribute is also known as variable, field,
characteristic, or feature
A collection of attributes describe an object
Object is also known as record, point, case,
sample, entity, or instance
Tid Refund Marital
Status
Taxable
Income Cheat
1 Yes Single 125K No
2 No Married 100K No
3 No Single 70K No
4 Yes Married 120K No
5 No Divorced 95K Yes
6 No Married 60K No
7 Yes Divorced 220K No
8 No Single 85K Yes
9 No Married 75K No
10 No Single 90K Yes
10
Objects
Attributes

ATTRIBUTE VALUES
Attribute values are numbers or symbols assigned to an attribute
Distinction between attributes and attribute values
 Same attribute can be mapped to different attribute values
 Example: height can be measured in feet or meters
 Different attributes can be mapped to the same set of values
 Example: Attribute values for ID and age are integers
 But properties of attribute values can be different
 ID has no limit, but age has a maximum and minimum value

MEASUREMENT OF LENGTH
The way you measure an
attribute is somewhat may not
match the attributes
properties.
1
2
3
5
5
7
8
15
10 4
A
B
C
D
E

LEVELS OF DATA MEASUREMENT
There are four levels of data measurment
 Nominal
 Examples: ID numbers, eye color, zip codes
 Ordinal
 Examples: rankings (e.g., taste of potato chips on a scale from 1-10), grades, height in {tall, medium, short}
 Interval
 Examples: calendar dates, temperatures in Celsius or Fahrenheit.
 Ratio
 Examples: temperature in Kelvin, length, time, counts

PROPERTIES OF ATTRIBUTE
VALUES
The type of an attribute depends on which of the following properties it
possesses:
 Distinctness: = 
 Order: < >
 Addition: + -
 Multiplication: * /
 Nominal : distinctness
 Ordinal : distinctness & order
 Interval : distinctness, order & addition
 Ratio : all 4 properties

Interval - In interval
measurement the distance
between attributes does have
meaning.
 Numerical data typically fall into
this category
 For example, when measuring
temperature (in Fahrenheit), the
distance from 30-40 is same as
the distance from 70-80. The
interval between values is
interpretable.

Ratio — in ratio measurement
there is always a reference
point that is meaningful (either
0 for rates or 1 for ratios)
 This means that you can construct a
meaningful fraction
(or ratio) with a ratio variable.
 In applied social research most
"count" variables are ratio, for
example, the number of clients in
past six months.

NOMINAL LEVEL DATA
Numbers are used to classify or categorize
Example: Employment Classification
 1 for Educator
 2 for Construction Worker
 3 for Manufacturing Worker

ORDINAL LEVEL DATA
Numbers are used to indicate rank or order
 Relative magnitude of numbers is meaningful
 Differences between numbers are not comparable
Example: Ranking productivity of employees
Example: Position within an organization
 1 for President
 2 for Vice President
 3 for Plant Manager
 4 for Department Supervisor
 5 for Employee

ORDINAL DATA
Faculty and staff should receive preferential treatment
for parking space.
1 2 3 4 5
Strongly
Agree
Agree Strongly
Disagree
Disagree
Neutral

INTERVAL LEVEL DATA
Interval Level data - Distances between consecutive integers are
equal
 Differences between numbers are comparable
 Location of origin, zero, is arbitrary
 Vertical intercept of unit of measure transform function is not zero
Example: Fahrenheit Temperature

RATIO LEVEL DATA
Highest level of measurement
 Differences between numbers are comparable
 Location of origin, zero, is absolute (natural)
 Vertical intercept of unit of measure transform function
is zero
Examples: Height, Weight, and Volume
Example: Monetary Variables, such as Profit and Loss, Revenues, Expenses,
Financial ratios - such as P/E Ratio, Inventory Turnover, and Quick Ratio.

Level of
Measurement
Description Examples Operations
Nominal The values of a nominal attribute are just
different names, i.e., nominal attributes
provide only enough information to
distinguish one object from another. (=, )
zip codes, employee ID
numbers, eye color, sex:
{male, female}
mode, entropy,
contingency
correlation, 2 test
Ordinal The values of an ordinal attribute provide
enough information to order objects. (<,
>)
hardness of minerals,
{good, better, best},
grades, street numbers
median, percentiles,
rank correlation, run
tests, sign tests
Interval For interval attributes, the differences
between values are meaningful, i.e., a unit
of measurement exists.
(+, - )
calendar dates,
temperature in Celsius or
Fahrenheit
mean, standard
deviation, Pearson's
correlation, t and F
tests
Ratio For ratio variables, both differences and
ratios are meaningful. (*, /)
temperature in Kelvin,
monetary quantities,
counts, age, mass, length,
electrical current
geometric mean,
harmonic mean,
percent variation

Attribute
Level
Transformation Comments
Nominal Any permutation of values If all employee ID numbers
were reassigned, would it
make any difference?
Ordinal An order preserving change of
values, i.e.,
new_value = f(old_value)
where f is a monotonic function.
An attribute encompassing
the notion of good, better
best can be represented
equally well by the values
{1, 2, 3} or by { 0.5, 1,10}.
Interval new_value =a * old_value + b
where a and b are constants
Thus, the Fahrenheit and
Celsius temperature scales
differ in terms of where
their zero value is and the
size of a unit (degree).
Ratio new_value = a * old_value Length can be measured in
meters or feet.

Introduction to statistics

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