Its all about the introduction on statistics and tools of measurement (Scaling techniques)

1. Introduction to
Statistics
Pooja Yadav,
Research Scholar
Curaj, Ajmer
Satyender Yadav
Research Scholar,
UCCMS, MLSU, Udaipur

2. Topics to be covered
Introduction to statistics.
Types of statistics.
Data measurement.
Levels of measurement.
Important statistical terms.

3. INTRODUCTION
• The word statistics conveys a variety of meaning to people in
different walks of life.
The word statistics comes from the Italian words Statista
meaning STATEMENT
The German word Statistik meaning POLITICAL STATE
Statistics is a branch of scientific methods used in dealing with
phenomena that can be described numerically either by count or
by measurement.

4. INTRODUCTION
• Statistics refers to dealing with quantitative information. A
branch of mathematics which deals with gathering,
organizing, analyzing, and interpreting numerical data.
• Statistics is the sciences and art of dealing with figure and
facts.
• Father of statistics is GOTTFRIED ARCHENWALL.

5. DEFINITIONS
Definitions –
• Webster’s Third New International Dictionary gives a
comprehensive definition of statistics as a science dealing
with the collection, analysis, interpretation and presentation of
numerical data.
• According to W.I. King – “The science of statistics is the
method of judging collection, natural or social phenomena
from the results obtained from the analysis or enumeration or
collection of estimates.”

6. FEATURES OF STATISTICS
1. It is aggregated of facts.
2. Numerically expressed (Quantitative).
3. Affected to a marked extent by multiplicity of causes.
4. Estimated according to reasonable standard of accuracy.
5. Collecting data in a systematic manner.
6. Statistics are collected for a predetermined purpose, well defined &
specific.
7. Should be placed in relation to each other.
8. Data can’t be expressed in qualitative form.

7. STATEMENT
• All Statistics are numerical statements (data) but
all numerical statements (data) are not statistics.
• E.g. Ram has 100 Rs. In his pocket is not
statistics. The average age of 5th class is 10 yrs. is a
statistical concept.

8. TYPES OF STATISTICS
Descriptive
statistics Inferential
statistics
Statistics can be divided into two branches: Descriptive statistics and
Inferential statistics.

9. DESCRIPTIVE STATISTICS
Descriptive statistics- Descriptive statistics results from gathering data
from a body, group, or population and reaching conclusions only
about that particular group or population.
For example-
If an instructor produces statistics to summarize a class’s
examination effort and uses those statistics to reach conclusions
about that class only, the statistics are descriptive.

10. INFERENTIAL STATISTICS
Inferential statistics- Sample is collected from the group or
population and statistics is used to reach conclusions about the
group or population from which the sample was taken, this statistics
is called inferential statistics.
For example-
Testing of new drug on a small sample of patients to reach the
conclusions about the drug and make inferences about the
population.

11. INFERENTIAL STATISTICS
• Two major types of inferential statistics are:
Parametric
Statistics
Non-Parametric
Statistics

12. INFERENTIAL STATISTICS
• Parametric Statistics: Certain assumptions are made about
the distribution of the data. Only Interval and Ratio data are
used in parametric statistics .
• Non-Parametric Statistics: When there is no assumptions
made about the distribution of the data. Only Nominal and
Ordinal data are used in non-parametric statistics .

13. DATA MEASUREMENT
Scaling is an extension of the concept of measurement. It is said
the result of measurement is a scale comprises of set of numerals
on which an object score is placed using a certain rule of
assignment.
According to Adward
• “Scaling is a procedure for the assignment of numbers to a
property of objects in order to impart some of characteristics
of numbers to the properties in question”.

14. LEVELS OF DATA MEASUREMENT
Four levels of data measurement as follow:
Measurement
Nominal Ordinal Interval Ratio

15. LEVELS OF
MEASUREMENT

16. NOMINAL LEVEL
• Nominal Level :- The lowest level of data measurement is the
nominal level. Nominal level data measurement is used to
define data as numbers, alphabets or symbols without any
quantitative value. Numbers representing nominal level data
can be used only to classify or categorize.
Examples: Employee identification numbers. The numbers
are used to differentiate employees and not to make a value
statement about them.

17. ORDINAL LEVEL
• Ordinal Level :- Ordinal level data measurement is higher
than the nominal level. Ordinal level measurement can be
used to rank, order or give preference to the objects.
For example: Using ordinal data, a supervisor can evaluate
three employees by ranking their productivity with the
numbers 1 to 3.

18. INTERVAL LEVEL
• Interval Level :- Interval level data measurement is the next
to the highest level of data in which the distances between
consecutive numbers have meaning and the data are always
numerical. The distances represented by the differences
between consecutive numbers are equal; i.e. interval data
have equal intervals.
For example, when we measure temperature (in Fahrenheit),
the distance from 30-40 is same as distance from 70-80

19. RATIO LEVEL
Ratio Level :- Ratio level data measurement is the highest level
of data measurement. Ratio data have the same properties as
interval data, but ratio data have an absolute zero and the ratio of
two numbers is meaningful. The value of zero can not be
arbitrarily assigned because it represent a fixed point.
Examples of ratio data are height, weight, time, volume etc.
Note: Ratio scale is also the part of interval scale. Interval scale
ranges from negative to positive while the ratio scale starts
from positive i.e. zero “0”.

20. COMPARISON…
Descripti
on
Order/
Preference
Interval Base
“0”
Examples Tests
Nominal *** Frequency %,
Chi-square
Ordinal *** *** Mode, Median
Interval *** **** *** 0C, 0F AM, GM
Regression, Anova
Ratio *** *** *** *** Age,
weight, 0F,
Kelvin
AM, GM
Regression

21. IMPORTANT
STATISTICAL TERMS
1. Population- Population is a collection of persons, objects or items
of interest.
2. Census- A process of gathering data from the whole population for
a given measurement of interest.
3. Sample- A sample is a portion of the whole population. A sample
represents the whole population.
4. Parameter- A descriptive measure of the population is called a
parameter. Parameters are usually denoted by Greek letters.
Examples of parameters are population mean (μ), population
variance (σ2) and population standard deviation (σ).

22. • Statistic- A descriptive measure of a sample is called a statistic.
Statistic are usually denoted by Roman letters. Example of statistics
are sample mean(x̄ ), sample variance(s2) and sample standard
variation (s).
Process of Inferential Statistics to estimate a Population mean (μ)
Calculate (x̄ ) to estimate (μ)
Select a random Sample
Population (μ)
(Parameter)
Sample (x̄ )
(Statistics)
IMPORTANT
STATISTICAL TERMS

23. For any query, doubt and help please mail us at:
pujayadav026@gmail.com
yadavsatyender724@gmail.com