Collage of Natural and Applied Sciences

Division of Mathematics, Physics and Statistics

Course : Probability and statistics

By: Seid Belay (M.Sc.)

Email: seid.belay@aastu.edu.et

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1
Unit one
Introduction

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Introduction to Statistics
Objectives:
At the end of this session, students should be able to:
 understand basic terminologies and statistics
 understand scales of measurement in statistics

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 Definition of Statistics
In its plural sense:
o Defined as: A collection of numerical facts or figures
(or the raw data themselves). (layman def.)
o Examples:
ü Vital statistics - numerical data on marriage, births, deaths …
ü Match statistics in a game
ü Average mark of students in an exam say 70% can be
considered as statistics
ü A student score of 90%. This is not statistics, as statistics
should be an aggregate of facts not single value.

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 Definition…
In its singular sense:
o Defined as: the science that deals with the methods
of
ücollecting,
üorganizing,
üpresenting,
üanalyzing and
ü interpreting statistical data.

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 Classification of Statistics
Statistics may be divided into two main
branches:
I. Descriptive Statistics
II. Inferential Statistics

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 Classification …
Descriptive statistics:
o Includes statistical methods involving the
̶ collection,
̶ presentation(numerically or graphically), and
̶ characterization of a set of data in order to describe the
various features of the data.
o Helps to obtain Meaningful and pertinent information from raw
data
o Does not allow us to make conclusions beyond the data we have
analyzed.

Inferential statistics:
o Includes statistical methods which facilitate estimation the
characteristics of a population or making decisions concerning a
population on the basis of sample results. Includes
o Example: Estimation and hypothesis testing

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 Classification …
Example: Consider blood type of a sample of 10 students
from a class of 100 students.
O A O AB A A O O B O
ü The propor tion of O blood type in t he sampl e is 50%.
(Descriptive statistics)
ü If one wants to get information on the proportion of students
with O blood type in the entire class, one may use the sample
proportion (50%) as an estimate of the corresponding value of
the entire class. (Hence inferring population value from sample -
inferential statistics).

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Stages in statistical investigation
Has Five stages:
 1: Data collection:
o involves acquiring data related with the problem at hand.
 2: Organizing:
o involves the classification or sorting the collected data based on some
characteristics or attributes such as age, sex, marital status e t c.
 3: presenting data:
o we may use tables, graphs, charts so on to present the data
 4: Data analysis:
o Required to draw conclusions or provide answers to a problem. The analysis
might require simple or sophisticated statistical tools depending on the type of
answers that may have to be provided.
 5: Interpretation of the result:
o Statistical analysis is followed by conclusions in order to be able to make a
decision. The technical terminology used to describe this last process of a
statistical study is referred to as interpretation.
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Definition of some terms/Phrases
 A population: Consists of all elements, individuals, items or
objects whose characteristics are being studied. The population
that is being studied is called target population.
 Sample: A portion of the population selected for study.
 Sample survey: The technique of collecting information from a
portion of the population.
 Census survey: A survey that includes every member of the
population.
 Variable: is a characteristic under study that assumes different
values for different element.
 Parameter: A statistical measure obtained from a population
data. Examples include population mean, proportion, variance
and so on.
 Statistic: A statistical measure obtained from a sample data.
Examples include sample mean, proportion, variance and so on.
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Definition …
 Quantitative variable: A variable that can be measured
numerically. Weight, height, number of students in a class,
number of car accidents, e t c.
 Discrete variable: a variable whose values are countable.
Example: number patients in a hospital, number of white
blood cells in a droplet of blood sample, number of
customers ...
 Continuous variable: a variable that can assume any
numerical value over a certain interval or intervals. Examples
include weight of new born babies, height of seedlings,
temperature measurements e t c.
 Unit of analysis: The type of thing being measured in the data,
such as persons, families, households, states, nations, etc.
 Qualitative / Categorical/ variable:
o Cannot assume a numerical value but can be classified
into two or more non numerical categories.
o Examples include sex(M,F), blood type(A,B,AB,O), marital
status(S, M, W, …), religion …
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Limitation of statistics
 Statistics deals with only those subjects of inquiry which are
capable of being quantitatively measured and
numerically expressed.
 Statistics deals only with aggregates of facts and no
importance is attached to individual items
 Statistical data is only approximates and not
mathematically correct
 Statistics is liable to be misused. Hence expertise in the
subject is very essential. Besides, honesty is very important
in the use of statistics.

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Scales of measurements
Nominal scale:

v It is the simplest measurement scale.

v There is no natural ordering of the levels or values of the
scale in nominal scale.
v For example, sex of an individual may be male or female.
There is no natural ordering of the two sexes. Others
examples include religion, blood type, eye color, marital
status e t c.
v The values of nominal scale can be coded using
numerical values;
v However, we cannot perform any mathematical
operations on the numbers used to code.

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Scales …
Ordinal scale:
 This measurement scale is similar to the nominal
scale but the levels or categories can be ranked or
order.
 That is, we can compare levels or categories of the
scale.
 Therefore, this scale of measurement gives better
information on the quantities being measured as
compared to nominal scale. For example, living
standard of a family can be poor, medium or
higher.
 These categories can be ordered as poor is less
than medium and medium is less than higher class.
 However, the distance or magnitude between the
levels, say between poor and medium, is not
clearly known.
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 Scales…
Interval scale:
 This measurement scale shares the ordering or
ranking and labeling properties of ordinal scale
of measurement. Besides, the distance or
magnitude between two values is clearly known
(meaningful).
 No True Zero/ Zero is arbitrary/(i.e., zero point is
not meaningful). For example, temperature in °C,
F° of an object. If the temperature of an object is
0°C, it doesn’t mean that the object lacks heat.
This means It doesn’t make sense to say that 80°F
is twice as hot as 40° F.
 We can do subtraction and addition on interval
level data but division and multiplication are
impossible.
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Scales …
Ratio scale:
 It is the highest level of measurement scale.
 It shares the ordering, labeling and meaningful distance
properties of interval scale.
 In addition, it has a true or meaningful zero point. The
existence of a true zero makes the ratio of two measures
meaningful. example includes, weight, height e t c.
 We can do subtraction, addition, multiplication and
division on ratio level data.
 The more precise variable is ratio variable and the least
precise is the nominal variable. Ratio and interval level
data are classified under quantitative variable and,
nominal and ordinal level data are classified under
qualitative variable.
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