What is Statistics?

It is difficult to define Statistics in a few words since its dimension, scope, function; use &

importance are constantly changing over time.

Facts & figures about any phenomenon whether it relates to population, production, income,

expenditure, sales, birth or death or any other quantitative measures of phenomenon or events are

called Statistics.

What are statistical methods?

The methods of analyzing statistical data are called statistical methods. There are two methods:

Experimental Method

Observational Method

What is Inferential Statistics?

In inferential statistics, it deals with techniques used for analysis of data, making the estimates

and drawing conclusions from limited information taken on sample basis and testing the

reliability of the estimates.

It provides the bases for predictions, forecasts, and estimates that are used to transform

information into knowledge.

e.g.; suppose we want to have an idea about the percentage of illiterates in our country. We take

a sample from the population and find the proportion of illiterates in the sample. This sample

proportion with the help of probability enables us to make some assumption about the population

proportion. This study belongs to inferential statistics.

What is Statistical Forecasting?

Statistical forecasting concentrates on using the past to predict the future by identifying trends,

patterns and business drives within the data to develop a forecast. This forecast is referred to as a

statistical forecast because it uses mathematical formulas to identify the patterns and trends while

testing the results for mathematical reasonableness and confidence.

What are the major functions of Statistics?

Some of its important functions are given below:

It presents facts in a definite form.

Statistics simplifies mass of figures. It helps in presenting complex data in a suitable

tabular, diagrammatic and graphic form for an easy and clear comprehension of the data.

It facilitates comparison.

It helps in formulating and testing hypothesis.

It helps in making decisions.

It helps in the formulation of suitable policies.

What are the scopes of statistics?

Statistics plays a vital role in every fields of human activity. Statistics has important role in

determining the existing position of per capita income, unemployment, population growth rate,

housing, schooling medical facilities etc…in a country. Now statistics holds a central position in

almost every field like Industry, Commerce, Trade, Physics, Chemistry, Economics,

Mathematics, Biology, Botany, Psychology, Astronomy etc…, so application of statistics is very

wide.

What are the limitations of statistics?

The important limitations of statistics are:

1. Statistics laws are true on average. Statistics are collections of facts. So single

observation is not a statistics, it deals with groups and aggregates only.

2. Statistical methods are best applicable on quantitative data.

3. Statistical cannot be applied to assorted data.

4. It sufficient care is not exercised in collecting, analyzing and interpretation the data,

statistical results might be misleading.

5. Only a person who has an expert knowledge of statistics can handle statistical data

efficiently.

6. Some errors are possible in statistical decisions. Particularly the inferential statistics

involves certain errors. We do not know whether an error has been committed or not.

What is data?

The term data refers to groups of information that represent the qualitative or quantitative

attributes of a variable or set of variables.

What are the sources of Data?

The data can be collected from:

i. Direct field operation such as census

ii. Already published data

Data can be broadly categorized into two types depending on their sources:

Primary Data:

The primary data are the first hand information collected, compiled and published by

organization for some purpose. They are most original data in character and have not undergone

any sort of statistical treatment.

Example: Population census reports are primary data because these are collected, complied and

published by the population census organization.

Secondary Data:

The secondary data are the second hand information which is already collected by someone

(organization) for some purpose and are available for the present study. The secondary data are

not pure in character and have undergone some treatment at least once.

Example: Economics survey of England is secondary data because these are collected by more

than one organization like Bureau of statistics, Board of Revenue, the Banks etc…

How to design questionnaire?

The steps required to design a questionnaire include:

1. Defining the Objectives of the survey

2. Determining the Sampling Group

3. Writing the Questionnaire

Pretesting a questionnaire

To determine the effectiveness of your survey questionnaire, it is necessary to pretest it

before actually using it. Pretesting can help you determine the strengths and weaknesses of

your survey concerning question format, wording and order.

There are two types of survey pretests: participating and undeclared.

Participating pretests dictate that you tell respondents that the pretest is a practice run;

rather than asking the respondents to simply fill out the questionnaire, participating pretests

usually involve an interview setting where respondents are asked to explain reactions to

question form, wording and order. This kind of pretest will help you determine whether the

questionnaire is understandable.

When conducting an undeclared pretest, you do not tell respondents that it is a pretest.

The survey is given just as you intend to conduct it for real. This type of pretest allows you to

check your choice of analysis and the standardization of your survey. According to Converse

and Presser (1986), if researchers have the resources to do more than one pretest, it might be

best to use a participatory pretest first, then an undeclared test.

Editing of Data:

After collecting the data either from primary or secondary source, the next step is editing.

Editing means the examination of collected data to discover any error and mistake before

presenting it. It has to be decided before hand what degree of accuracy is wanted and what

extent of errors can be tolerated in the inquiry. The editing of secondary data is simpler than

that of primary data.

Q: How the data can be presented?

Data can be presented as:

i. Tabulated form such as frequency distribution table

ii. Charting

Diagrams

Graphs

Type of data classification

The process of arranging data into homogenous group or classes according to some common

characteristics present in the data is called classification.

Geographical classification:

When the data are classified by geographical regions or location, like states, provinces,

cities, countries etc…

Chronological classification:

When the data are classified or arranged by their time of occurrence, such as years,

months, weeks, days etc… For Example: Time series data.

Qualitative Base:

When the data are classified according to some quality or attributes such as sex, religion,

literacy, intelligence etc…

Quantitative Base:

When the data are classified by quantitative characteristics like heights, weights, ages,

income etc…

Tabulation of table

Parts of table:

Table number

Each table should be numbered. There are different practices with regard to the place

where this number is to be given. Table number helps to give easy reference.

The Title:

A title is the main heading written in capital shown at the top of the table. It must explain

the contents of the table and throw light on the table as whole different parts of the

heading can be separated by commas there are no full stop be used in the little.

Caption:

The vertical heading and subheading of the column are called columns captions. The

horizontal headings and sub heading of the row are called row captions.

Stub:

The space where the rows headings are written is called stub. Stubs are the designation of

rows or rows heading.

The Body:

It is the main part of the table which contains the numerical information classified with

respect to row and column captions.

Head Notes:

A statement given below the title and enclosed in brackets usually describe the units of

measurement is called head notes.

Foot Notes:

It appears immediately below the body of the table providing the further additional

explanation.

Types of table:

Simple table:

In a simple table only one character is shown. Hence, this type of table is also known as

one-way table.

Complex table:

In a complex table two or more character are shown. Complex tables enable fill

information to be incorporated and facilitate a proper consideration of all related facts.

General purpose table:

General purpose tables, also known as the reference tables or repository tables, provide

information for general use or reference.

Special purpose table:

Special purpose tables, also known as summary or analytical tables, provide information

for particular discussion. They show relationship between two different groups of figures.

11. Charting data

Diagrams:

A diagram is a two-dimensional geometric symbolic representation of information.

Graphs:

In mathematics, a graph is an abstract representation of a set of objects where some pairs

of the objects are connected by links. The interconnected objects are represented by

mathematical abstractions called vertices, and the links that connect some pairs of

vertices are called edges. Typically, a graph is depicted in diagrammatic form as a set of

dots for the vertices, joined by lines or curves for the edges.

12. Types of diagrams:

One-dimensional diagrams e.g. bar diagram:

In this these diagrams there are bars/ thick lines, of which only the length matter not the

width. When a large number of observations are to be compared, these are the only form

that can be used effectively.

Two-dimensional diagrams:

Here the length as well as the width of the bars is considered. Thus the area of the bar

represents the given data.

Pictograms:

A pictogram is an ideogram that conveys its meaning through its pictorial resemblance to

a physical object.

Cartograms:

A cartogram is a map in which some thematic mapping variable – such as travel time or

Gross National Product – is substituted for land area or distance.

Types of bar diagrams

Simple bar diagrams: A simple bar chart is used to represents data involving only one

variable classified on spatial, quantitative or temporal basis.

Sub-divided bar diagrams: Sub-divided or component bar chart is used to represent

data in which the total magnitude is divided into different or components.

Multiple bar diagrams: By multiple bars diagram two or more sets of inter-related data

are represented (multiple bar diagram facilities comparison between more than one

phenomenon)

Percentage bar diagrams: Sub-divided bar chart may be drawn on percentage basis. To

draw sub-divided bar chart on percentage basis, we express each component as the

percentage of its respective total. In drawing percentage bar chart, bars of length equal to

100 for each class are drawn at first step and sub-divided in the proportion of the

percentage of their component in the second step.

Deviation bar diagrams: They represent net quantities which can have positive or

negative value.

Broken bars: In certain type of data there may be wide variations in values. In order to

gain space for the smallest bars of the data, the large may be broken.

In the figure below a simple bar diagram is shown:

Batting Average of Shakib Al Hasan in different years

Pie diagrams:

A pie chart (or a circle graph) is a circular chart divided into sectors, illustrating proportion. In a

pie chart, the arc length of each sector (and consequently its central angle and area), is

proportional to the quantity it represents. When angles are measured with 1 turn as unit then a

number of percent is identified with the same number of centiturns. Together, the sectors create a

full disk. It is named for its resemblance to a pie which has been sliced. The diagram below is a

Pie diagram:

0 5 10 15 20 25 30 35 40 45

2011

2010

2009

2008

No. of Students in Different Faculties in NSU

BBA

English

Physics

Economics

Graphs

i) Graphs of time series or line graphs: A time-series graphs is a line graph where

time is measured on the horizontal axis and the variable being observed is measured

on the vertical axis. It is of two types

a)Range chart: It is a method of showing the range of variation, i.e. the minimum and maximum

value of a variable. In the fig below a range chart is shown:

Range Chart for Missing Doses/ Nursing Unit- ICU’s

b) Band Graph: It is a type of line graph which shows the total for successive time periods

broken up into sub-totals for each of the component parts of the total. In other words, band graph

shows how and in what proportion the individual items comprising the aggregate are distributed.

In the fig below a band graph is shown:

Taste Band Clearance Profile

ii) Graphs of frequency distribution:

a) Histogram: A histogram consists of tabular frequencies, shown as adjacent rectangles,

erected over discrete intervals (bins), with an area equal to the frequency of the observations in

the interval. In the fig below a Histogram is shown:

Salary of Employees in a company

b) Frequency polygon: It is a graph of frequency distribution. It has more than four sides. It is

particularly effective in comparing two or more frequency distribution.

Annual Transaction Count

c) Smoothed frequency curve: It can be drawn through the various points of the polygon. The

curve is drawn freehanded in such a manner that the area included under the curve is

approximately the same as that of the polygon.

Smoothed Frequency Curve

d)Cumulative frequency curves or ‘Ogive’: Data may be expressed using a single line. An

ogive (a cumulative line graph) is best used when you want to display the total at any given

time. The relative slopes from point to point will indicate greater or lesser increases; for

example, a steeper slope means a greater increase than a more gradual slope. An ogive,

however, is not the ideal graphic for showing comparisons between categories because it simply

combines the values in each category and thus indicates an accumulation, a growing or

lessening total. If you simply want to keep track of a total and your individual values are

periodically combined, an ogive is an appropriate display.

Ogive

16. Frequency Distribution: In statistics, a frequency distribution is a tabulation of the values

that one or more variables take in a sample. Each entry in the table contains the frequency or

count of the occurrences of values within a particular group or interval, and in this way the table

summarizes the distribution of values in the sample.

Name of the Family No. of Members in Family

Turin 8

Lemon 5

Tulish 4

Nayim 9

No. of Members in different Families

Formation of frequency distribution:

a) Grouped data: Data which have been arranged in groups or classes rather than showing all

the original figures.

b) Ungrouped data: Data that has not been organized into groups.

c)Class limits: This is the lowest and the highest value that can be included in the class.

d)Class intervals: The span of the class, which is the difference between the upper limit and

the lower limit, is known as class intervals.

e)Class frequency: The number of observations corresponding to the particular class is known

as class frequency.

f)Class mid-point: It is the value lying half-way between the lower and the upper class limit of

a class interval.

d)Exclusive method: When the class intervals are so fixed that the upper limit of one class is

the lower limit of the next class, it is known as the ‘exclusive method’ of classification.

e) Inclusive method: Under the ‘inclusive method’ of classification, the upper limit of one

class is included in that class itself.

Principals of classification:

The number of classes should preferably be between 5 and 15.

As far as possible one should avoid odd values of class-intervals e.g. 3,7,11, etc.

The starting point i.e., the lower limit of the first class, should either be 0 or 5 or multiple

of 5.

To ensure continuity and to get correct class-interval we should adopt ‘exclusive’ method

of classification. However, where ‘inclusive’ method has been adopted it is necessary to

make an adjustment to determine the class-interval and to have continuity.

Whenever possible all classes should be of the same size.

References:

http://en.wikipedia.org/

www.emathzone.com

Business Statistics” by S.P. GUPTA & M.P. GUPTA

An Introduction to Statistics & Probability by M. Nurul Islam

School Of Business

North South University

Semester: Fall 2010

Course code: BUS172

Course Title: Introduction To Statistics

Submitted By

xxxxxxxxxxxxxx

Submitted to

xxxxxxxxxxxxxx

Prepared By

Dept. of APECE (2008-09 Session)

University of Dhaka

lemon.apece.du@gmail.com

Sazzad Hossain Lemon