unit i-chapter 1-collection & presentation of data

7/31/2019 Unit I-chapter 1-Collection & Presentation of Data

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BUSINESS STATISTICS

UNIT 1 - COLLECTION &

PRESENTATION OF DATA

6/27/2012KOPPAR & ASSOCIATES, CHARTEREDACCOUNTANTS


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HISTORICAL PERSPECTIVE

The word 'Statistics' is derived from the Latin word 'Statis'which means a "political state."

Clearly, statistics is closely linked with the administrativeaffairs of a state such as facts and figures regarding defenseforce, population, housing, food, financial resources etc.

The word 'statistics' is defined by Croxton and Cowden asfollows:-

"The collection, presentation, analysis and interpretationof the numerical data."



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INTRODUCTION

Definition of Statistics:

Statistics is the scientific method employed for collecting,analyzing and presenting data, leading finally to drawing

statistical inferences about important characteristics.

Statistics may also be defined as data qualitative as well asquantitative , that are collected for statistical analysis.



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STAGES OF STATISTICAL INVESTIGATION

There are 5 stages of statistical investigation. They are:

1. Collection

2. Organization

3. Presentation

4. Analysis

5. Interpretation



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LIMITATIONS OF STATISTICS Statistics deals with the aggregate. An individual has no

significance except the fact that it is a part of the aggregate.

Statistics is concerned with qualitative data. However, qualitativedata can also be converted to quantitative data.

Future projection of sales, production, price and quantity etc arepossible under some specific conditions. If any of theseconditions are violated, projections are likely to be inaccurate.

The theory of statistical inferences is built upon randomsampling. If rules of random sampling are not followed, theconclusions from the unrepresentative sampling would beinaccurate.



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COLLECTION OF DATA

Data may be defined as quantitative information aboutparticular characteristic(s) under consideration.

For statistical analysis of a given characteristic, qualitativedata must be converted to quantitative data by providing anumeric description to the given characteristic.

A qualitative characteristic is known as an attribute. Thegender of a baby, the colour of a flower are examples ofattributes.



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COLLECTION OF DATA

Quantitative characteristic is know as a variable. Avariable may be discrete or continuous.

A discrete variable is one which assumes a finite or acountably infinite number of isolated values. Examples arethe number of petals in a flower, the number of roadaccidents in a locality etc.

A continuous variable, on the other hand, can assume anyvalue from a given interval. Examples include height,weight, sales, profit and so on.



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COLLECTION OF DATA

We can classify data as:

PRIMARY

SECONDARY

The data collected for the first time by an investigator areknown are Primary data where as data already collected

when used by a different investigator are known as

Secondary data.



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COLLECTION OF PRIMARY DATA

Methods employed for the collection of primary data are:

i. Interview Method

ii. Mailed Questionnaire Method

iii. Observation Method



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COLLECTION OF PRIMARY DATAI) Interview Method again can be divided into:

a) Personal Interview Method: The investigator meets therespondents directly and collects the required information onthe spot from them. In case of natural calamities, the necessaryinformation may be collected more quickly and accurately byapplying this method.

b) Indirect Interview Method: Due to some practical problems inreaching the respondents directly, the investigator collectsnecessary data from the people associated with the problems.

c) Telephone Interview Method: It is quick and inexpensive wayto collect the primary data. The first two methods, though moreaccurate, are inapplicable for covering a large area. This method,though less consistent, has a wide coverage. Also the amount ofnon-responses is maximum for telephone interview method.



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COLLECTION OF PRIMARY DATA

III) Observation Method: The data are collected by directobservation or using instrument.

Although this is likely to be the best method for data

collection, it it time consuming, laborious and covers only asmall area.

Examples include obtaining data on the height and weight

of a group of students.



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ADVANTAGES OF PRIMARY DATA

Advantages:

Finding data that suits your problems or needs.

It can include a large population and wide geographicalcoverage.

Primary data is current and it can better give a realistic viewto the researcher about the topic under consideration.



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DISADVANTAGES OF PRIMARY DATA

Disadvantages:

The major disadvantage of primary data is that it has designproblems like how to design the surveys. Incompletequestionnaires always give a negative impact on research.

Usually more costly and time consuming than collectingsecondary data.

Collected after secondary data is collected.



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SECONDARY DATA Pre-existing data is secondary data.

Data gathered by another source. Some important sources of

secondary data are:

i. International sources like WHO, ILO< IMF, World Bank

ii. Government sources like Indian Agricultural Statistics by

Ministry of Food & Agriculture.iii. Private and quasi-government sources like ISI, ICAR, NCERT

iv. Unpublished sources of various research institutes,researchers.



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SECONDARY DATA

Secondary data is gathered before Primary data to find outwhat is already know about a subject before you embark on

your own investigation.

WHY? : Because possibly some of your answers may havealready been answered by other investigators.

As a general rule, a thorough research of the secondarydata should be undertaken prior to conducting primaryresearch.



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ADVANTAGES OF SECONDARY DATA The two major advantages of using secondary data in

research are time and cost savings.

Resource implications usually easier to gather thanPrimary data.

Unobtrusive already collected data.

Quality and permanence of data e.g. Governmentsurveys.



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DISADVANTAGES OF SECONDARY DATA Suitability - Secondary information pertinent to theresearch topic is either not available, or is only available ininsufficient quantities.

Cost and Access May still be difficult inspite of resourceadvantages.

Validity of some secondary data- e.g. Internet sources. Evengovernment publications and trade magazines statistics

can be misleading .

Much secondary data is several years old and may notreflect the current market conditions.



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INTERNAL DATA Secondary sources of information may be divided into two categories:

internal sources and external sources.

Internal Data includes the following:

A) Sales Data: All organizations collect information in the course oftheir everyday operations.

- Sales by territory- Sales by customer type- Prices and discounts

- Average size of order by customer, customer type, geographical area- Average sales by sales person etc.

This type of data is useful for identifying an organization's mostprofitable product and customers.



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INTERNAL DATAB) Financial data: An organization has a great deal of data within

its files on the cost of producing, storing, transporting andmarketing each of its products and product lines. Such data hasmany uses in marketing research including allowing

measurement of the efficiency of marketing operations.

C) Transport data: Companies that keep good records relating totheir transport operations are well placed to establish which arethe most profitable routes, and loads, as well as the most costeffective routing patterns.

D)Storage data: The rate of stock turn, stock handling costs,assessing the efficiency of certain marketing operations and theefficiency of the marketing system as a whole.



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DESIGNING A QUESTIONNAIREImportant characteristics of a good questionnaire are:

User-friendly format.

Gather demographic data age, gender etc when necessary. Guarantee anonymity.

Ensure ease of tabulation.

Ask well-phrased and unambiguous questions than can be

answered. Develop for completeness- ask all the information

required.

Pilot test the instrument.



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DESIGNING A QUESTIONNAIRETo construct a proper questionnaire, one must select the correct

type of questions:

Open-ended Harder to score but give richer information.

Closed- ended Offer two either/or responses (true/false;yes/no; for/against).

Multiple choice select one or more than one option.

Scaled response Gather range of values (strongly disagree,somewhat disagree, neutral, somewhat agree, strongly agree).



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SCRUTINY OF DATA

Make sure that the data is accurate as well as consistent.

Check for measurement error- during field trials.

Check for source bias - Those responsible for their compilationmay have reasons for wishing to present a more optimistic orpessimistic set of results for their organization.

Check for reliability

Use multiple sources of secondary data. These different sourcescan be cross-checked as confirmation of one another.



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CLASSIFICATION OF DATA Process of arranging data on the basis of the characteristic

under consideration into a number of groups or classesaccording to the similarities of the observations.

Classification:

Puts the data in a neat, precise and condensed form.

Makes comparison possible between variouscharacteristics.

Statistical analysis is possible only for the classified data.



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PRESENTATION OF DATA Once the data are collected and verified for their

homogeneity and consistency, we need to present them in aneat and condensed format.

Any statistical analysis is dependent on a properpresentation of the data under consideration.

Data is presented in the following ways:A. Textual Presentation

B. Tabular Presentation

C. Diagrammatic Presentation



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PRESENTATION OF DATAA) Textual Presentation: This method comprises

presenting data with the help of a paragraph or a numberof paragraphs.

The merit of this mode of presentation lies in itssimplicity. It can be taken as the first step towards theother methods of presentation.

However, textual presentation is not preferred because itis dull and comparison between different observations isnot possible.



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PRESENTATION OF DATAB) Tabular Presentation/ Tabulation:

Presentation of data with the help of statistical tablehaving a number of rows and columns and complete withreference number, title, description of rows and columns.

Guide lines for tabulation:

The table should have a self-explanatory title with a serialnumber.



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The table should be divided into Caption, Box-Head, Stuband Body. Row and column headings must explain thefigures therein.

The table should be well- balanced in length & breadth.

Data must be arranged in such a way that comparisonbetween different figures are made possible.

Presentation of data must be appealing to the eye and alsoprovide clarity.



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Units of the measurement should be clearly stated alongthe titles or headings.

Sources of the data should be given at the bottom of thedata.

In case irregularities creep in table or any feature is notsufficiently explained, references and foot notes must begiven.



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Example of Tabular Presentation:



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PRESENTATION OF DATAC) Diagrammatic Presentation: An attractive method of

presentation of data is provided by charts, diagrams andpictures.

Diagrammatic presentation can be used for both the educatedand uneducated sections of society.

Any hidden trend present in the given data can be noticed onlyin this mode of presentation.

However, compared to tabulation, this method is less accurate.



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PRESENTATION OF DATA Diagrammatic Presentations include:

I. Line Diagram / Histogram

II. Bar Diagram

III. Pie Chart



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BAR DIAGRAM

Two types: Horizontal Bar Diagram & Vertical Bar Diagram.

Horizontal BD is used for qualitative data or data varying overspace.

Vertical BD is used for quantitative data or time series data.

Bars i.e. rectangles of equal width and usually of varying lengths

are drawn either horizontally or vertically.

Multiple or Grouped BDs are used to compare related series.

6/27/2012 KOPPAR & ASSOCIATES, CHARTEREDACCOUNTANTS


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BAR DIAGRAM



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PIE CHART Disadvantages: Not Exact - Since pie charts use

percentages to illustrate numerical values, specific figuresare not provided.

Cant Compare 2 Data Sets - Pie charts are capable ofvisually displaying only one set of data.

Individuals who need to display and compare multiple sets

of data need to find another type of graph for theirpresentation. This limits the use of pie charts in morestatistically intense presentations.



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PIE CHART



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DIAGRAMS Vs. TABLES

DIAGRAMS TABLES

Diagrams and Graphs are meantfor a layman.

Diagrams give only an

approximate idea. Diagrams can be more easily

compared, and can beinterpreted by a layman.

Diagrams and graphs cannot

present much information. Diagrams are more attractive and

have a visual appeal.

Tables are meant for statisticiansfor the purpose of furtheranalysis.

Tables contain precise figures.Exact values can be read fromtables.

Comparison and interpretationsof tables can only be done bystatisticians and it is a difficulttask.

Tables can present moreinformation.

Tables are dry for a layman ( maybe attractive to a statistician.)



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FREQUENCY DISTRIBUTION Frequency may be defined as the number of times a

particular variate or a group of variate occurs.

Frequency distribution is the tabular representation ofstatistical data, usually in ascending order, relating to ameasurable characteristic according to individual value or agroup of values under study.



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SIMPLE FREQUECY DISTRIBUTION A discrete variable is one

which assumes a finite or acountably infinite number ofisolated values.

Example: the number ofrooms in a house, the numberof members in a family, thenumber of families in acolony etc.

The process of preparing thistype of distribution is verysimple. It is done by the useoftally marks.



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GROUPED FREQUENCY DISTRIBUTION A continuous variable,on the other hand, canassume any value in agiven interval.

Examples includeheight and weight,sales, profit and so on.

This table gives marksof 30 students in a class.



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EXCLUSIVE VS. INCLUSIVE METHOD There are two methods classifying the data according to the

class interval:

Exclusive method: In the exclusive type, the upper limit ofone class coincides with the lower limit of the next class.

Inclusive method: The upper limit of one class does notcoincide with the lower limit of the next class.

Inclusive type of frequency distribution can be convertedinto exclusive type by extending the class limits by 0.5



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TERMS ASSOCIATED WITH FREQUENCY

DISTRIBUTION Class interval: While arranging large amount of data (in

statistics), the variables are grouped into different classesto get an idea of the distribution, and the range of such

class of data is called the Class Interval.

Class intervals are generally equal in width and aremutually exclusive.

The ends of a class interval are called class limits, and themiddle of an interval is called a class mark.



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DISTRIBUTION Variables: A set of observations is called a called a

collection of data. These observations should possess somecommon characteristics. The quantities such as age, heightand number of students are called variables.

Class Limit: The class limits may be defined as theminimum value and the maximum value the class intervalmay contain.

The minimum value is known as the lower class limit (LCL)and the maximum value is the upper class limit (UCL)



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DISTRIBUTION Class Boundary: It may be defined as the actual class limit of the

class interval. For overlapping or mutually exclusiveclassification that excludes the UCL lie 10-20, 20-30 etc, the class

boundaries coincide with class limits. However, for non-overlapping or mutually inclusive classification that includesboth the class limits like 0-9, 10-29, 20-29, we have:

LCB = LCL D/2 and UCB= UCL +D/2

Where D is the difference between the LCL of the next class

interval and the UCL of the given class interval.



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DISTRIBUTION Cumulative Frequency:Cumulative Frequencycorresponding to a particular valueis the sum of all the frequencies up

to and including that value. The cumulative frequency

classified into two types:

Less than type cumulativefrequency

Greater than type cumulativefrequency

Weight inkg (CB(

Less than Morethan

43.50 0 36

48.50 3 33

53.50 7 29

58.50 12 24

63.50 19 17

68.50 28 8

73.50 36 0

Cumulative Frequency Distributionof weights of 36 students.



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CONSTRUCTING A FREQUENCY

DISTRIBUTION Find the largest and the smallest observation in the given data

and calculate the range , i.e. the difference between them.

Divide the range into suitable number of classes. The number ofclasses be preferably between 5 and 15 but there is no hard andfast rule.

Count the number of cases within each class.

The counts within each class are the frequencies of that class.



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GRAPHICAL REPRESENTATION OF

FREQUENCY DISTRIBUTION Graphical techniques are used for representing the values

of a grouped Frequency Distribution .

There are several graphical techniques. The mostcommonly

used graphs are :

1. Histogram

2. Frequency polygon or Frequency Curve

3. Ogive or the Cumulative Frequency Curve



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HISTOGRAM For drawing a Histogram : X axis is used to represent the

class intervals and Y axis for frequencies.

Histogram consists of a series of rectangles attached to oneanother . The height of each rectangle is proportional tothe frequency of the corresponding class .

Histogram is a convenient way to represent a frequencydistribution. A comparison among the frequencies fordifferent class intervals is possible in this mode ofdiagrammatic representation.


of broken cookies per pack yesterday.


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p p y y

Number ofbroken cookies

Number of Packs

0-5 10

6-10 5

11-15 15

16-20 5

21-25 20

26-30 25

31-35 5

36-40 10



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FREQUENCY POLYGON Usually meant for single frequency distributions. However

they can be used for representing grouped frequencydistribution, but only when all the class intervals are equal .

In such a case ,frequency of each class is plotted against themid values of that class interval.

The plotted points are joined successively by line segmentsand the figure, so drawn, is the given shape of a polygon, aclosed figure, by joining two extreme ends of the drawnfigure to two additional points .



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FREQUENCY POLYGON

We can also obtain afrequency polygonstarting with a histogramby adding the mid-

points of the upper sidesof the rectanglessuccessively and thencompleting the figure by

joining the two ends asbefore.



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Income($)

300-400

400-500

500-600

600-700

700-800

800-900

900-1000

People 18 32 35 30 21 12 4



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OGIVE or CUMULATIVE FREQUENCY GRAPH

By plotting cumulative frequency against the respective class

boundary, we get Ogives.

There are two types:

i) Less than type ogives : In drawing a less than type Ogive the

upper class boundaries are plotted along the X axis and thecorresponding less than type cumulative frequencies areplotted along the Y axis.

ii) More than type ogives: For drawing a more than type Ogivethe lower class boundaries are plotted along X axis and thecorresponding more than type Cumulative frequencies areplotted along the Y axis

There after the plotted points are joined successively by linesegments.



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OGIVE

More-

than type



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