Business statistics dcm 214 notes

RECOMMENDED FOR STUDYING BUSINESS STATISTICS SUBJECT.

1. TOPIC 1 & 2 NOTES
By Mr.Abok
BUSINESS STATISTICS-DCM 214-By Mr. Abok
Meaning of statistics- Statistics may be defined as the science of collection, presentation
analysis and interpretation of numerical data.
IMPORTANCE OF STATISTICS ;
 An aid to supervision- The statistical records maintained are used to evaluate the
performance of an organization in order to enable the management decide on whether the
policies are being implemented or not.
 Base for future planning- plans prepared for the expansion of the business and the
development of a country are derived from the accurate and relevant statistical data
collected
 Eyes of administration- statistics are required by the government to study the causes and
find out the remedies of various problems of the country.
 Helpful in business- all types of business decisions are based on the future estimates and
expectations
 Helpful in data processing
Functions of statistics
 Statistics simplifies complicated data and presents them in such a manner that they at
once becomes intelligible
 The data collected by an individual will enable him to get more clear and adequate
information about that particular problem
 Statistics furnishes a technique of comparison
 Statistics endeavors to interpret conditions
 In order to form certain policies, statistics provides us with adequate numerical data
relevant to that phenomena
The use of statistics in a business organization
 Used for planning and controlling business activities
 Statistical methods help the manufacturer to check the quality of his output more
efficiently
 Time series analysis offers a statistical method for using past performance figures to help
to produce a forecast for the future
 Using sampling theory, the results from the sample can be interpreted to give information
about all invoices
 The techniques of correlation and regression enable the statistician to determine the
relationship between two variables e.g. costs and advertising
LIMITATIONS OF STATISTICS

2. TOPIC 1 & 2 NOTES
By Mr.Abok
 Statistics deals only with those objects of inquiry which are capable of being
quantitatively measured and numerically expressed. All subjects cannot be expressed in
number e.g. health, poverty and intelligence
 Statistics deals only with aggregate of facts and no importance is attached to individual
items
 Statistical data is only approximately and not mathematically correct for example greater
emphasis is put on sampling technique of collection of data
 Statistics can be used to establish wrong conclusions and, therefore, can be used only by
experts
COLLECTION, COMPILATION AND PRESENTATION OF QUANTITATIVE AND
QUALITATIVE CATEGORICAL DATA.
COLLECTION OF STATISTICAL DATA
Statistical data are actual facts and figures collected from various sources for a particular inquiry.
TYPES OF DATA
Data can be classified according to
1. By source-primary/secondary data
Primary data- is an inquiry in which the data is collected for the first time by the investigator for
a specific purpose
Secondary data- is the name given to data that are being used for some purpose rather than that
for which they were originally collected.
Distinguishing primary data from secondary data
PRIMARY DATA SECONDARY DATA
Original or basic in nature Second hand in nature
Very expensive to collect Less expensive to collect
Requires less precaution in its use Requires extra precautions in its use
Collected for very specific purpose Not collected for a particular purpose
Requires a lot of time and energy to collect Less time and energy
Methods of collecting primary data
 Direct observation- the investigator uses direct visual observation of the geographical
phenomena. Precaution needed is to choose the sites free from any kind of obstructions.

3. TOPIC 1 & 2 NOTES
By Mr.Abok
Advantages

 Data collected are highly reliable
 It is relatively cheaper
 Relevant and accurate information
Disadvantages
 Very labour intensive
 Visual impairment may limit it
 Results may be different under different conditions
 INTERVIEWS
According to this method the investigator interviews different persons and asks them
various questions relating to the problem under investigation may take form of telephone
interview or personal interview or street(informal) interview.
Advantages

 Yields reliable and accurate information
 Gives satisfactory results if scope of inquiry is narrow
 Good method for intensive inquiry
Disadvantages
 Avery expensive method if wide geographical areas is taken
 There remains possibility of interviewer bias
 Relatively more time consuming
 Informants may be reluctant to give information


 QUESTIONNAIRE METHOD
Refers to preparing a standard list of questions to be administered to the respondents.
Features of a questionnaire (essentials / prime requirements)

 Short and clear- should be short and clear so that they can be understood easily
by the informants
 Few in numbers- should be few in numbers to a void irritating the informants
 Definiteness’- frame the questions in a way that the answers to them are perfectly
definite i.e. preferably in the form of ‘yes’ or ‘no’.
 Non-confidential- should be of non –confidential in nature because nobody would
like to answer questions relating to personal or confidential aspects of life.

4. TOPIC 1 & 2 NOTES
By Mr.Abok
 Logical in sequence- should be put in some logical order to help in analyzing the
replies easily an d quickly
 Relevant questions-The questions should be relevant to the problem under
investigation
Merits

 Low cost even if the universe is large
 Free from bias
 Can be used to reach respondents who are not easily approachable
Demerits
 Low rate of return of the dully filled in questionnaires
 Can only be used if the respondents are educated and cooperating
 The control of questionnaire may be lost once sent
Sources of secondary data
 Official publications by the central or provincial governments
 Semi- official publications by the municipalities, central bank and districts board
 Publications by research institutions, Reports by business concern, different journals.


2. By preciseness-discrete or continuous data
A variable which can theoretically assume any value between two given values is called a
continuous variable, otherwise it is called a discrete variable. Numerical discrete data occur
when the measurements are integers that correspond to a count of some sort. Measurements
on a variable are discrete if only a countable number of distinct values are possible.
Measurements on a variable that result from the process of measuring rather than counting
are continuous rather than discrete. Theoretically, each measurement on a continuous
variable falls somewhere along a continuum i.e. theoretically, each measurement is capable
of being subdivided into smaller and smaller units (there is no indivisible unit). Unlike a
discrete variable a continuous variable is not limited to particular values such as the integers.
3.By number of variables: - (Univariate, Bivariate and Multivariate data)
Univariate Data:
Univariate data is used for the simplest form of analysis. It is the type of data in which analysis
are made only based on one variable. For example, there are sixty students in class VII. If the
variable marks obtained in math were the subject, then in that case analysis will be based on the
number of subjects fall into defined categories of marks.

5. TOPIC 1 & 2 NOTES
By Mr.Abok
Bivariate Data:
Bivariate data is used for little complex analysis than as compared with univariate data. Bivariate
data is the data in which analysis are based on two variables per observation simultaneously.
Multivariate Data:
Multivariate data is the data in which analysis are based on more than two variables per
observation. Usually multivariate data is used for explanatory purposes.
Two types of data: qualitative and quantitative. The way we typically define them, we call data
'quantitative' if it is in numerical form and 'qualitative' if it is not. With qualitative data there is
no measurable meaning to the “difference” in numbers. For example, one basketball player is
assigned the number “20” and another player has the number “10” we cannot conclude that the
first player is twice as good as the second player. However, with quantitative data there is a
measurable meaning to the difference in numbers. When one student scores 90 on an exam and
another student scores 45, the difference is measurable and meaningful. Notice that qualitative
data could be much more than just words or text. Photographs, videos, sound recordings and so
on, can be considered qualitative data.


PRESENTATION OF STATISTICAL DATA

I. Use of diagrams and graphs
Diagrams and graphs help to understand the information in an easy and comprehensive
form
Advantages of diagrams
 They provide an easy and attractive means of representing data
 They make the information contained in data readily intelligible
 Facilitate comparison
 Save time and labour
 Have great memorizing value as compared to mere figure
Limitations
 Can be misused easily
 Do not give accurate results but rough idea
 The method is very expensive
II. USE OF CHARTS

6. TOPIC 1 & 2 NOTES
By Mr.Abok
A) Pie charts- it is a circle divided by radial lines into sections so that the area of each
section is proportional to the size of the figure represented.
Angle of each component= 360 × Component
Total Component
Example
From the following information, construct a pie chart.
Product Sales (sh 000’s)
A 200
B 150
C 100
D 150
Total 600


Advantages of pie chart-
Useful where it is desired to show the relative proportion of the figures that make up a single
overall total
Disadvantages
Cannot be used effectively where a series of figures is involved
B) Bar charts- in bar charts, data are represented by a series of bars. Bars charts may be of the
following kinds: -
a) Simple bar charts- here data are represented by a series of bars in which the height or
length of each bar indicates the size of the figure represented.
b) Component bar charts (sub-divided bar charts)- the bars are subdivided into components
parts. They can be of the two kinds
 Actual component bar charts

7. TOPIC 1 & 2 NOTES
By Mr.Abok
 Percentage component bar charts
C) Multiple bar charts- in this type of charts, the component figures are shown as separate bar
charts adjoining each other. The height of each bar represents the actual value of the component
figure




Example
ABC Ltd is manufacturers of three products i.e. Butter, Bread and Cakes. There sales for a
period of four years were as under: -
Sales (sh 000’s)
Year Butter Bread Cakes Total
2005 50 80 40 170
2006 60 100 50 210
2007 70 110 30 210
2008 90 120 50 260
From the above information construct: -
1) Simple bar chart
2) Draw a component bar chart
3) Draw a percentage component bar chart
4) Draw a multiple bar chart
Answer

8. TOPIC 1 & 2 NOTES
By Mr.Abok







0
50
100
150
200
250
300
1 2 3 4
Total
Year
0
50
100
150
200
250
300
1 2 3 4
Cakes
Bread
Butter

9. TOPIC 1 & 2 NOTES
By Mr.Abok



Task /ASSIGNMENT I
The following table shows the details of monthly expenditure for two families A and B. Present
this data in a suitable diagram.
ITEMS A B
FOOD 40 30
CLOTHING 52 50
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
1 2 3 4
Cakes
Bread
Butter
0
20
40
60
80
100
120
140
1 2 3 4
Butter
Bread
Cakes

10. TOPIC 1 & 2 NOTES
By Mr.Abok
RENT 64 60
EDUCATION 44 40
TOTAL 200 180







D) The z- chart
It is simply a time series chart incorporating 3 curves for individual monthly figures, Monthly
cumulative figures for the year, a moving annual total
Example
The following are the sales of ABC Ltd for the years 1995 and 1996
Month Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec
1995 400 480 420 580 600 800 750 600 550 500 600 900
1996 420 450 600 640 580 700 800 750 600 480 550 950
REQUIRED: Construct a z chart for the year 1996.
TABULATION OF DATA IN DATA ORGANIZATION PROCESS
This is a systematic arrangement of the statistical data in columns and rows. The main advantage
of tabulation is that a mass of data which is confusing the mind is presented in a logical sequence
giving the shape of statistical tables which answer all the questions of the problem under
investigation.
Advantages
 Tabulated data can be understood easily as compared to data given in narrative form
 The comparison between different classes of data can be made easily

11. TOPIC 1 & 2 NOTES
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 The required data can be located easily.
 The unnecessary details are avoided
 Tabulated data takes less space
Principle of table construction/Features of a good table
 The table should be self-explanatory and easy to understand
 Each table should have a title
 Should have a suitable size
 The source the data must be stated
 Headings of columns and rows should be clear
 The units of measurements should be clearly mentioned

Example
In January 1995, A firm employed 90 staff whom 79 were men. During the year 17 staff left and
13 of these were men. The total recruitment during the year was 13 of whom 3 were women.
During 1996 wastage declined by 3 amongst men compared with 1995 and no women left. 6
more men but 2 fewer women were recruited than in the previous year. The total number
employed on 1
st
January 1997 amounted to 93.
Arrange the above information in a concise tabular form showing all relevant totals and sub-
totals
Solution;
Employees of the firm
1995 1996
Men Women Total Men Women Total
Employees
as at
January 1
79 11 90 76 10 86
Recruited
during the
year
10 3 13 16 1 17
Left during
the year
(13) (4) (17) (10) - (10)

12. TOPIC 1 & 2 NOTES
By Mr.Abok
Total 76 10 86 82 11 93

Source: Payroll




Example 2
The city of Kisumu was divided into three areas: The administrative district, other Urban
districts, and rural districts. A survey of housing conditions was carried out and the following
information was gathered: There were 677,100 buildings of which 176,100 were in rural
districts. Of the buildings in other urban districts 4, 06,400 were inhabited and 4,500 were under
construction. In the administrative districts 4,000 buildings were inhabited and 500 were under
construction of the total of 61,600. The total buildings in the city that are under construction are
6,200 and those uninhabited are 44,900. Tabulate the above information so as to give the
maximum possible statistical information. How many buildings are under construction in rural
areas?
Solution: -
Table showing the distribution of buildings in the three districts of Kisumu according to
inhabitation (in hundreds)

District Inhabited Uninhabited Under
construction
Total
Administrative 571 40 5 616
Other Urban 4,064 285 45 4,394
Rural 1,625 124 12 1,761
Total 6,260 449 62 6,771
There were 1,200 buildings under construction in rural areas.

13. TOPIC 1 & 2 NOTES
By Mr.Abok
SAMPLING TECHNIQUES
SAMPLING- Is the process of examining a representative number of items out of the whole
universe (population).
Population- is the set of all the individual or objects which have a given characteristic.
A sample- is a relatively small subset of a population
Sampling frame- is a complete list of all items of a population, for example a complete list of all
the students in a university.
Sampling design- is a definite statistical plan concerned with all principle steps taken in
selection of a sample and the estimation procedure to be carried.
Sample survey- process of collecting data from a sample i.e. asking the selected voters their
political views.
Pilot survey- Is a trial run carried out by sampling a very small proportion of the sample which
will be used in the final survey
Census-the process of collecting data from the entire population
Reasons for sampling(benefits)
 Cost- saving: -a sample will cost much less than the entire population
 Ease of Control- a sample survey is easier to control than a complete census
 Speed- time taken to collect data from a sample is much shorter
 Quality- when only few subjects are studied, there will be better quality
 More detailed information can be obtained from a sample survey than from census
 Sampling errors can as well be estimated especially in case of random sample inquiry.
 The results obtained by sampling are more accurate than those of census
The sample size
The larger the sample size the more precise will be the information given about the population
and vice versa is true.
General factors involved in the selection of a sample size
 Availability of money, time and man power.
 Aims of the inquiry
 Complexity of the inquiry
 Degree of the precision required
 Number of sub samples required
 The availability of the sampling frame

14. TOPIC 1 & 2 NOTES
By Mr.Abok





METHODS OF SAMPLING
Important features of a good sampling techniques;
 The sample should be a true representative of the universe from where it is drawn
 There should remain no bias in selecting a sample
 It should be possible to measure or estimate the sampling error
 The results of the sample study in general should be applicable to all items of the
universe
Methods are:
A. NON-PROBABILITY SAMPLING TECHNIQUES

Sampling procedures which do not afford any bias for estimating the probability that each item
in the population has of being included in the sample.
a) Quota sampling- under this method the interviewer is simply given quotas to be filled from
the different strata with some restrictions on how they are to be filled. To avoid undue bias,
the quota is subdivided into various categories e.g. male/female, young/old,
working/unemployed
Merits
 Sampling is very convenient and relatively inexpensive
 Normally used for large populations
Demerits
 Sampling is non-random and thus selection bias can be significant
 Severe interviewer bias can be introduced into the survey by inexperienced or
untrained interviewers
b) Purposive sampling (judgmental sampling) or deliberate- a method in which one uses
his/her own judgments to select cases that will best enable him/her to answer her/his
research question(s) and to meet her/his objectives
Merits
 Ideal for very small samples such as case study
Demerits

15. TOPIC 1 & 2 NOTES
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 The element of bias is always there
 Sampling error cannot be estimated
c) Snowball sampling- in snowball sampling the researcher selects a respondent known to
him/her to poses the desired characteristics. After obtaining the information required, the
respondent direct/leads the researcher to his/her next respondent with similar
characteristics. This is repeated until the desired sample size is attained
d) Convenience sampling- involves selecting haphazardly those cases that are easiest to
obtain for your sample

Merits
 Widely used
Demerits
 Prone to bias and influences that are beyond one’s control
PROBABILITY SAMPLING METHODS
a) Systematic sampling – is a sampling technique in which we select some starting point
and then selecting every k
th
element.
Merits
 Very easy and economical
 Saves time
 Can be used where there is no sampling frame
Demerits
 Not truly random
 Lies in the presence of hidden periodicities
b) Stratified sampling- sampling method in which the population is subdivided into
homogenous (non-overlapping) subpopulations known as strata in such a way that units
within each group are similar as possible.

16. TOPIC 1 & 2 NOTES
By Mr.Abok
Example;
Assume it is required to sample 100 staff at a group of hospitals whose total staff could be
stratified as follows;
Proportion
Number selected

Doctors 200 10%
10
Nurses 600 30%
30
Auxiliary workers 800 40%
40
Administrators 400 20%
20
Total 2000 100%
100
Merits
 Sample itself is free from bias
 It is a more efficient method
Demerits
 Requires an extensive sampling frame
 Increased costs due to the extra time and manpower
c) Multistage sampling- a technique in which the population is divided into first sampling
units. The selected units are then divided into second stage units and a sample is selected.
The selected second stage units are then further subdivided into third stage unit’s etc.
Merits
 Less time and manpower is needed
 It is cheaper
Demerits
 Possible bias if a very small number of regions is selected

17. TOPIC 1 & 2 NOTES
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 The method is not truly random
d) Cluster sampling- It is a non-random sampling method which can be employed where
no sampling frame exits and often the population is distributed over some geographical
area. It therefore involves grouping the population and then selecting the groups
(clusters) rather than individual elements.
Merits
 Generally cheaper.
Demerits
 Sampling is not truly random and thus selection is biased
e) Simple random sampling
Refers to a sampling technique in which every item has equal chance of being included in the
sample. Example includes raffle tickets, rotating drum method etc.