3. Statistics for Management Ass-1

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Spring/February 2012

Master of Business Administration MBA Semester 1

MB0040 Statistics for Management 4 Credits

(Book ID: B1129)

AssignmentSet 1 (60 Marks)

Q1). What are the functions of Statistics? Distinguish betweenPrimary data and Secondary data?

Answer:Functions of Statistics

Statistics is used for various purposes. It is used to simplify mass data and tomake comparisons easier. It is also used to bring out trends and tendencies

in the data as well as the hidden relations between variables. All this helps tomake decision making much easier. Let us look at each function of Statisticsin detail.1. Statistics simplifies mass data

The use of statistical concepts helps in simplification of complex data. Usingstatistical concepts, the managers can make decisions more easily. Thestatistical methods help in reducing the complexity of the data andconsequently in the understanding of any huge mass of data.

2. Statistics makes comparison easier

Without using statistical methods and concepts, collection of data andcomparison cannot be done easily. Statistics helps us to compare datacollected from different sources. Grand totals, measures of central tendency,measures of dispersion, graphs and diagrams, coefficient of correlation allprovide ample scopes for comparison.

3. Statistics brings out trends and tendencies in the data

After data is collected, it is easy to analyse the trend and tendencies in thedata by using the various concepts of Statistics.

4. Statistics brings out the hidden relations between variables

Statistical analysis helps in drawing inferences on data. Statistical analysisbrings out the hidden relations between variables.

5. Decision making power becomes easier

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With the proper application of Statistics and statistical software packages onthe collected data, managers can take effective decisions, which can increasethe profits in a business.

Primary data

Data collected for the first time keeping in view the objective of the survey isknown as primary data. They are likely to be more reliable. However, cost ofcollection of such data is much higher. Primary data is collected by thecensus method. In other words, information with respect to each and everyindividual of the population is observed.

Collection of primary data can be done by any of the following methods.1. Direct personal observation2. Indirect oral interview3. Information through agencies4. Information through mailed questionnaires5. Information through schedule filled by investigators

Secondary data

Any information, that is used for the current investigation but is obtainedfrom some data, which has been collected and used by some other agency orperson in a separate investigation, or survey, is known a secondary data.

They are available in published or unpublished form.

In published form, secondary data is available in research papers, newspapers, magazines, government publication, international publication, andwebsites. Secondary data is collected for different purposes. Therefore, careshould be exercised while making use of it.

The accuracy, reliability, objectives and scope of secondary data should beexamined thoroughly before use. Secondary data may be collected either bycensus or by sampling methods.

The various sources of published data are:

Reports and official publications of international and national

organisations as well as central and state governments

Publications of several local bodies such as municipal corporations and

district boards

Financial and economic journals

Annual reports of various companies

Publications brought out by research agencies and research scholars

Some of the journals (both academic and non-academic) are published atregular intervals like yearly, monthly, weekly whereas other publications aremore ad hoc. Internet is a powerful source of secondary data, which can beaccessed at any time for any further analysis of the study.

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Q2). Draw a histogram for the following distribution

Age 0-10

10-20 20-30

30-40

40-50

No. ofpeople

5 10 15 8 2

Answer:

0

2

4

6

8

10

12

14

16

0-10 10-20 20-30 30-40 40-50

We join the upper left corner of highest rectangle to the right adjacentrectangles left corner and right upper corner of highest rectangle to leftadjacent rectangles right corner. From the intersecting point of these lineswe draw a perpendicular to the X-axis. The X-reading at that point gives themode of the distribution.

If the widths of the rectangles are not equal then we make areas ofrectangles proportional and draw the histogram.

Q3). Find the median value of the following set of values

45, 32, 31, 46, 40, 28, 27, 37, 36, 41, 47, 50

Solution:Arranging in ascending order, we get:

27, 28, 31, 32, 36, 37, 40, 41, 45, 46, 47, 50

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We have, n = 12 (even).

+=

thth

andmeanMedian 12

12

2

12

=2

4037 +

=38.5

The median for the given set of values is 38.5.

Q4). Calculate the standard deviation of the following data:

Marks 78-80

80-82

82-84

84-86

86-88

88-90

No. ofStudents

3 15 26 23 9 4

Solution:ClassInterv

al

Midvalue x

Frequency f

fx fx2 C

78-80 79 3 237 18723 79

80-82 81 15 1215 98415 81

82-84 83 26 2158 179114 83

84-86 85 23 1955 166175 8586-88 87 9 783 68121 87

88-90 89 4 356 31684 89

80 6704 562232

( ) 22

2

CN

fx

N

fxSD

=

( ) 22

280

6704

80

562232

=SD = 2.336

Standard Deviation = SD = 2.336 (mm)

Q5). An unbiased coin is tossed six times. What is the probabilitythat the tosses will result in:

i) Exactly two heads

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ii) At least five heads

Solution:Let A be the event of getting head. Given that:

Binominal distribution is =

i) The probability that the tosses will result in exactly two heads isgiven by:

Therefore, the probability that the tosses will result in exactly two heads is15/64.

ii) The probability that the tosses will result in at least five heads isgiven by:

Therefore, the probability that the tosses will result in at least five headsis 7/64.

Q6). Explain briefly the types of sampling

Answer:

The sampling techniques may be broadly classified into

1. Probability sampling2. Non-probability sampling

1. Probability Sampling:

Probability sampling provides a scientific technique of drawing samplesfrom the population. The technique of drawing samples is according to thelaw in which each unit has a probability of being included in the sample.

Simple random samplingUnder this technique, sample units are drawn in such a way each andevery unit in the population has an equal and independent chance ofbeing included in the sample. If a sample unit is replaced before drawingthe next unit, then it is known as simple Random Sampling withReplacement. If the sample unit is not replaced before drawing the nextunit, then it is case, probability of drawing a unit is 1/N, where N is thepopulation size. In the case probability of drawing a unit is 1/Nn.

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Stratified random samplingThis sampling design is most appropriate if the population isheterogeneous with respect to characteristic under study or thepopulation distribution is highly skewed.

Table: Merits and demerits of stratified random sampling

Merits Demerits1. Sample is morerepresentative

1. Many times the stratification is noteffective

2. Provides more efficientestimateeach of the stratum

2. Appropriate sample sizes are notdrawn from

3. Administratively moreconvenient4. Can be applied in situationwhere different degrees of

accuracy is desired for differentsegments of population

Systematic samplingThis design is recommended if we have a complete list of sampling unitsarranged in some systematic order such as geographical, chronological oralphabetical order.

Table: Merits and demerits of systematic sampling

Merits Demerits

1. Sample is more representative 1. Many times the stratification is not

effective

2. Provides more efficient estimate 2. Appropriate sample sizes are notdrawn from each of the stratum

3. Administratively more convenient

4. Can be applied in situation wheredifferent degrees of accuracy isdesired for different segments ofpopulation

Cluster samplingThe total population is divided into recognizable sub-divisions, known asclusters such that within each cluster they are homogenous. The units areselected from each cluster by suitable sampling techniques.

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Multi-stage samplingThe total population is divided into several stages. The sampling processis carried out through several stages.

Figure: Multistage sampling

2. Non-probability sampling:

Depending upon the object of inquiry and other considerations apredetermined number of sampling units is selected purposely so thatthey represent the true characteristics of the population.

Judgment samplingThe choice of sampling items depends exclusively on the judgment of theinvestigator. The investigators experience and knowledge about thepopulation will help to select the sample units. It is the most suitablemethod if the population size is less.

Table: Merits and demerits of judgment sampling

Merits Demerits1. Most useful for small population 1. It is not a scientific method.2. Most useful to study some unknowntraits of a population some of whosecharacteristics are known.

2. It has a risk of investigatorsbias being introduced.

3. Helpful in solving day-to-dayproblems.

Convenience samplingThe sampling units are selected according to convenience of theinvestigator. It is also called chunk which refer to the fraction of the

population being investigated which is selected neither by probability norby judgment.

Quota samplingIt is a type of judgment sampling. Under this design, quotas are set upaccording to some specified characteristic such as age groups or incomegroups. From each group a specified number of units are sampledaccording to the quota allotted to the group. Within the group theselection of sampling units depends on personal judgment. It has a risk of

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personal prejudice and bias entering the process. This method is oftenused in public opinion studies.

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3. Statistics for Management Ass-1

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