MB0040 – Statistics for Management

Master of Business Administration – MBA Semester 1

MB0040 – Statistics for Management – 4 Credits

(Book ID: B1129)

Assignment

Set – 1 (60 Marks)

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

Ans: Functions of Statistics

Statistics is used for various purposes. It is used to simplify mass data and to make 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 to make decision making much easier. Let us look at each function of Statistics in detail.

1. Statistics simplifies mass data

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

2. Statistics makes comparison easier

Without using statistical methods and concepts, collection of data and comparison cannot be done easily. Statistics helps us to compare data collected from different sources. Grand totals, measures of central tendency, measures of dispersion, graphs and diagrams, coefficient of correlation all provide 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 the data 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 analysis brings out the hidden relations between variables.

5. Decision making power becomes easier

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

Q2). Draw a histogram for the following distribution

Age	0-10	20-Oct	20-30	30-40	40-50
No. of people	5	10	15	12	8

We join the upper left corner of highest rectangle to the right adjacent rectangle’s left corner and right upper corner of highest rectangle to left adjacent rectangle’s right corner. From the intersecting point of these lines we draw a perpendicular to the X-axis. The X-reading at that point gives the mode of the distribution.

If the widths of the rectangles are not equal then we make areas of rectangles 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

we have, n = 12

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. of Students	3	15	26	23	9	4

Class Interval	Mid value X	Frequency ‘f’	d = x-83	fd	fd2
			2
78-80	79	3	-2	-6	12
80-82	81	15	-1	-15	15
82-84	83	26	0	0	0
84-86	85	23	1	23	23
86-88	87	9	2	18	36
88-90	89	4	3	12	36
		80		32	122

s2 =

s2 =

Standard deviation = s = 2.336 (mm)

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

      i)    Exactly two heads

     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 is given by:

Therefore, the probability that the tosses will result in exactly two heads is 15/64.

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

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

Q6). Explain briefly the types of sampling

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 Home Management Explain briefly the types of sampling.

Explain briefly the types of sampling.

6 days ago by GEP Faculty 0 .Q. Explain briefly the types of sampling.

Answer:

The sampling techniques may be broadly classified into

1.Probability sampling

2.Non-probability sampling

Probability Sampling:

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

Simple random sampling

Under this technique, sample units are drawn in such a way each and every unit in the population has an equal and independent chance of being included in the sample. If a sample unit is replaced before drawing the next unit, then it is known as simple Random Sampling with Replacement. If the sample unit is not replaced before drawing the next unit, then it is case, probability of drawing a unit is 1/N, where N is the population size. In the case probability of drawing a unit is 1/Nn.

Stratified random sampling

This sampling design is most appropriate if the population is heterogeneous with respect to characteristic under study or the population distribution is highly skewed.

Table: Merits and demerits of stratified random 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 not drawn from each of the stratum

3. Administratively more convenient 

4. Can be applied in situation where different degrees of accuracy is desired for different segments of population 

Systematic sampling

This design is recommended if we have a complete list of sampling units arranged in some systematic order such as geographical, chronological or alphabetical 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 not drawn from each of the stratum
3. Administratively more convenient
4. Can be applied in situation where different degrees of accuracy is desired for different segments of population

Cluster sampling

The total population is divided into recognizable sub-divisions, known as clusters such that within each cluster they are homogenous. The units are selected from each cluster by suitable sampling techniques.

Multi-stage sampling

The total population is divided into several stages. The sampling process is carried out through several stages.

  Figure: Multistage sampling

Non-probability sampling:

Depending upon the object of inquiry and other considerations a predetermined number of sampling units is selected purposely so that they represent the true characteristics of the population.

Judgment sampling

The choice of sampling items depends exclusively on the judgment of the investigator. The investigator’s experience and knowledge about the population will help to select the sample units. It is the most suitable method if the population size is less.

Table: Merits and demerits of judgment sampling

Merits

 Demerits

1. Most useful for small population 1. It is not a scientific method.

2. Most useful to study some unknown traits of a population some of whose characteristics are known. 2. It has a risk of investigator’s bias being introduced.

3. Helpful in solving day-to-day problems. 

Convenience sampling

The sampling units are selected according to convenience of the investigator. It is also called “chunk” which refer to the fraction of the population being investigated which is selected neither by probability nor by judgment.

Quota sampling

It is a type of judgment sampling. Under this design, quotas are set up according to some specified characteristic such as age groups or income groups. From each group a specified number of units are sampled according to the quota allotted to the group. Within the group the selection of sampling units depends on personal judgment. It has a risk of personal prejudice and bias entering the process. This method is often used in public opinion studies.