IGNOU| QUANTITATIVE ANALYSIS FOR MANAGERIAL APPLICATIONS (MS - 08)| SOLVED PAPER – (DEC - 2022)| (MP)
MANAGEMENT PROGRAMME (MP)
Term-End Examination
December - 2022
MS-08
QUANTITATIVE ANALYSIS FOR MANAGERIAL
APPLICATIONS
Time: 3 Hours
Maximum Marks: 100
Note: (i) Section A has six questions, each carrying
15 marks. Attempt any four questions from this Section.
(ii) Section B
is compulsory and carries 40 marks. Attempt both questions.
(iii) Use of
calculator is permissible.
Section-A
1. What do you understand by the term 'Statistics'? Explain various statistical techniques which can be helpful for a decision maker in solving problems.
Ans:- Statistics is a branch of applied mathematics
that deals with the collection, analysis, interpretation, presentation and
organization of data. It is a science that helps in collecting and analyzing
large amounts of numerical data.
Statistics is
based on mathematical principles such as differential and integral calculus and
linear algebra. It can be used to predict the future, determine the probability
of a specific event occurring, or help answer questions about a survey.
Statistics is
important in the field of economics and its various branches. For example,
statistics can be used to indicate the problem of income expenditure on
different sections of people, production of national wealth, adjustment of
demand and supply and the impact of economic policies on the economy.
The term
"statistics" was first introduced by Gottfried Eichenwall in 1749. It
originally specified the analysis of data about the state, which referred to
the "science of the state" (then called political arithmetic in
English). It generally acquired the meaning of collection and classification of
data in the early 19th century.
Statistics is
the science concerned with the development and study of methods of collecting,
analyzing, interpreting, and presenting empirical data.
Statistical
methods and techniques are used to aid decision making. This may involve
analyzing data, predicting trends, or making comparisons. Statistical methods
and strategies can help identify data patterns that can be used to make
decisions.
Applying
statistical techniques and appropriate methods to measure the risk and
uncertainty associated with a decision. Statistical methods and techniques can
be used to evaluate the cost-effectiveness of a decision and its potential
impact. Finally, they can be used to develop strategies to achieve desired
results.
(i)
Statistical Analysis: Statistical analysis is a valuable tool for business
and data science decision making. Data scientists and business owners can gain
valuable insights into their data and make decisions that best benefit their
business or data set by looking at the data and analyzing its characteristics.
Statistical analysis may include descriptive statistics, inferential
statistics, and predictive analytics.
Making
business and data science decisions requires careful consideration of the
available data. Statistical methods are beneficial for making informed business
decisions. They allow businesses and data scientists to gain insight into their
data and make informed decisions.
(ii) Statistics
in decision making: While making decisions, statistics can be used to
determine the probability of success of a decision or to compare different
alternatives. For example, a business may use statistics to determine the
likelihood of success of a new product or service. Even a data scientist can
use statistics to compare different machine learning models.
Statistics
also provide information about how people make decisions. By examining the
decisions people make, researchers can gain information about what influences
them and how they make decisions. This can help businesses and data scientists
make more informed decisions.
(iii)
Statistical Methods: The statistical methods used in drawing informed
conclusions vary depending on the type of decision. Generally, descriptive
statistics are used to understand data; Inferential statistics are used to
compare different options. Predictive analytics is used to determine the
probability of success of a decision. Businesses and data scientists can gain
valuable insights into their data and make better decisions using these
methods.
Overall,
statistical methods and techniques are valuable tools for making intelligent
decisions in business and data science. It is important to understand the
statistical methods used in decision making. With these insights, businesses
and data scientists can gain valuable insights into their data and make
informed decisions.
2. Calculate the median from the following data:
|
Marks (less than) |
No. of Students |
|
80 70 60 50 40 30 20 10 |
100 90 80 60 32 20 13 5 |
Solution:-
Let us now
convert the given numbers into class intervals and find the frequency of all
the intervals. Here, there is no cumulative frequency. of students.
To find the
frequency of each interval, we have to subtract the cumulative frequency of the
upper interval from the lower interval.
Let's tabulate
and find the frequencies.
We first need to
consider the least squares interval.
|
Class Intervals |
Cumulative frequency (cf) |
Frequency (f) |
|
0-10 10-20 20-30 30-40 40-50 50-60 60-70 70-80 |
5 13 20 32 60 80 90 100 |
5 13-5=8 20-13=7 32-20=12 60-32=28 80-60=20 90-80=10 100-90=10 |
Now, we have
found the frequency of each interval.
Now we have to
find the median of the above data.
We know that the
total number of students in the class is 100.
Let N=100.
To find the
median interval we have to find N/2.
Substituting the
value of N, we get
In the class
interval 40-50, we find that 50 is the upper limit.
Hence the median
interval is 40-50.
We know that the
formula to find the median in the median interval is
Where l is the
lower interval of the median interval, N is the total number of students, cf is
the cumulative frequency of the median interval, f is the frequency of the
median interval and h is the difference of the intervals.
We find that
l=40, N=100, cf=32, f=28 and h=10.
Substituting
these values, we get
3. The customer accounts of a certain departmental stores
have an average balance of 120 and a standard deviation of 40. Assuming the
account balances are normally distributed:
(i) What
proportion of the accounts is over 150?
(ii) What
proportion of the accounts is between 100 and 150?
Given:
Probability (0
≤ z < 0.5) is 0.1915
Probability (0
≤ z < 0.75) is 0.2734
Step-by-step
explanation:
1. If X is
a random variable from a normal distribution with mean (μ) and standard
deviation (σ), its Z-score may be calculated by subtracting mean from X and
dividing the whole by standard deviation.
2. It is
given that mu is 120 (mean) and sigma is 40 (standard deviation) and we are
asked to find
3. Here Z
is the standard normal variable,
P(-1.5<Z<-0.75)
= Left area of -0.75 in normal curve - Left area of -1.5
=
0.2266 – 0.0668 = 0.1598
4. What is sampling'? List the various reasons that make
sampling so attractive in drawing conclusions about the population.
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