11/23/2011 12:11:41 PM 



Solve Assignment MB0040


MBA SEMESTER 1
MB0040 – STATISTICS FOR MANAGEMENT 4 Credits
(Book ID: B1129)
Assignment Set 1 (60 Marks)
Note: Each question carries 10 Marks. Answer all the questions
Q 1. (a) ‘Statistics is the backbone of decisionmaking’. Comment.
Ans: Due to advanced communication network, rapid changes in consumer behaviour, varied expectations of variety of consumers and new market openings, modern managers have a difficult task of making quick and appropriate decisions. Therefore, there is a need for them to depend more upon quantitative techniques like mathematical models, statistics, operations research and econometrics.
As you can see, what the General Manager is doing here is using Statistics to solve a problem and to increase profits.
Decision making is a key part of our daytoday life. Even when we wish to purchase a television, we like to know the price, quality, durability, and maintainability of various brands and models before buying one. As you can see, in this scenario we are collecting data and making an optimum decision. In other words, we are using Statistics.
Again, suppose a company wishes to introduce a new product, it has to collect data on market potential, consumer likings, availability of raw materials, feasibility of producing the product. Hence, data collection is the backbone of any decision making process.
Many organisations find themselves datarich but poor in drawing information from it. Therefore, it is important to develop the ability to extract meaningful information from raw data to make better decisions. Statistics play an important role in this aspect.
Statistics is broadly divided into two main categories. Figure 1.1 illustrates the two categories. The two categories of Statistics are descriptive statistics and inferential statistics.
Divisions in Statistics
Descriptive Statistics: Descriptive statistics is used to present the general description of data which is summarised quantitatively. This is mostly useful in clinical research, when communicating the results of experiments.
Inferential Statistics: Inferential statistics is used to make valid inferences from the data which are helpful in effective decision making for managers or professionals.
Statistical methods such as estimation, prediction and hypothesis testing belong to inferential statistics. The researchers make deductions or conclusions from the collected data samples regarding the characteristics of large population from which the samples are taken. So, we can say ‘Statistics is the backbone of decisionmaking’.
Q.1. (b) Give plural meaning of the word Statistics?
Ans: Plural of Word “Statistic”:
The word statistics is used as the plural of the word “Statistic” which refers to a numerical quantity like mean, median, variance etc…, calculated from sample value.
In plural sense, the word statistics refer to numerical facts and figures collected in a systematic manner with a definite purpose in any field of study. In this sense, statistics are also aggregates of facts which are expressed in numerical form. For example, Statistics on industrial production, statistics or population growth of a country in different years etc.
For Example: If we select 15 student from a class of 80 students, measure their heights and find the average height. This average would be a statistic.
Q 2. a. In a bivariate data on ‘x’ and ‘y’, variance of ‘x’ = 49, variance of ‘y’ = 9 and covariance (?x,y) = 17.5. Find coefficient of correlation between ‘x’ and ‘y’.
Ans: We know that:
Given
Hence, there is a highly negative correlation.
Q 2. b. Enumerate the factors which should be kept in mind for proper planning.
Ans: Planning a Statistical Survey
The relevance and accuracy of data obtained in a survey depends upon the care exercised in planning. A properly planned investigation can lead to best results with least cost and time. Steps involved in the planning stage.
Q 3. The percentage sugar content of Tobacco in two samples was represented in table 11.11. Test whether their population variances are same.
Table 1. Percentage sugar content of Tobacco in two samples
Sample A 2.4 2.7 2.6 2.1 2.5
Sample B 2.7 3 2.8 3.1 2.2 3.6
Ans:
Required values of the method I to calculate sample mean
X d = X  2.5 d2
2.4 0.1 0.01
2.7 0.2 0.04
2.6 0.1 0.01
2.1 0.4 0.16
2.5 0 0
Total 0.2 0.22
Required values of the method II to calculate sample mean
X d = X – 3 d2 3
2.7 0.3 0.09
3 0 0
2.8 0.2 0.04
3.1 0.1 0.1
2.2 0.8 0.64
3.6 0.6 0.36
Total 0.6 1.23
S 2 = 1 [ ?d2  (?d)2 ]
1 n1 1 n1
= 1 [ 0.22  0.04 / 5 ]
4
= 0.053
S 2 = 1 [ ?d2  (?d)2 ]
2 n2 1 n2
= 1 [ 1.230.053 ]
5 6
= 0.244 not significant
Q 4. a. Explain the characteristics of business forecasting.
Ans: Characteristics of business forecasting
Based on past and present conditions
Business forecasting is based on past and present economic condition of the business. To forecast the future, various data, information and facts concerning to economic condition of business for past and present are analysed.
Based on mathematical and statistical methods
The process of forecasting includes the use of statistical and mathematical methods. By using these methods, the actual trend which may take place in future can be forecasted.
Period
The forecasting can be made for long term, short term, medium term or any specific period.
Estimation of future
The business forecasting is to forecast the future regarding probable economic conditions.
Scope
The forecasting can be physical as well as financial.
Q 4. b. Differentiate between prediction, projection and forecasting.
Ans: Prediction, projection and forecasting
A great amount of confusion seem to have grown up in the use of words ‘forecast’, ‘prediction’ and ‘projection’.
Forecasts are made by estimating future values of the external factors by means of prediction, projection or forecast and from these values calculating the estimate of the dependent variable.
Q 5. What are the components of time series? Bring out the significance of moving average in analysing a time series and point out its limitations.
Ans: Components of Time Series
The behaviour of a time series over periods of time is called the movement of the time series. The time series is classified into the following four components:
i) Long term trend or secular trend
ii) Seasonal variations
iii) Cyclic variations
iv) Random variations
Method of moving averages
Moving averages method is used for smoothing the time series. That is, it smoothes the fluctuations of the data by the method of moving averages.
When period of moving average is odd
To determine the trend by this method, the procedure is described in
Procedure for determining the trend when moving average is odd
By plotting these trend values (if desired) you can obtain the trend curve with the help of which you can determine the trend whether it is increasing or decreasing. If needed, you can also compute shortterm fluctuations by subtracting the trend values from the actual values.
When period of moving averages is even
When period of moving average is even (such as 4 years), we compute the moving averages by using the steps described in below
Procedure for determining the trend when moving average is even
Merits and demerits of moving averages method
Merits Demerits
This is a simple method. No functional relationship between the values and the time. Thus, this method is not helpful in forecasting and predicting the values on the basis of time.
This method is objective in the sense that anybody working on a problem with this method will









