SIKKIM MANIPAL UNIVERSITY-DEStudent Name: Course: MBA

Registration Number: LC Code:

Subject Name: Statistics for Management Subject Code: MB0040

Question: 1Statistics plays a vital role in almost every facet of human life. Describe the functions of Statistics. Explain the applications of statistics.

Answer:According to Seligman, Statistics is a science which deals with the method of collecting, classifying, presenting, comparing and interpreting the numerical data to throw light on enquiry.

Functions of StatisticsStatistics used to simplify mass data and to make comparisons easier. It is also used to bring out trends and tendencies in the data, and the hidden relations between variables. All these help in easy decision making. Functions of the statistics are:

1. Statistics simplifies mass dataThe 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 in the understanding of any huge mass of data.2. Statistics brings out trends and tendencies in the dataAfter data is collected, it is easy to analyse the trend and tendencies in the data by using the various concepts of Statistics.3. Statistics brings out the hidden relations between variablesStatistical analysis helps in drawing inferences on the data. Statistical analysis brings out the hidden relations between variables.4. Decision making power becomes easierWith 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.5. Statistics makes comparison easierWithout using statistical methods and concepts, collection of data and comparison would be difficult. Statistics helps us to compare data collected from various sources. Grand totals, measures of central tendency and measures of dispersion, graphs and diagrams and coefficient of correlation all provide ample scope for comparison. Hence, visual representation of the numerical data helps to compare the data with less effort and effective decisions can be made.

Application of StatisticsStatistical methods are applied to specific problems in various fields such as Biology, Medicine, Agriculture, Commerce, Business, Economics, Industry, Insurance, Sociology and Psychology.Insurance companies decide on the insurance premiums based on the age composition of the population and the mortality rates. A governments administrative system is fully dependent on production statistics, income statistics, labour statistics, economic indices of cost, and price. Economic planning of any nation is entirely based on the statistical facts. Cost of living index numbers are also used to estimate the value of money. In business activities, analysis of demand, price, production cost, and inventory costs help in decision making.

Question: 2(A) Explain the various measures of Dispersion.

Answer:DispersionA measure of Dispersion may be defined as a statistics signifying the extent of the scattering of items around a measure of central tendency.The property of deviations of values from the average is called Dispersion or Variation. The degree of variation is found by the measures of variation. They are as follows:1. Range (R)2. Quartile Deviation (Q.D)3. Mean Deviation (M.D)4. Standard Deviation (S.D)We may want to compare two different distributions whose measurements are in terms of kilograms and in terms of centimetres. Then, we use the following relative measures that do not have any units attached to them. The relative measures are as follows:1. Coefficient of Range2. Coefficient of Quartile Deviation3. Coefficient of Mean Deviation4. Coefficient of Variation

Question: 2(B)Obtain the values of the median and the two Quartiles.39138459140767252277773324881490

Answer:Median:First, Arranging in ascending order, we get:384, 391, 407, 522, 591, 672, 733, 777, 1490, 2488

We have, N=10

Median= Size ofth itemMedian= th item = 5.5th itemWe have to take the average of 5th and 6th itemMedian= = 631.5The median for the given set of values is 631.5

Two Quartile (Q1 and Q3):

Q1= th item = th item = 2.75th item= 2nd item + .75(3rd item 2nd item)=391 + .75(407 391)=403

Q3= th item = th item = 8.25th item= 8nd item + .25(9rd item 8nd item)=777 + .25(1490 777)=955.25

So, Median = 631.5 , Q1=403 and Q3=955.25

Question: 3(a)What is correlation? Distinguish between positive and negative correlation.

Answer:When two or more variables move in sympathy with the other, then they are said to be correlated. If both variables move in the same direction, then they are said to be positively correlated. If the variables move in the opposite direction, then they are said to be negatively correlated. If they move haphazardly, then there is no correlation between them. Correlation analysis deals with the following: Measuring the relationship between variables. Testing the relationship for its significance. Giving confidence interval for population correlation measure.According to Croxton and Cowden, When the relationship is of a quantitative nature, the appropriate statistical tool for discovering and measuring the relationship and expressing it in a brief formula is known as correlation.

Distinguish between Positive and negative correlations: Both the variables (X and Y) will vary in the same direction. If variable X increases, variable Y also will increase; and if variable X decreases, variable Y also will decrease; then the correlation in such cases is known as positive correlation. If the given variables vary in opposite direction, then they are said to be negatively correlated. If one variable increases, the other variable will decrease. In other words, the variables are negatively correlated if there is an inverse relationship between the variables. For example, price and supply of the commodity. On the other hand, correlation is said to be negative or inverse if the variables deviate in the opposite direction, i.e., if the increase (decrease) in the values of one variable results, on the average, in a corresponding decrease (increase) in the values of the other variable. For example, temperature and sale of woolen garments.

Question: 3(b)Calculate coefficient of correlation form the following data.X123456789

Y9810121113141615

Answer:XYX2Y2XY

191819

2846416

310910030

4121614448

5112512155

6133616978

7144919698

81664256128

91581225135

X=45Y=108X2=285Y2=1356XY=597

Applying the formula for r and substituting the respective values from the table we get r as:r =

r = r = 513/540 = 0.95Hence, Karl Pearsons correlation coefficient is 0.95

Question: 4Index number acts as a barometer for measuring the value of money. What are the characteristics of an index number? State its utility.

Answer:An index number is a statistical measure which is designed to express changes or differences in a variable or a group of related variables. It is usually expressed in percentage them.

Characteristics of Index Numbers1. Expressed in number: Index numbers represent the relative changes such as increase in production; reduction in prices etc. in the numbers.2. Expressed in percentage: Index numbers are expressed in terms of percentages so as to show the extent or relative change where the value of base is assumbed to be 100 but the sign of percentage(%) is not used.3. Relative measure: Index numbers measure changes which are not capable of direct measurement.4. Specified averages: Index number represents a special case of average, in general known as weighted average. It is a special type of average, because in a simple average, the data is homogenous having the same unit of measurement, whereas the average variables have different units of measurement.5. Basis of comparison: Index numbers by their very nature are comparative. They compare changes over time or between places or similar categories.

Utility and Importance of Index NumbersThe primary purpose of index numbers is to measure relative temporal or cross-sectional changes in a variable or a group of related variables which are not capable of being directly measured. The greatest purpose of index numbers has been to measure and compare the changes in prices and purchasing power of money which have received great attention from economists for many years.Today, index number is not only used for measuring price changes alone. Factors like wages, employment, production, trade, demand, supply, business condition, industrial activity, financial problems etc. are also studied thorugh this statistical device. Just as a barometer measure the pressure of economic behavior. Thus, index numbers are called economic barometers.

Question: 5Business forecasting acquires an important place in every field of the economy. Explain the objectives and theories of Business forecasting.

Answer:Business ForecastingBusiness forecasting refers to the analysis of past and present economic conditions with the object of drawing inferences about probable future business conditions. The process of making definite estimates of future course of events is referred to as forecasting and the figure or statements obtained from the process is known as forecast; future course of events is rarely known.

Objectives of forecasting in businessForecasting is a part of human nature. Businessmen also need to look to the future. Success in business depends on correct predictions. Success or failure would depend upon the ability to successfully forecast the future course of events. Without some element of continuity between past, present and future, there would be little possibility of successful prediction. But history is not likely to repeat itself and we would hardly expect economic conditions next year or over the next 10 years to follow a clear cut prediction. A businessman cannot afford to base his decisions on guesses. Forecasting helps a businessman in reducing the areas of uncertainty that surround management decision making with respect to costs, sales, production, profits, capital investment, pricing, expansion of production, extension of credit, development of markets, increase of inventories and curtailment of loans.

Theories of Business ForecastingThere are a few theories that are followed while making business forecasts. They are:1. Sequence or time-lag theoryThis is the most important theory of business forecasting. It is based on the assumption that most of the business data have the lag and lead relationships, that is, changes in business are successive and not simultaneous. There is time-lag between different movements.2. Action and reaction theoryThis theory is based on the following two assumptions. Every action has a reaction Magnitude of the original action influences the reactionWhen the price of rice goes above a certain level in a certain period, there is a likelihood that after some time it will go down below the normal level.3. Conomic Rhythm TheoryAccording to this theory, the speed and time of all business cycles are more or less the same and by using statistical and mathematical methods, a trend is obtained which will represent a long term tendency of growth or decline. It is done on the basis of the assumption that the trend line denotes the normal growth or decline of business events.4. Specific historical analogyHistory repeats itself is the main foundation of this theory. If conditions are the same, whatever happened in the past under a set of circumstances is likely to happen in future also. A time series relating to the data in question is thoroughly scrutinized such a period is selected in which conditions were similar to those prevailing at the time of making the forecast. This theory depends largely on past data.5. Cross-cut analysis theoryThis theory proceeds on the analysis of interplay of current economic forces. Forecasting is made on the basis of analysis and interpretation of present conditions because the past events have no relevance with present conditions.

Question: 6The weekly wages of 1000 workers are normally distributed around a mean of Rs. 70 and a standard deviation of Rs. 5. Estimate the number of workers whose weekly wages will be:a. Between 70 and 72b. Between 69 and 72c. More than 75d. Less than 63

Answer:1000 workerMean=70Rs/weekS.D()=5x=70, =5,z=(x- x)/ z=

a) To estimate the number of worker whose wage from 70 to 72i.e

=1000dz where z=, z1= and z2= = 2/5= 1000dz=1000 X 0.1554 worker have wages from 70 to 72.b) Between 69 to 72z1 = = = -0.2so Area of Normal distribution curve left to z1A(z1) = 0.0793 and for z2= = = 0.4A(z2) = 0.1554Total Area A(z1)+A(z2) represents probability of workers in this wages range.So estimate of worker s is = 1000(A(z1)+A(z2)) =1000X(0.0793+0.1554) = 1000X0.2347 =234.7 or 235 workersc) More than 75i.e z= = 5/5 = 1.0So A(z) =0.3413So p(more than 75Rs) = 0.5000-0.3413 = 0.1587So worker whose wages is more than 75 Rs= 1000X0.15837= 158.7 workersd) No of worker whose wages less then 63 z= = = = -1.4Region of Normal Distribution correspondingZ = -1.4 is A(z) = 0.4192So P(less than 63 Rs) = - P(z=-1.4) = 0.5-0.4192 = 0.0808

So Number of worker whose less than 63Rs/week is= 1000X0.0808=80.8=81(nearest whole number)1