MBA 1st Year Business Statistics Unit 1 Short Question Answer Study Notes Study Material Unit wise Chapter Wise Notes Syllabus Scope, function and limitations of statistics, Measures of Central Tendency-Mean, Median, Mode, Percentiles, Quartiles, Measures of Dispersion-Range, Interquartile range, Mean Deviation, Mean absolute deviation, Standard Deviation, Variance, Coefficient of Variation. Measures of Shape and Relative location; Skewness and Kurtosis; Chebyshev’s Theorem. Topic Wise Syllabus Of The Content Study Notes.
SHORT QUESTIONS ANSWER
Q.1. Discuss the application of statistics in managerial decision.(2008-09)
Or Define statistics and discuss its application in managerial decision-making.
Or What is statistics? What are the various uses of statistics in the management of an organisation?
Or Discuss briefly the role of statistics in the successful management of business enterprise.
Ans. Statistics: Statistics is considered as analysis of figures for forecasting or drawing inferences. Statistical methods are becoming very useful in every sphere of life.
“The citizen today is indulged with white papers, economic surveys and a multitude of reports not from the government but from banks, insurance companies and the individual firms, all of which present and argue from the mass of statistical data.’
-Moore ‘Statistics born of the practical needs of the state is finding increasing applications in everyday life.’
Uses and Role of Statistics in Management
Uses and role of statistics in management is described as under:
1. Statistics is a branch of applied mathematics which specialises in data and its analysis is helpful in marketing.
2. Statistics is widely used in economics study and research and is concerned with production
and distribution of wealth, savings and investments.
3. Statistical techniques are proved extremely useful in the study of samples for statistical quality control.
4. Statistics is widely used in entrepreneurship and is necessary for the formulation of policies
to start a new business.
5. Statistics is essential in research work and experiments are conducted with the help of
statistical methods to gather and analyse data.
6. Statistics are lifeblood of successful commerce and is indispensable in business and commerce.
7. Statistics is vital in making a sound investment whether it is in buying or selling of stocks and
securities or real estate.
Applications of Statistics in Managerial Decision-making
Applications of statistics in managerial deicision-making are as follows:
1. Product selection and competence strategies in marketing and sales.
2. Product mix and product positioning in production management.
3. Buying policy, material planning and lead time in case of material management.
4. Optimum organisation level, job evaluation in personnel management.
5. Project selection in research and development.
Q.2. Write down the functions of statistics.(2012-13)
Ans. There are many functions of statistics among which the most important are as follows:
1. Condensation: It means to reduce or to condense which is mainly applied at embracing the understanding of huge mass of data providing new observations thus reducing the complexity of data.
2. Comparison: Collected data is compared using the methods of classification and tabulation. As statistics is an aggregate of facts and figures, comparison is possible and helps to understand it.
3. Forecasting: It means to predict or to estimate before hand. It plays a dominant production sales, time series analysis, etc.
4. Estimation: Unknown value of the population parameter is estimated on the basis of observations.
5. Hypothesis Testing: Statistical methods are useful in formulation and hypothesis testing population is characterised on the basis of available information from sample observations,
Q.3. “Statistics are numerical statements of facts in any department of enquiry and placed in relay to each other’. Comment and discuss the characteristics of statistics.
Ans. Statistics is defined by using two concepts by the statisticians:
1. Statistics as a Statistical Data: It refers to collection of numerical data. Statistics are numeri statement of facts in any department of enquiry placed in relation to each other. This gives importan to numerical aspects and provides comparative study of figures.
2. Statistics as Statistical Methods: This is based on the concept that statistics is what it dope what statisticians do. Statistics may be called the science of counting in which data is collected hue making estimates. It is a science of averages.
‘Statistics are numerical statements of facts in any department of enquiry that are related to each other. This does not include the statistical methods.’-A.L. Bowley Statistics are expressed in numbers and all statistical statements are facts but all numerical statements of facts are not statistics.
Characteristics of Statistics
Following are the characteristics of statistics:
1. Statistics are the aggregation of facts. Single or isolated figures are not stated as statistics as they cannot perform some of the tasks of statistics. For example, single death or birth do not form any statistics but when these figures show birth rate or death rate, they become part of statistics.
2. Statistics are expressed in numbers. Qualitative statements do not show accurate interpretations and hence are not statistics.
3. Statistics can be compared with other subjects and statistical data can also be compared to each other. For example, the performance appraisal of two departments can be used to compare the efficiency of the two departments.
4. Statistics are affected by multiplicity of causes and a number of factors. So, only one cause is not responsible to given data. Statistics are collected in a systematic manner for a predetermined purpose. So, statistics are
collected for a purpose and under a plan.
Q.4. Discuss the limitations of statistics. Give its uses also.
Ans. Limitations of Statistics: Statistics is applicable in all sciences where quantitative measurement of phenomenon is possible, but it is not without limitation. Therefore, for the proper application statistics, it is also necessary to know the limitations and misuses of statistics.
The following are the limitations of statistics:
1. Statistics Deals with Aggregates of Items and not with Individual: Statistics is the study of mass data and deal with aggregates or group. In fact over data on an item considered individual does not constitute statistical data.
2. Statistics Deals Only with Quantitative Data: If the study yield qualitative data which cann be meaningfully converted to quantitative data, valid conclusion cannot be drawn from such stue using statistical analysis. Qualitative phenomena like honesty, intelligence, poverty, etc. cannot analysed statistically unless these attributes are assigned suitable quantitative measures.
3. Statistical Laws are True Only on an Average: Law of statistics are not universally applicable as the law of Physics, Chemistry and Mathematics. These may not be true for a particular individual. If it is statistically established that a particular food results in an increase in weight, the statement will be true on an average and may not be true for an individual.
4. Statistics is Only One of the Method of Studying a Phenomenon: Statistical methods do not always provide us best v Statstics Vo possible solution to a given problem. In varying cultural and is what statistics does religious situations, it may fail to reveal and pin point the or statistics is what underlying factors responsible for the variation in a phenomenon under study. Thus, statistical conclusion need to be supplemented by statisticians do. the other variations.
5. Statistics can be Misused and Misinterpreted: The greatest limitation of statistics is that it is likely to be misused. The misuse may arise due to several reasons, e.g. when conclusions are based on incomplete information or are drawn by unskilled investigators.
Inadequate and faulty procedure of data collection and inappropriate comparison may arrive at fallacious conclusion.
Uses of Statistics
Statistics is a numerical statement of facts and is a body of methods for making decisions in the face of uncertainty. It has various uses:
1. Statistics helps in giving a better understanding and correct explanation of natural phenomenon.
2. Statistics helps in assembling appropriate quantitative data.
3. Statistics helps in suitable and efficient planning of statistical investigation in any area of study.
4. Statistics is helpful in drawing valid inferences by calculating consistent parameter regarding population through the model data.
5. Statistics helps in presenting complex data in tabular, diagrammatic and graphical form for its
Q.5. What is meant by measure of central tendency? What are the characteristics of a good measure of central tendency?(2007-08)
Ans. Measures of Central Tendency: A central tendency is a single value which is used to represent an entire set of data. It is basically such type of typical value around which most of other values cluster. It can be said that the tendency of the observations to concentrate around a control point is known as central tendency.
Statistical measures indicate the location or position of a control value to describe the central tendency of the entire data and is called the measure of central tendency. There are a lot of measures of central tendency, some of which are broadly classified as mathematical averages and positional averages.
An ideal measure of central tendency should possess the following characteristics:
1. It should be clearly defined and not admit of misconstruction.
2. It should be representative of the whole group under consideration.
3. It should be precisely expressed in a single figure.
4. It should be chosen from a large amount of data so as to nullify the effect of abnormalities and to avoid undue fluctuations where additional matter is introduced.
5. It should be stable, i.e. it should not materially change if some more units of same group are
included at random.
6. It should be easy to understand specially.
7. It should admit of mathematical treatment.
Q.6. Differentiate between parameter and statistics.
Ans. Parameter and Statistics: A parameter is a numerical value that is equivalent to an entir population. The value of parameter is a fixed number and it doesn’t depend on the sample. It can seen in the case of population mean or mode.
A statistics is a numerical value that states something about a sample. It finds ever increasin application in everyday life and is born of the practical needs of the state to register its population. Th value of statistics can vary from sample to sample and it is said that it is dependent on the sample. The best example is seen in sample mean.
Q.7. What do you understand by dispersion? What is the need of studying dispersion? (2006-07)
Ans. Meaning of Dispersion: The term dispersion refers to the variability in the size of items cates that the size of items in a series is not uniform. The values of various items differ from other. If the variation is substantial, dispersion is said to be considerable and if the variation is little dispersion is insignificant. This is rather a general sense in which this term is used.
however, the term, dispersion not only gives a general impression about the variability of a serie but also a precise measure of this variation. Usually in a precise study of dispersion, the deviations of Size of items from a measure of central tendency, are found out and then these deviations are averaged to give a single figure representing the dispersion of the series.
‘Dispersion is the measure of the variation of the items.’
‘Dispersion is a measure of the extent to which the individual vary.’
Need of Studying Dispersion/Objectives of Dispersion
Need of studying dispersion is described as under:
1. To Judge the Reliability of Measures of Central Tendency: Measure of dispersion is the only means to test the representative character of an average. If the extent of the scatter is less, it indicates a greater degree of uniformity in the value of items and as such the average may be regarded as representative. On the other hand, if the scatter is large, average is bound to be less reliable since it shows a lower degree of uniformity in the value of observations. It is observed that when dispersion is small, the average is a typical value which closely represents the individual values.
2. To Control the Variability Itself: Measures of dispersion are indispensable in analysing the nature and locating the causes of variation.
‘In matters of health variations in body temperature, pulse, beat and blood pressure are basic guides to diagnosis. Prescribed treatment is designed to control their variation. In industrial production, efficient operation requires control of quality variation, the causes of which are sought through inspection and quality control programmes.’–Spurr and Bonini
In social sciences, the measurement of inequality in the distribution of income and wealth requires the measures of variation.
3. To Compare Two or More Series with Regard to their Variability: When two series are to be compared, due consideration has to be given to their dispersion, i.e. the extent to which the items are spread around their respective averages. Using measures of dispersion, one can find out degree of uniformity or consistency in two or more sets of data. For example, if it is desired to make a comparison between the prices of equity shares of two or more companies over a period of time, a measure of dispersion for each such series of prices would be very helpful.
4. To Facilitate the Use of other Statistical Measure: Many other important statistical techniques like correlation, regression, test of hypothesis, analysis of fluctuations in a time series have roots in the measures of variation of one kind or the other.