1. (a) What is the difference between internal and external data? (b) What do you mean by unbiased errors? (a) Internal data are those which are collected by the organisation from its own internal operations like production, sales, profits, loans, etc. whereas, external data are obtained from the publications of some other agencies. (b) The errors are termed as unbiased errors, if the estimated or approximated values are likely to err on either side, i.e. if the chances of making an over-estimate are almost the same as the chance of making an under-estimate.
2. (a) What is the law of statistical regularity? (b) What do you mean by statistical hypothesis? (a) The law of statistical regularity lies down that a group of objects chosen at random from a larger group tends to possess the characteristics of that large group (universe). (b) A statistical hypothesis is some assumption or statement which may or may not be true, about a population or equivalently about the probability distribution characterising the given population, which we want to test on the basis of the evidence from a random sample.
3. What do you mean by quota sampling? In this method, the investigator is told in advance the number of the sample units he is to examine or enumerate from the stratum assigned to him. The sampling quotes may be fixed according to some specific characteristic such as income group, sex, occupation, etc. 4. (a) What do you mean by linear and non-linear correlation ? (b) What do you mean by line of regression of X on Y? (a) The correlation between two variables is linear, if corresponding to a unit change in one variable, there is constant change in other variable over the entire range of the values and, if not, then it is non-linear correlation. (b) The line of regression of X on Y is the line which gives the best estimate of X for any given value of Y It is obtained by the principle of least squares or minimising the sum of squares of the errors parallel to the x-axis.
5. What do you mean by Data Processing? Name five areas where computer application is very beneficial. Data processing means the processing of information, especially, business type information by computer. Computer application is highly beneficial in the following areas (a) In business forecasting, (b) To keep records up-to-date, (c) To carry out automatic checks on the stock of a particular item, (d) To prepare pay bills and personal records, (e) In accounting, invoicing and billing. 6. What do you understand by the collection of data? The process of counting or enumeration with the systematic recording of results is called the collection of data.
For any statistical enquiry, whether it is in business, economics or social sciences, the basic problem is to collect facts and figures relating to particular phenomenon. 7. Why does the need for sampling arise? The need for sampling arises in order to: (i) Obtain the optimum results i.e.
the maximum information about the characteristics of the population with the available sources at our disposal in terms of time, money and manpower by studying the sample values only. (ii) To obtain the best possible estimates of the population parameters 8. Describe why the entire business is done on the basis of display of a few specimen samples only. On inspecting the sample of a particular stuff, we arrive at a conclusion about accepting or rejecting it.
For example, a consumer examines only a handful of the rice, pulses or any commodity in a shop to assess its quality and then decides to buy it or not. Thus we can say that the entire business is done on the basis of display of a few specimen samples only. 9.
What do you understand by ‘errors’ in statistical sampling? The word ‘error’ is used to denote the difference between the true value and the estimated or approximated value. Errors arise due to a number of factors such as approximations in measurements, approximations in rounding of the figures, due to faulty collection, personal bias of the investigators. 10. What are sampling errors? In a sample survey, since only a small portion of the population is studied, its results are bound to differ from the census result and thus have a certain amount of error known as sampling error. 11. What are non-sampling errors? Non-sampling errors are not attributed to chance and are a consequence of certain factors which are within human control. Non-sampling errors are thus present both in census surveys as well as sample surveys.
They are due to certain causes, which can be traced and may arise at any stage of enquiry viz., planning and execution of the survey and collection, processing and analysis of the data, etc. 12. What is meant by biased errors? Biased errors arise because of investigator whose personal beliefs and prejudices are likely to affect the results of the enquiry. The biased errors have a tendency to grew in magnitude with an increase in the number of the observations and hence also known as cumulative errors. 13.
Which type of errors may be termed as unbiased errors? The errors are termed as unbiased errors if the estimated values are likely to err on either side, i.e., if the chances of making an over estimate is almost same as the chance of making an underestimate.
The errors in one direction are more or less neutralized by the errors in the opposite direction and consequently the ultimate result is not much affected. 14. What are absolute and relative errors? Absolute errors are the difference between the true value of any particular observed item and its estimated value Relative errors are the ratio of the absolute error to the actual value. 15. What is probability sampling? It is a scientific technique of drawing samples from the population according to some laws of chance in which each unit in the universe has some definite reassigned probability if being selected in the sample. 16. What do you understand by mixed sampling? Sampling method in which the sample units are selected partly according to some probability laws and partly according to fixed sampling rule (no use of chance) is known as mixed sampling.
17. What is simple random sampling? It is a method in which sample is so drawn that each unit in the population has an equal and independent chance of being included in the sample. A random sample may be selected by a lottery method or by use of table of random numbers.
18. What is quota sampling? In quota sampling, the investigator is told in advance the number of the sample units he is to examine and enumerate from the stratum assigned to him. The sampling quotas may be fixed according to some specified characteristics such as income group, sex, occupation, political or religious affiliations, etc. 19. Write short note on hypothesis testing. The inductive inference is based on deciding about the characteristics of the population on the basis of sample study.
Such decisions involve an element of risk, the risk of taking wrong decisions. The theory of testing of hypothesis was initiated by J. Veyman and E.S. Pearson and employs statistical techniques of arrive at decisions in certain situations where there is an element of uncertainty on the basis of a sample whose size is fixed in advance.
20. What is correlation? There are certain series where each item of the series may assume the values of two or more variables. Such distribution, in which each unit of the series assumes two values, is called a binariate distribution. The correlation is a statistical tool, which studies the relationship between two variables and correlation analysis involves various methods and techniques used for studying and measuring the extent of the relationship between the two variables. 21. What is scatter diagram method of correlation? It is the simplest way of diagrammatic representation of a binariate distribution.
From this diagram we can form a fairly good, though rough, idea about the relationship between the two variables. In the diagrammatic representation, there may be perfect positive correlation, negative correlation, low or high degree of positive correlation low or high degree of negative correlation or no correlation. 22. Describe Karl Pearson’s coefficient of correlation.
It is also known as covariance method. It is a method for measuring the intensity or the magnitude of linear relationship between two variable series. It is correlation coefficient between two variables x and y, usually denoted by r (x, y) or rxy, is a numerical measure of linear relationship between them and it is the ratio of the covariance between x and y and is denoted as Co v. (x, y) to the product of the standard deviations of x and y. 23. Write down the limitations of standard deviation. 1. It is difficult to understand.
2. The extreme values are given more weight because values are squared up. The Lorenz curve is graphic method of studying dispersion. This curve was used for the first time to measure the distribution of wealth and income. Lorenz curve is a cumulative percentage curve.
In the diagram, OZ is the line of equal distribution OBZ curve has higher degree of variability as compared to the points lying on the curve OAZ Thus, a measure of variability of the distribution is provided by the distribution of the curve of the cumulated percentages of the given distribution from the line of equal distribution. 24. What is the range of the values of correlation? Correlation is a statistical method to determine the relationship between two or more variables. Its values can lie between +1 and -1. The direction of the relation is determined by sign.
If increase in one variable leads to increase in dependent variable, then correlation is positive. On the other hand, if increase in one variable leads to decrease in dependent variable, then value will be negative. In case no relation exists between two variables, correlation will be zero.