Elements of Statistics Tutor Marked Assignment (TMA) Course Code :ECO-07 Assignment Code :ECO-07/TMA/2012-13 Total Marks: 100 Attempt all the questions

1. “All statistics are numerical statements of facts but all numerical statements of facts are not statistics” comment. (20). Solution: According to this definition the numerical facts (data) should possess the following characteristics to be treated as statistics. (i) Aggregate of facts: Single, isolated or unrelated figures are not statistics, because they are not comparable. These figures tell nothing about any problem. For example the age of a student or the price of a commodity is not statistics. Because they are just abstract numbers. But when we consider age of a group of students, or the prices of a basket of commodities it is statistics as they comparable. Statistics must be expressed as aggregate of facts relating to any particular enquiry. Thus ‘not a datum’ but the data represent statistics.

(ii) Affected by multiplicity of causes : Numerical facts should be affected by a number of factors to become statistics.These may include both normal as well as exceptional factors. For example, the yield of rice depends on a number of factors like the rainfall, fertility of the soil, method of cultivation, quality of seeds used etc.Some of these factors are normal and some are exceptional. Hence the data relating to the yield of rice over a period of time become statistics. On the other hand if we write numericals l,2,3,4,5,6,7,8,9,and 10, they are not statistics. Because they are not affected by any factors.

(iii) Numerically expressed: Statistics are quantitative phenomena. Mostly, statistical techniques deal with quantitative factors than with qualitative aspect. So statistics should be always numerically expressed. For example, ‘there are 30 districts in Orissa’, is a numerical statement. But the standard of living of the people of Orissa have improved over the years’ is not a numerical statement. Here the first statement is statistical where as the second is not. So the subjective statements relating to qualitative information like honesty, beauties etc. are not statistics. Only statements which can be expressed numerically are statistics.

(iv) Enumerated accurately: In an enquiry statistics (data) should be collected with a reasonable standard of accuracy. This affects the findings of the enquiry. The degree of accuracy of statistics depends on the nature and purpose of the enquiry. Generally data are collected in two ways - by enumerating all the units of the population (complete enumeration method) or enumerating some units (sampling Method) and the result is generalized for the whole group. No doubt the first method involves more time and cost but provides more accurate information than the second. Depending on the nature of enquiry and the degree of accuracy desired only one of the above...