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Explain the characteristic of statistics. ANSWER 1 Various characteristics of statistics as summarized as under : 1. Statistics deals with an aggregate of facts. A single figure cannot be analyzed. 2. Statistics gets affected to a great extent by multiplicity of causes The Statistics of the yield of a crop is the result of several factors, such as the fertility of soil, amount of rainfall, the quality of seed used, the quality and quantity of fertilizer used. 3. Statistics are numerically expressed

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Only numerical facts can be statistically analyzed. The qualitative data such as, the categorical data cannot be called as statistics, for example, the eye color of a person or the brand name of an automobile. 4. Statistics are enumerated or estimated with required degree of accuracy The facts have to be collected from the field or estimated (computed) with the required degree of accuracy. 5. Statistics are collected in a systematic manner The facts should be collected according to planned and scientific methods otherwise, they are likely to be wrong and misleading. 6.

Statistics are collected for a pre-determined purpose There must be a definite purpose for collecting facts. Otherwise, indiscriminate data collection might take place which would lead to wrong diagnosis. 7. Statistics are placed in relation to each other The facts must be placed in such a way that a comparative and analytical study becomes possible. |b. What are the components of Statistics? Give a brief description of each of the components. | The four components of Statistics are collection, presentation, analysis and interpretation of data. 1. Collection of data

Careful planning is required while collecting data. Two methods used for collecting data are census method and sampling method. 2. Presentation of data The collected data is usually presented for further analysis in a tabular, diagrammatic or graphic form and it is condensed, summarised and visually represented in a tabular or graphical form. For the representation of data in diagrams, we use different types of diagrams such as one-dimensional, two-dimensional and three dimensional diagrams. Pie-charts are two-dimensional diagrams which are in the form of a circle. 3. Analysis of data

The data presented has to be carefully analysed to make any inference from it. 4. Interpretation of data The final step is to draw conclusions from the analysed data. Interpretation requires a high degree of skill and experience. Thus, Statistics contains the tools and techniques required for collection, presentation, analysis and interpretation of data. |Q 2 Explain the objectives of Statistical Average. What are the requisites of a good average. | |The basic purpose of the statistical analysis is to determine the value which represents the whole series. This value is termed as central | |value or an average.

In other words, average is a statistical measure representing a group of individual values in simple and comprehensive | |manner. | |The following are the main’ objectives of an average: | |1. Facilitates Comparison: | |The foremost purpose of average is that it facilitates comparison | |2. Formulation of Policies: | |Averages are of great use in the formulation of various policy measures. |3. Short Description: | |Averages help to present the raw data in a brief a systematic manner. | |4. Representation of Universe: | |Average represents universe. According conclusions can be drawn in respect of the universe as a whole. | Requisites of a Good Average Since an average is a single value representing a group of values, it is desired that such a value satisfies the following properties: (i) It should be easy to understand.

Since statistical methods are designed to simplify complexity. It is desirable that an average is such that can be readily understood; otherwise, its use is bound to be very limited. (ii) It should be simple to compute. Not only an average should be easy to understand but also it should be simple to compute so that it can be used widely. (iii) It should be based on all the items. The average should depend upon each and every item of the series so that if any of the items is dropped the average itself is altered. (iv) It should not be unduly affected by extreme observations.

Although each and every item should influence the value of the average, none of the items should influence it unduly. Extremes may distort the average and reduce its usefulness. (v) It should be rigidly defined. An average should be properly defined so that it has one and only one interpretations. It should preferably be defined by an algebraic formula so that if different people compute that average from the same figures they all get the same answer. (vi) It should be capable of further algebraic treatment. We should prefer to have an average that could be used for further statistical computations so that its utility is enhanced. vii) It should have sampling stability. Last, but not the least, we should prefer to get a value which has what the statisticians call ‘sampling stability’ This means that if we pick 10 different groups of college students, and compute the average of each group, we should expect to get approximately the same value. |Q 3 a. Mention the Characteristics of Chi-square test. | ANSWER 3 a. Any statistical test that uses the Chi-square distribution can be called chi square test. It is applicable both for large and small samples-depending on the context.

The Chi-square test is also defined as the test we use to measure the differences between what is observed and what is expected according to an assumed hypothesis is called the chi-square test. Chi-square test is used as a test of goodness of fit and also as a test of independence. The X2 test is based on frequencies and not on parameters. It is a no-parametric test where no parameters regarding the rigidity of population of populations are required. Additive property is also found in X2 test. The X2 test is useful to test the hypothesis about the independence of attributes.