discuss the scope of statistics?

Answer 1

Statistics deals basically with the estimation of model parameters from data and with the testing of hypotheses about their values; do comparable parameter values in two samples differ significantly, or does a particular parameter value differ significantly from some given value? These ideas may be used for optimizing experimental design and sampling strategies.

Statistics cannot deal with problems like: is this model ``correct'', or does this model fit significantly better than that model? Statistics treats the model as given. The goodness of fit of a model can be quantified. Only stochastic models can be tested against data; deterministic models are usually extended to stochastic ones, by introducing a `measurement error', and treating it as a regression model. This is convenient, but rarely realistic. Models might fit data well for the wrong reasons; models are idealizations of reality, so we can only expect some deviations from model predictions. To what extend deviations from model predictions are problematic depends on the purpose, so on the context. Since we deal with probabilities, we cannot be sure of anything while using statistics; a correct model might fit data poorly.

A model gets its value from the mechanistically inspired assumptions from which it is derived. Without such assumptions (so if the model itself is the assumption), the model is close the useless, including all statistical inference based on it. This is the reason why one should never transform data, wherever statistical text books might tell about this; transformations destroy the relationship between the model and its assumptions, and so the usefulness of the model.

Many statistical methods are based on linear models (e.g. ANOVA, multiple correlation, principal component analysis, factor analysis, auto-regression). Since such models rarely apply in biology, these methods are not discussed here.

Answer 2

Its everywhere and used very widely by all the business as well the government. Its used in insurance and manufacturing business to the highest extent and use.