MSc(Mathematical Statistics) @ LUCKNOW UNIVERSITY
I have done MSc in Mathematical Statistics,MBA in Finance and PGDCA. I like to play Cricket, Badminton, Carrom. i am working Govt. research and Development Institute from last 7 years.I like maths and statistics problems.
I work on the basic of Students and try to make the problem easy so that the student himself do the problem.If he is unable to do that than i will explain it through similar examples.I have around 18 years of teaching experience as a Tutor.So I know better than the student what they want.
Simple random sampling (SRS) is a method of selection of a sample comprising of n number of sampling units from the population having N number of units such that every sampling unit has an equal chance of being chosen. The samples can be drawn in two possible ways. ->The sampling units are chosen without replacement in the sense that the units once chosen are not placed back in the population . -> The sampling units are chosen with replacement in the sense that the chosen units are placed back in the population.
An important objective in any estimation problem is to obtain an estimator of a population parameter which can take care of all salient features of the population. If the population is homogeneous with respect to the characteristic under study, then the method of simple random sampling will yield a homogeneous sample and in turn, the sample mean will serve as a good estimator of population mean. Thus, if the population is homogeneous with respect to the characteristic under study, then the sample drawn through simple random sampling is expected to provide a representative sample.Moreover, the variance of sample means not only depends on the sample size and sampling fraction but also on the population variance. In order to increase the precision of an estimator, we have to use a sampling scheme which reduces the heterogeneity in the population. If the population is heterogeneous with respect to the characteristic under study, then one such sampling procedure is stratified sampling. The basic idea behind the stratified sampling is to ->divide the whole heterogeneous population into smaller groups or subpopulations, such that the sampling units are homogeneous with respect to the characteristic under study within the subpopulation and heterogeneous with respect to the characteristic under study between/among the subpopulations. Such subpopulations are termed as strata. ->Treat each subpopulation as separate population and draw a sample by SRS from each stratum.
The systematic sampling technique is operationally more convenient than simple random sampling. It also ensures, at the same time that each unit has an equal probability of inclusion in the sample. In this method of sampling, the first unit is selected with the help of random numbers, and the remaining units are selected automatically according to a predetermined pattern. This method is known as systematic sampling.
In cluster sampling ->divide the whole population into clusters according to some well-defined rule. ->Treat the clusters as sampling units. ->Choose a sample of clusters according to some procedures. ->Carry out a complete enumeration of the selected clusters, i.e., collect information on all the sampling units available in selected clusters.
Frequency tables and empirical cumulative distribution functions are useful in providing a numerical summary of a variable. Graphs are an alternative way to summarize a variable’s information. In many situations, they have the advantage of conveying the information hidden in the data more compactly
variance is the expectation of the squared deviation of a random variable from its mean
the standard deviation is a statistic that measures the dispersion of a dataset relative to its mean and is calculated as the square root of the variance.
skewness is a measure of the asymmetry of the probability distribution of a real-valued random variable about its mean.
Kurtosis is a measure of whether the data are heavy-tailed or light-tailed relative to a normal distribution. That is, data sets with high kurtosis tend to have heavy tails, or outliers. Data sets with low kurtosis tend to have light tails, or lack of outliers. A uniform distribution would be the extreme case
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