Harmonic-Statistics-Notes, Study notes of Statistics

Statistics study consist on topics like estimates, estimator, F distribution, sampling, multiplication theorems, probability, random variable, T distribution, geometric probability distribution, marginal probability, skewness, symmetrical distribution and transformation. This lecture note includes: Harmonic, Mean, Reciprocal, Value, Arithmetic, Quantile, Sub-division, Variable, Index, Number, Standard, Deviation, Variance, Regression

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2011/2012

Uploaded on 08/12/2012

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Harmonic
Mean :
Harmonic mean is defined as the reciprocal of the arithmetic mean of the
reciprocals of the values.
Quartiles : Quartiles are those three quantities that divide the distribution into four
equal parts.
Quantiles : Collectively the quartiles, the deciles,percentiles and other values
obtained by equall sub-division of the data are called quantiles.
Index
Number :
An Index Number is a statistical measure which shows changes in a
variable or group of related variables with respect to time, geographic
location or other characteristics such as income, profession etc.
Standard
Deviation :
Standard Deviation is defined as the positive square root of the mean of
the squared deviations of the values from their mean.
Variance : Variance is defined as the square of the standard deviation.
Regression
:
Dependence of one variable on the other variable is called regression. OR
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HarmonicMean :Harmonic mean is defined as the reciprocal of the arithmetic mean of thereciprocals of the values.Quartiles : Quartiles are those three quantities that divide the distribution into fourequal parts.Quantiles : Collectively the quartiles, the deciles,percentiles and other valuesobtained by equall sub-division of the data are called quantiles.IndexNumber :An Index Number is a statistical measure which shows changes in avariable or group of related variables with respect to time, geographiclocation or other characteristics such as income, profession etc.StandardDeviation :Standard Deviation is defined as the positive square root of the mean ofthe squared deviations of the values from their mean.Variance : Variance is defined as the square of the standard deviation.Regression: Dependence of one variable on the other variable is called regression. OR

Estimation or prediction of one variable on the basis of other variable iscalled regression.RandomExperiment: An experiment which produces different results even though it is repeateda large number of times under essentially similar conditions is called arandom experiment.Sub Set : A set that consists of some elements of an other set is called a subset ofthat set.Non-SamplingError :Such errors which are not attributable to sampling but arise in the processof data collection even if a complete count is carried out.Skewness : Skewness is the lack of symmetry in a distribution around some centralvalue (mean,median or mode).It is thus the degree of a symmetry.Permutation:

the obtained result really is.Test Statistic :A statistic (i.e. a function of sample data not containing any parameter),which provides a basis for testing a null hypothesis, is called a teststatistics.Additionlaw :A probability law used to compute the probability of a union of twoevents, denoted A and B. It is P(AÈB)=P(A)+P(B)-P(AÇB). For mutuallyexclusive events, because P(AÇB)=0, it reduces to P(AÈB)=P(A)+P(B).AlternativehypothesisThe hypothesis concluded to be true if the null hypothesis is rejected.: ANOVAtable :A table used to summarize the analysis of variance computations andresults. It contains columns showing the source of variation, the sum of

squares, the degrees of freedom, the mean square, and the F values.Bayes'theorem :A method used to compute posterior probabilities.Binomialprobabilitydistribution: A probability distribution showing the probability of x successes in ntrials of a binomial experiment.Binomialprobabilityfunction :The function used to compute probabilities in a binomial experiment.Blocking : The process of using the same or similar experimental units for alltreatments. The purpose of blocking is to remove a source of variationfrom the error term and hence provide a more powerful test for adifference in population or treatment means.Box plot : A graphical summary of data. A box, drawn from the first to the thirdquartiles, shows the location of the middle 50% of the data. Dashed lines,called whiskers, extending from the ends of the box show the location of

The hypothesis tentatively assumed true in the hypothesis testingprocedure. or A null hypothesis, generally denoted by the symbol H0, isany hypothesis which is to be tested for possible rejection or nullificationunder the assumption that it is true.Normalprobabilitydistribution: A continuous probability distribution. Its probability density function isbell shaped and determined by its mean m and standard deviation s.Observation: The set of measurements obtained for a single element.Ogive : A graph of a cumulative distribution.One-tailedtest :A hypothesis test in which rejection of the null hypothesis occurs forvalues of the test statistic in one tail of the sampling distribution. or Theentire rejection region lies in only one of the two tails, either in the right

tail or in the left tai, of the sampling distribution of the test-statistic, iscalled a one-tailed test or one-sided test.Parameter : numerical characteristic of a population, such as a population mean, apopulation standard deviation, a population proportion, and so on.Pointestimate :A single numerical value used as an estimate of a population parameter.Pointestimator :The sample statistic that provides the point estimate of the populationparameter.Poissonprobabilitydistribution: A probability distribution showing the probability of x occurrences of anevent over a specified interval of time or space.Poissonprobabilityfunction :The function used to compute Poisson probabilities.