(b) Calculate the sample variance and sample standard deviation.Example 9: Which of the following are the major sources of variability inthis experiment?•Standard Score/ Z score Number of standard deviations an observation is more orless than the mean of the distribution in which it occursExample 10:A popular food chain administered an aptitude examinationof 2 groups of practicum students working on different shifts. They weregiven special practical task that they should finish under time pressure. Astudent from each group was selected to assess performance. Which of thetwo perform well on examinations relative to the shift when each belongs?This was reflected by his z-score of 1.4 (implies that his performance isonly 1.4 SD less than or below his group mean)z=X−
μ
σ
deviationStandardskewnessoft coefficiensPearson'4. Measures of Symmetry and Measures of PeakednessSkewnessThe term skewness refers to the lack of symmetry. Measures of SkewnessIf Mean > Mode, the skewness is positive.If Mean < Mode, the skewness is negative.If Mean = Mode, the skewness is zero.Many distribution are not symmetrical.They may be tail off to right or to the left and as such said to beskewed. One measure of absolute skewness is difference between meanand mode. A measure of such would not be true meaningfulbecause it depends of the units of measurement. The simplest measure of skewness is the Pearson’s coefficient ofskewness:Kurtosisis the degree of peakedness of a distribution, usuallytaken in relation to a normaldistribution. Maybe described asLeptokurtic Platykurtic Mesokurtic Normal DistributionWhy are normal distributions so important?Many dependent variables are commonly assumed to be normallydistributed in the populationIf a variable is approximately normally distributed we can makeinferences about values of that variableExample: Sampling distribution of the meanNormal DistributionSymmetrical, bell-shaped curveAlso known as Gaussian distributionPoint of inflection = 1 standard deviation from meanFor normal distributions+1 SD ~ 68%+2 SD ~ 95%+ 3 SD ~ 99.9%Z-scoreIf we know the population mean and population standard deviation, for any value of X we can compute a z-score by subtracting the population mean and dividing the result by the population standard deviationImportant z-score infoZ-score tells us how far above or below the mean a value is in terms of standard deviationsIt is a linear transformation of the original scores