(iii) Median and Mode of the data are the same and they represent the ample in a better manner. This is because, this being a small sized sample, the outliners will significantly affect the value of the sample mean, while median and mode are relatively less affected. Hence…
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Q1. (vi) The data points outside the range [Q1-1.5*IQR, Q3+1.5*IQR] are termed as outliers. For the dataset this range is [6.5, 82.5]. As there is no data point outside of this range. Hence there are no outliers.
Q2 (ii) He should definitely construct two frequency histograms. Only then he will be able to visualize the true picture of the difference in capabilities of the two sexes in solving the mental rotation problems.
(a) A histogram of a variable and residual should be drawn. If the histogram of the variables shows rough normality and that of residuals show normality then it is taken as an evidence of normality. (http://faculty.chass.ncsu.edu/garson/PA765/assumpt.htm)
(b) Kolmogorov-Smirnov D test or K-S Lilliefors test, is a test of normality for large samples. This test is available in SPSS under Analyze, Descriptive Statistics, Explore, Plots. Here one needs to check "Normality plots with
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