Five numbers 4, 7, 10, 13, 16 represent the scores obtained by a student in five practice quizzes.
(i) Compute the variance and standard deviation of the scores.
(ii) If every score is multiplied by 3 to convert them to a different scoring scale, find the new variance and the new standard deviation without recalculating individual deviations.
(iii) Explain briefly why the relationship obtained in part (ii) between the old and the new measures of dispersion must always hold when each observation of a data set is multiplied by a constant.