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As one of the oldest multivariate statistical methods of data reduction, Principal Component Analysis (PCA)simplifies a dataset by producing a small number of derived variables that are uncorrelated and that account for most of the variation in the original data set. Eventually, the derived variables are combinations of the original variables. For example, it might be ?hat students take 10 examinations and some students do well in one exam whilst other students do better in another. It is difficult to compare one student with another when we have marks from 10 examinations to consider. One obvious way of comparing students is to calculate tlie mean score. This is a constructed combination of the existing variables,. However. we may get a more useful comparison of overall performances by considering other constructed combinations of the 10 exam marks. The PCA is one way of constructing such combinations, doing so in such ewakas to account for as much as possible of the variation in the original data. One can then compare students' performance by considering this much sn~aller number of variables.
Show how the Normal bin width rule can be modied if f is skewed or kurtotic. Examine the effect of bimodality. Compare your rules to Doane's (1976) extensions of Sturges' rule.
Examples of grouped, simple and frequency distribution data
Waht is the product of £ x
Mode Mode is the value of the observation which occurs with the greatest frequency and thus it is the most fashionable value, Mode has been derived from French word La m
This probability rule determined by the research of the two mathematicians Bienayme' and Chebyshev, explains the variability of data about its mean when the distribution of the dat
mark number of student 0-10 4 10-20 8 20-30 11 30-40 15 40-50 12 50-60 6 calculate frequency distribution
Standard Deviation The concept of standard deviation was first introduced by Karl Pearson in 1893. The standard deviation is the most important and the popular measure of disp
Harmonic Mean The harmonic mean also called harmonic average, in the total numbers of items of variable divided by the sum of r reciprocals of the values of the variable. In
Testing of Hypothesis One objective of sampling theory is Hypothesis Testing. Hypothesis testing begins by making an assumption about the population parameter. Then we gather
Steps in ANOVA The three steps which constitute the analysis of variance are as follows: To determine an estimate of the population variance from the variance that exi
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