By Abdul Quader Miah
This ebook addresses the appliance of statistical options and techniques throughout a variety of disciplines. whereas its major concentration is at the software of statistical tools, theoretical features also are supplied as primary heritage details. It deals a scientific interpretation of effects usually came upon more often than not descriptions of equipment and methods equivalent to linear and non-linear regression. SPSS is additionally utilized in all of the program elements. The presentation of information within the kind of tables and graphs during the ebook not just publications clients, but additionally explains the statistical program and assists readers in reading vital gains. The research of statistical info is gifted constantly through the textual content. educational researchers, practitioners and different clients who paintings with statistical information will reap the benefits of studying utilized data for Social and administration Sciences.
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Mo ¼ Lm þ Cm Ã a aþb where Lm lower limit of modal class Cm class width of the modal class a absolute value of the difference in frequency between the modal class and the preceding class b absolute value of the difference in frequency between the modal class and the following class. The modal class is the class with the highest frequency. The following example illustrates the use of the formula. 6 The modal class for owners is 30–45 and that for renters is 6–12. For owners: Mo ¼ Lm þ Cm Ã a aþb 51 À 18 ð51 À 18Þ þ ð51 À 45Þ 33 ¼ 30 þ 15 Ã 33 þ 6 ¼ 30 þ 12:69 ¼ $42:69 ¼ 30 þ 15 Ã For renters: a aþb 220 À 186 ¼ 6þ6 Ã ð220 À 186Þ þ ð220 À 65Þ 34 ¼ 6þ6 Ã 34 þ 155 ¼ 6 þ 1:08 ¼ $7:08 Mo ¼ Lm þ Cm Ã If there are two adjacent classes having the same highest frequency, the two classes may be combined together to form one single class and the calculation for mode can be done in the usual process.
8 Crushing strength of bricks (histogram) Histogram Frequency 35 Frequency 30 25 20 15 10 5 0 30 0 0 28 0 26 0 22 0 20 0 18 0 16 14 12 0 0 Crushing Strength of Bricks (PSI) Fig. F. 2 Graphical Presentation 23 Fig. 6 Line Diagram Line diagrams are drawn by plotting the values of two continuous variables. These show trends or changes in one variable resulting from changes in the other. One important application of the line diagram is to study the changes of various economic indicators over time. Line diagrams may be presented in the form of continuous lines or segmented lines depending on the phenomenon under study.
The geometric mean is deﬁned as Geometric mean ðGM) ¼ ﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ p n ðX1 Ã X2 Ã X3 Ã Á Á Á Xn Þ The calculations can be simpliﬁed by taking the logarithm of both sides. 4. Calculate the mean percentage change over the 5-year period. 55 per year. The calculations can be simpliﬁed by using logarithm. 4 Yearly sales ($) Year Sales ($) Percentage compared with a year earlier 1986 1987 1988 1989 1990 1991 4500 5000 7500 10,000 12,000 12,500 – 111 150 133 120 104 36 3 Descriptive Statistics For frequency distribution the formula should be modiﬁed in the following way: GM ¼ r ﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ ﬃ n X1f 1 Ã X2f 2 Ã X3f 3 Ã Á Á Á Xnfn ) log GM ¼ 1=nff1 Ã log X1 þ f2 Ã log X2 þ f3 Ã log X3 þ Á Á Á fn Ã log Xn g An important application of the concept of the geometric mean is growth rate calculation.
Applied Statistics for Social and Management Sciences by Abdul Quader Miah