General statistic - Statistics Project Example

?GS and Section # of Analyzing Data Statistically For a Research Paper The following report contains study results performed on 100 students of a university, who had been chosen randomly from different areas of the university and were enquired about their ages. The data was collected from students at different times of the schooling hours. The data was collected has been presented in tabulated form in fig i and fig i (a) No.of students   Student ages       1   17-18 5   18-19 15   19-20 19   20-21 22   21-22 21   22-23 14   23-24 3   24-25 Figure i (a) Type of Data There are two basic types of data quantitative and qualitative. Quantitative data refers to an observation based upon facts and numbers, where as if it is not then that is called Qualitative data. In this research, the data used to make conclusions is of Quantitative type, since the number of students falling in an age group has been collected. Level of Measurement There are four basic types of levels of measurements. Nominal Variables can be assigned names but their quantity cannot be determined. Ordinal The variables have a sense of quantitative distinction but the level of distinction is not determined. Interval The distinction between variables has a quantitative sense. Ratio A scale is set that refers to an absolute zero and measurements made take that point as a reference. In this study, the levels of measurement used to scale variables are INTERVAL variables, because there are distinct groups of people that are placed at equal distant from each other so the most appropriate variable form for this case is the INTERVAL form. Frequency Distribution Table No. of students Student ages Cumulative frequency Relative frequency 1 17-18 1 0.01 5 18-19 6 0.05 15 19-20 21 0.15 19 20-21 40 0.19 22 21-22 62 0.22 21 22-23 83 0.21 14 23-24 97 0.14 3 24-25 100 0.03 Figure i By looking at the frequency distribution graph, it is prominent that the majority of the students lie in the age group of 19-23. The largest number of students lies in the age group of 21-22 years of age. Cumulative Frequency The cumulative frequency predicts the trend that with increasing age the cluster of students lying in a class increases up to the age group of 21-22 years. Formula used for cumulative frequency calculations is Relative Frequency The relative frequency of the distribution shows the largest share of frequencies lies in the age groups of 21-22 and 22-23. The relative frequency also depicts that the majority share of the students lie in the middle age groups Class Boundaries The class boundaries are calculated to be .05 from the class limits. The Mean, Median and Mode The class boundaries and data for the calculations of mean, median and mode have been represented in the table below No. of students F Student ages Class boundaries X (F)*(X) 1 17-17.9 16.95-17.95 17.45 17.45 5 18-18.9 17.95-18.95 18.45 92.25 15 19-19.9 18.95-19.95 19.45 291.75 19 20-20.9 19.95-20.95 20.45 388.55 22 21-21.9 20.95-21.95 21.45 471.9 21 22-22.9 21.95-22.95 22.45 471.45 14 23-23.9 22.95-23.95 23.45 328.3 3 24-24.9 23.95-24.95 24.45 73.35 ?F = 100 2135 Figure ii Mean The mean is calculated from the table to be Mean = = 21.35 The mean suggests that the average of the data lies at the age of 21.35. Median Here, the number of observations ?F= n=100 This is an even number, so the median is average of (n / 2) th and (n / 2 + 1)th Observations I.e. average of ( 100 / 2 )th and [(100 / 2) + 1]th observation. I.e. average of 50th and 51st observations. Where l = lower limit of median class C.F = cumulative frequency of class prior to median class. f = frequency of median class. h = class size. Median= = 21.4 Mode The mode of a data is the value that has maximum number of frequency. Where: l = lower limit of modal class f1 = frequency of modal class fm = frequency of class preceding the modal class. f2 = frequency of class succeeding the modal class h=class size Here the modal class is of age groups 21-22. Hence, the mode becomes MODE= = 21.7 Hence, the mode is 21.7. This suggests that the most number of students are aged around 21.7 years. The mean, median and mode are close to each other, this represents a normal frequency distribution. The close values of mean and median depict the data to be a normal distribution, if the median and mean were far apart that would have meant that the data with the higher value of F*X is dominating the average. But since the median and mean are close together this shows neither the higher nor lower frequencies are affecting the data nor the data average is independent of the extreme end values of the distribution. Histogram The graph that shows the frequency distribution is shown below. The graph clearly predicts a normal distribution of frequency that is the age groups of Middle Ages 20-23 have the highest frequencies, and the frequencies fall at either side of the midpoint. The trend line follows a normal bell curve shape. Figure iii Conclusion The conclusion can be deduced from looking at the results is that most of the students in a university starting their university at the ages of 19. A few students who excel at school or high school level are granted leaps in their grades and start the university at an earlier age. That is why there are a small group of students in the age category of 17-18. In addition, the age group of 24 and above indicates students who have been relegated in semesters or have started their university at a later age. But looking at the relative frequency they only form 3% of the total specimen. So the majority of the students are normal students who start university at the age of 19 and end up at the age of 23. Reference Formulae retrieved from www.2classnotes.com Read More