Data Provided on Blackboard by the Instructor - Statistics Project Example

Statistics Project Introduction: This project is aimed at providing information and analysis about the enrolment trend in a Private College for the 41 years period from the year 1965 to 2005 (both inclusive). It shows how the trend changed during these 41 years and it also shows the year wise enrolment as well as decade wise enrolment. Suitable graphs are also given along with stem and leaf diagram for the data. A table of descriptive statistics is also given. A table of frequencies, relative frequencies and cumulative relative frequencies also being given to enable the reader more comprehensive look at the data. A. Graph the data over time, and use the graph to explain how student enrolment has changed since 1965. Graph showing the student enrolment over the past 41 years from 1965 to 2005 Interpretation: By viewing the graph, we observe that the student enrolment has been constantly non decreasing over the past 40 years. The trend line is almost a straight line. If we form an equation with year as independent variable (1965 as 1 and 2005 as 41), the regression equation so formed is y=51.46x+1773.228 with R2=0.935. Almost 94% of the dependent variable enrolment is based on the year (for every increase in the variable year, there is a corresponding increase in the variable enrolment). The student enrolment is constantly increasing over the year and for only few years it got a slight decrease say during the years 1968, 1971, 1972 and 1984. For all the other years the enrolment never came down even for a single year. B. Draw a Stem and Leaf Diagram using the data provided. Explain what your graph reveals. The stem and leaf diagram was drawn using SPSS in the AnalyseDescriptive StatisticsExploreenrolment option of the SPSS menu. Enrolment Stem-and-Leaf Plot  Frequency    Stem &  Leaf      1.00        1900.51      3.00        2000.418296      5.00        2100.0844445384      1.00        2200.35      2.00        2300.5059 2.00 2400.3974      1.00        2500.33      1.00        2600.40      7.00        2700.25306568829093      1.00        2800.94      2.00        2900.6174      1.00        3000.49      3.00        3100.164569      1.00        3200.47      2.00        3300.0669      1.00        3400.82      1.00        3500.60      1.00        3600.95   1.00        3800.60      1.00        4000.43      1.00        4200.92      1.00 Extremes    (>=4466)  Stem width:   100.00  Each leaf:       0.5 case(s) Interpretation: Stem-and-leaf plots use the original data values to display the distributions shape. The plot for enrolment visualizes the positive skew statistic seen in the descriptives table; the values cluster uniformly in a range of 2000 to 3000, then disperse gradually for the forthcoming years. Interpretation: From the above boxplot, the median is somewhere around 2800 and we observe that more values are above median. Also Mean>Median>Mode. So the distribution is positively skewed. Most of the years had admission above 2800. There is one outlier that is, the 41st observation which has a value 4465.64. This indicates that the last year that is, 2005 the enrolment is much more than the average enrolment. This may have an influence on skewness. C. Present a Table of Descriptive Statistics for the enrolment variable. Explain your results. Table of descriptive statistics for the variable Enrolment Mean 2854.004 Median 2782 Mode 2144 Sample Variance 406378 Standard Deviation 637.4778 Coefficient of variation 22.34% Standard Error 99.55731 Minimum 1951 Maximum 4465.643 Range 2514.643 Kurtosis 0.014717 Skewness 0.693185 Confidence Level(95%) 201.2128 Confidence interval (95%) Lower 2652.79 Confidence interval (95%) Upper 3055.22 Count 41 Interpretation: From the above table of descriptive statistics, it is clear that the minimum is 1900 and the maximum is 4465.64 with range 2514.643. The median is 2782 and the mean of enrolment is 2854.04. The standard deviation is 637.48 with coefficient of variation nearly 22%. It is reliable data since the coefficient of variation is not above 25%. So the data is somewhat consistent. The skewness is 0.693 is close to 0 and the kurtosis is 0.0147 which is more close to 0. So, the distribution is almost normal and it is positively skewed and leptokurtic (very nearer to mesokurtic). The standard error is 99.56 and the 95% confidence interval for population mean is (2652.79, 3055.22). D. Develop a Table of Frequencies, Relative Frequencies and Cumulative Relative Frequencies. Explain how you determined the classes and class limits. Frequency table for enrolment in a Private college Procedure and interpretation: First of all we have to decide how many number of classes we need. Usually the classes would be from 5 to 10 depending on the total frequency. If the total frequency is in terms of 1000s we need 10 class intervals. Here the total frequency is only 41, it is enough if we divide them into 5 or 6 class intervals. Here, the minimum is 1951 and the maximum is 4465.643, the range is Maximum – Minimum = 2514.643/6=419~420 (nearest 10 for convenience), which is the class interval width. The class intervals are given by (starting from nearest 10) 1950-2370, 2370-2790, 2790-3210, 3210-3630, 3630-4050 and 4050-4470. The frequency table is given below: Frequency distribution of enrolment S.No. Class interval Frequency Relative Frequency Cumulative Relative Frequency 1 1950-2370 12 0.2927 0.2927 2 2370-2790 10 0.2439 0.5366 3 2790-3210 9 0.2195 0.7561 4 3210-3630 5 0.1220 0.8780 5 3639-4050 3 0.0732 0.9512 6 4050-4470 2 0.0488 1.0000 Total 41 1 - E. Using the Table in (D) above, 1. Draw a histogram. Explain how it compares to your Stem and Leaf diagram in part B above. Interpretation: The histogram is also a pictorial representation, but it gives rough idea about the distribution of frequencies whereas the stem and leaf gives very clear picture about the distribution of frequencies. The only disadvantage in stem and leaf is if the data values are very large, it is quite difficult to comprehend and it requires enormous pages where as the histogram is more comprehensible even when the frequencies are large. In the above diagram most of the years the admission occurred in the range 2000 to 2500. This is also depicted in the stem and leaf diagram 2. Draw an Ogive. Explain what the Ogive reveals. Interpretation: Ogive is the cumulative frequency curve. There are two ogives, 1. less than ogive and 2. more than ogive. The median is the X axis point where the less than ogive and more than ogive meet. It is some where around 2800. Read More