Refer to the Data provided on Blackboard by the Instructor The data shows student enrolment in a private college from 1965 to 2005
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.
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.
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.
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