Measures of Central Tendency and Dispersion With SPSS Research Paper

GPA is interval level data one can report all measures of central tendency and dispersion (Creswell, 2012). In the original data case 38 had a GPA reported as 9.00. This value is of course impossible and since there were no missing values defined in the data set this case was treated as missing data. If used as reported it would have resulted in a much larger standard deviation and slightly larger mean for the calculations. The mean GPA of the sample was 3.2941. The median GPA was 3.2750 with a mode of 4.00. The standard deviation was .50644 (with the miscoded value the standard deviation would be .82215). The range for GPA in the sample was 2.00 with a minimum value of 2.00 and a maximum value of 4.00 (including the miscoded value would inflate the range to seven).

The syntax and output files for the analysis follows are presented in the appendix. The syntax for the analysis is as follows:

FREQUENCIES VARIABLES=gpa

/STATISTICS=STDDEV VARIANCE RANGE MINIMUM MAXIMUM MEAN MEDIAN MODE

/HISTOGRAM NORMAL

/ORDER=ANALYSIS.

Figure One displays a histogram of the GPA for the sample. As can be seen in Figure One the data appears to be slightly positively skewed.Because marital status is a categorical variable the mean and the median are not very good descriptors of central tendency. In the current data set there only two values for marital status either married or unmarried (0, 1). The mode can be a useful measure of central tendency for categorical variables as it does give information regarding the most frequently occurring category in the data. Means and medians are better descriptors for non- -- nominal variables (Jackson, 2012). The modal value in this case was the non-married category with 73 cases (nearly 95% of the sample) reporting that they were not married. As this particular variable is a dichotomous variable the standard deviation or range are not useful measures of dispersion. Moreover, for categorical data looking at the percentages in the sample that belong to the different specific categories is a better description of dispersion within categorical data than the range, the minimum and maximum, or the standard deviation as these descriptive statistics imply some type of quantitative relationship (Runyon, Coleman, & Pittenger, 2000). The coding of nominal data simply assigns numbers as descriptors to the data and does not imply any.....