Discussion: Central Tendency and Variability

ENTRAL TENDENCY AND VARIABILITY

The measure of central tendency can be referred to as a single value that describes a set of data through the identification of the central position within a data set (Frankfort-Nachmias, Leon-Guerrero & Davis, 2020). Although the mean is often used to measure central tendency, the median and mode are equally valid measures of central tendency depending on different conditions.

CONTINOUS VARIABLE

From the Global Social Survey (GSS) Dataset, the continuous variable I selected is: The highest year of school completed by respondent.

Data Source:  Smith, Tom W., Davern, Michael, Freese, Jeremy, and Stephen L. Morgan. General Social Surveys, 1972-2018. [machine-readable data file]. Principal Investigator, Tom W. Smith; Co-Principal Investigators, Michael Davern, Jeremy Freese and Stephen L. Morgan, NORC ed. Chicago: NORC, 2019.

For the variable - highest year of school completed by respondents, the GSS Dataset reports 507 valid cases with 0 of the cases, missing. The  mean  of the highest year of school completed is 14.29, the  median  is 15.00 and the  mode  is 16.

Given the above continuous variable, the mean is the better measure for central tendency because in calculating the mean, all the other values in the data set are included (Frankfort-Nachmias, Leon-Guerrero & Davis, 2020). Any change in any of the scores in the data set would directly affect the value of the mean.

The GSS reports the standard deviation for the highest year of school completed as 3.353, which is the difference between each data from the mean. With the standard deviation being the typical amount that scores deviate from the mean, 3.353 indicates that the dispersion is closer to the mean. Variability represents the amount of dispersion in a dataset. A lower variability in the distribution indicates that the values in the dataset are consistent, while a higher variability shows inconsistency in the distribution of values in the dataset. A variance of 11.245 also indicates consistency/low variability in the highest year of school completed by the respondents.

With most respondents haven attained some level of education, obstacles to positive social change such as superstition and parochialism would be eroded, creating a smooth flow of informed dialogue in society on matters of common good.

CATEGORICAL VARIABLE

From the Global Social Survey (GSS) Dataset, the continuous variable I selected is: Are you a citizen of America?

Data Source:  Smith, Tom W., Davern, Michael, Freese, Jeremy, and Stephen L. Morgan. General Social Surveys, 1972-2018. [machine-readable data file]. Principal Investigator, Tom W. Smith; Co-Principal Investigators, Michael Davern, Jeremy Freese and Stephen L. Morgan, NORC ed. Chicago: NORC, 2019.

Giving that the variable I selected from the GSS is a nominal variable, the only appropriate measure of central tendency is the mode, which is the category with the greatest frequency (Wagner, 2020). From the data set, out of 507 participants, 254 respondents answered YES or NO to the question on American citizenship and of the 254 respondents, 228 answered YES while 26 answered NO. The mode is therefore 1, representing the category with the greatest frequency as displayed on the pie chart above. From the distribution of the values of respondents in the pie chart above, there is a high variability in the data. With a majority of the respondents being American citizens, it depicts a unitary concept for positive change in society.

Reference

Frankfort-Nachmias, C., Leon-Guerrero, A., & Davis, G. (2020). Social statistics for a diverse society (9th ed.). Thousand Oaks, CA: Sage Publications.

Wagner, III, W. E. (2020). Using IBM® SPSS® statistics for research methods and social science statistics (7th ed.). Thousand Oaks, CA: Sage Publications.