# Descriptive Statistics and Research Data Analysis Coursework

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Updated: Jun 9th, 2022

## Abstract

Descriptive statistics are the mathematical expression of data characteristics of a population sample. The aim of this essay is to provide a brief yet comprehensive review on what are descriptive statistics and the purpose they serve in analyzing data obtained from research.

## Introduction

There are four main types of research data; the first is nominal data where the expression of data categories is in numbers. The second is ordinal data where data are put in ranks in a comparative layout (as highest and lowest IQ in a class). Third, data are arranged in scales when values allocated to levels of observable facts are arranged at equal intervals. Finally; ratio data is the number of observed facts (behavior, personality type…). In this case, there must be a reference or a comparison point to allow forming of ratios (Gabrenya, 2003). Statistical methods are applied to variables; a variable explains the traits of individuals in a data set. It is significant to know which type of variables in order to deal with data in a proper statistical methodology. Variables are commonly one of three types, namely continuous where the variable value is obtained through measurements such as blood pressure, temperature. Discrete variables are those described qualitatively as gender, occupation, mild, moderate or severe. Ordinal variables are described in a semi-quantitative manner as expressing a set of data in + and – ways (Shi and Tao, 2008).

## What are descriptive statistics?

Descriptive statistics are the mathematical expression of data characteristics of a population sample. They are the first step in analyzing collected data in a research process and form the basis for further mathematical calculations needed for inferential statistics as tests for significance, correlation, regression, and analysis of variance. Although they are simple to calculate; they are important as they provide an idea about the data collected as regards the most typical value in a data set. They also provide an idea about the variability of data, finally, they can graphically summarize and represent the data collected (Shi and Tao, 2008).

## What are the purposes of descriptive statistics?

Descriptive statistics have three functions: 1- To measure the central tendency of data that is how the data collected aggregate around a most typical value. Three values measure the central tendency of data: a- the mean, which is the average value for a column of data, b- the median, which is the middle observation of a column of data (the largest value of the smaller half of data). Besides, c- The mode, this is the most frequent value in a column of data. The mean is the most significant because of its sensitivity (affected by changes in the sample size) (Robson, 2002). The second function of descriptive statistics is to measure data dispersion (data spread or variability around the mean). Three measurements are commonly used for this purpose: A- the range: It is the difference between the highest and lowest value in a column of data. B- Standard deviation, which quantifies data inconsistency around the mean. C- Variance, is an expression of the observed differences from what would be expected if there were no natural variation (the same as the standard deviation). It is the mean of squared deviations from the mean and is used when sign (- or +) is considered (Robson, 2002).

Research data can be summarized and graphically represented by a histogram, which is a graphic display of how data are distributed in a data set. A normal curve (histogram) points to data collected from a representative sample. Data can also be summarized and represented by bar, line, or box plot graphs (Robson, 2002).

## Conclusion

Statistical analysis of research includes two processes, descriptive (basic statistics) and inferential statistics. Descriptive statistics besides being an essential step to perform inferential statistics is important to give an idea about central tendency and data variability. It is essential to properly arrange the data collected in frequency tables and obtain numerical values of central tendency and dispersion measures. Graphic representation summarizes the data collected and provides an idea about the normality of data collected from the sample research.

Gabrenya Jr, W. K. (2003). Descriptive Statistics. Web.

Robson, C. (2002). Real-World Research: A Resource for Social Scientists and Practitioner-Researchers (Regional Surveys of the World). Chicago, Illinois: Blackwell Publishing Limited.

Shi, Ning-Zhong, and Tao, Jian (2008). Statistical Hypothesis Testing: Theory and Practice. Singapore: World Scientific Publishing Co. Pte. Ltd.