LESSON 47 - DESCRIPTIVE STATISTICS: THE THREE METHODS OF ANALYSING DATA DESCRIPTIVELY

Descriptive statistics turn messy field data into manageable summaries—using a small set of numbers, tables, and graphs—so research findings can be presented and interpreted for an audience. Because descriptive statistics summarize a sample rather than the whole population, they limit generalization: results should be treated as describing the group actually observed, not claiming population-wide conclusions.

In social science research, data analysis often appears in Chapter 4, and it can be done manually or with software such as SPSS. The lesson frames data analysis as the process of reducing collected data to meaningful summaries. It also distinguishes descriptive statistics from inferential statistics: descriptive work focuses on summarizing what the sample looks like, while inferential methods are reserved for drawing broader conclusions.

Three methods organize descriptive statistics. First are tabular summaries, which rely on tables to present frequencies and relationships. Two common table types are frequency distribution tables and cross tabulation tables (crosstabs). Frequency tables show how often categories occur, while crosstabs compare categories across variables. The lesson also notes formatting conventions: tables are numbered by chapter (e.g., Table 4.1 for Chapter 4), and the table title appears at the top.

Second are graphical representations, using graphs selected according to the type of data and its scale of measurement. For categorical data, the lesson highlights bar graphs and pie charts; for continuous data, it points to histograms, frequency polygons, and scatter diagrams. A key practical link is that graph choice is not arbitrary: the data type determines the appropriate figure. The lesson further notes that histograms (drawn from continuous data) can provide distribution information such as the mean and standard deviation.

Third are numerical representations, which reduce many observations to single summary values. These include measures of central tendency and measures of variability. Central tendency uses the mean (for continuous data), the median (for continuous data), and the mode (for categorical data). The mean represents the typical value, the mode is the most frequent category/value, and the median is the middle value after ordering data. Because central tendency measures can be distorted by extreme values, the lesson stresses pairing them with variability.

Variability describes how spread out the data are around the mean. The lesson names range-related concepts and focuses on standard deviation and variance: variance is the sum of squared deviations, while standard deviation is the positive square root of variance. Interpretation is tied to distribution shape: a high standard deviation signals inconsistency and wide spread, while a low standard deviation indicates clustering near the mean. The lesson also references distribution shape concepts such as kurtosis and skewness (noting they describe how the distribution looks).

The takeaway is straightforward: descriptive statistics describe the sample and use three complementary approaches—tabular, graphical, and numerical—to summarize data accurately. The next step, deferred to a later lesson, is inferential statistics, which moves from description toward generalization.