Statistics for Research - L8 - Descriptive Statistics using R

Descriptive statistics boil down to two goals: summarize what’s “typical” in a dataset and quantify how widely values spread. Central tendency answers what a typical value looks like—using the mean, median, or mode depending on the measurement scale—while dispersion (variability) shows whether those typical values are reliable or whether observations are scattered. Together, these measures form the baseline evidence researchers report in theses and papers.

Central tendency starts with the mean, the arithmetic average found by summing all observations and dividing by the number of cases. Mean is the go-to measure for interval and ratio variables, such as heights. When values are ordered but not evenly spaced—ordinal data—median becomes the better choice, defined as the middle value once data are arranged from lowest to highest. For nominal variables, where categories have no natural order, the mode is used: the category value that appears most often. The transcript illustrates mode with a small example where “male” (coded as 1) appears more frequently than “female” (coded as 2), making 1 the mode.

Dispersion then addresses a different question: even if there’s a typical value, how tightly do observations cluster around it? The range provides a quick sense of spread by subtracting the minimum from the maximum. For a more informative measure, standard deviation is used to indicate how much values generally vary from the mean. Lower standard deviation means most observations sit close to the mean, while higher standard deviation signals wider scattering. Standard error refines this idea for inference by estimating how accurately a sample mean represents the true population mean; it’s computed by dividing the standard deviation by the square root of the sample size. In practice, lower standard error implies greater accuracy.

The session then shifts from concepts to implementation in R, positioning R as a free, open-source statistical computing language used to write and run data-analysis code. After recommending an IDE like RStudio, it walks through the workflow: download R and RStudio, create an R script, load a CSV dataset using read.csv, and verify the import with head. From there, summary statistics are produced with summary, which returns key distribution metrics such as minimum, quartiles, median, mean, and maximum for each variable.

For specific measures, the transcript demonstrates mean(), median(), and standard deviation calculations by targeting a variable via the dataset object and the $ operator (e.g., data$V1). It also notes a practical limitation: R doesn’t provide a built-in mode function by default, so the workflow uses an external package. Installing and loading the package (via install.packages and library) enables a mode() function to compute the most frequent value for numeric variables and categorical codes (e.g., mode for a gender variable). The result is a repeatable recipe for reporting central tendency and dispersion in research settings, with a promise of more advanced statistics in later sessions.