Sociology Plus
Descriptive Statistics Definition
Descriptive statistics are methods used to summarise and describe the distribution of a set of data, either from a sample or an entire population. They provide a statistical summary that allows researchers to understand the characteristics of the observed scores and categories within a dataset.
Measures of Central Tendency
Measures of central tendency are used to identify the typical or central point of a distribution. The three most common measures are the mean, median, and mode. The mode is the category or score that occurs most frequently in the distribution; however, it does not necessarily represent the exact centre of the data. The median is the value that divides the distribution exactly in half, meaning 50 per cent of the scores lie above it and 50 per cent lie below it. The mean is the arithmetic average, calculated by summing all scores and dividing by the total number of observations. While the mean is mathematically useful, it is highly susceptible to influence from extreme values or outliers, which can distort the true centre of a distribution, particularly in skewed samples. Consequently, the median is often considered a more robust measure of central tendency when dealing with skewed data.
Measures of Dispersion
Measures of dispersion quantify the spread or variability of the data around the central point. The range is the simplest measure of dispersion, calculated as the difference between the highest and lowest scores in the distribution. Variance measures the average squared difference of each score from the mean; however, because it is measured in squared units, it is less intuitively understood than other measures. The standard deviation is derived by taking the square root of the variance, making it a more interpretable measure that represents the average distance scores are from the mean. These measures help distinguish between heterogeneous samples, which exhibit high dispersion, and homogeneous samples, which show very little variation.
Sample vs. Population
It is important to distinguish between statistics and parameters. Descriptive statistics are typically calculated from a sample of data; these values are referred to as statistics. Conversely, when describing the entire population, the corresponding values are termed parameters. Therefore, when using descriptive statistics, the focus is generally on the observed sample rather than the complete population.