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Descriptive Statistics

Descriptive statistics is exactly what it is. It is generally used to describe a population (for example, height of adult males in England) using a sample collected from that population. It provides a statistical summary of the sample with a view to understand the population that the sample represents. Several techniques can be used to describe the sample data:

  • Graphical description in which one uses graphs and charts to summarize data.

  • Tabular description in which one uses tabular forms to summarize data.

  • Summary statistics in which one calculates certain values to summarize data. For example:

    • the mean, and the number of measurements (N) that it was based on;

    • a measure of the variability of the data about the mean (standard deviation); and

    • other useful information derived from the mean and standard deviation, such as (1) the range within which 95% or 99% or 99.9% of measurements of this sort would be expected to fall - the confidence intervals, and (2) the range of means that we could expect 95% or 99% or 99.9% of the time if we were to repeat the same type of measurement again and again on different samples - this is often called the standard error.

When we are summarizing a quantity like height or weight or age, it is common to describe the central tendency of the data with the mean, the median, or the mode.

The measures of central tendency page contains the descriptions and applications of mean, median, and mode. These pages also contain information about the calculation of confidence intervals and standard errors for mean.

The spread of the data are useful measures to describe variations within the data. For example, the range of weight or height of students in a class. Assessing these variations are important to understand, for example, extremes in weather or climate.

The spread of the data are usually assessed by calculating the range, variance, standard deviation, and coefficient of variation etc. For the complete details and formulations of these measures go to the measures of dispersion (also known spread measures) page.

Descriptive statistics is an important part of the Information Techniques.

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Next: Central Measures