Descriptive and Inferential Statistics

Descriptive and Inferential Statistics

Both descriptive and inferential statistics are used in analysis of numeric data. Descriptive statistics are used to reveal patterns through this analysis. Descriptive statistics describe the group it belongs to. Examples of descriptive statistics are frequency counts, ranges, means, median scores, modes, and standard deviation. A specific example would be “the class had an average score of 90.2 %”. Inferential statistics are used to draw conclusions and make predictions through this analysis. Inferential is about a larger group. Examples of inferential statistics are experiments, probability, population, sampling, and matching. A specific example is “65% of Americans approve of the bill”.

Example of the Relationship between Descriptive and Inferential Statistics

This graph is a classical example of the normal curve, a theoretical standard statistical calculation. The graph is theoretical because it is rarely duplicated exactly in everyday life; however the curve itself represents a benchmark for the graphical understanding of statistical data (Aron, Aron, & Coups, 2009). In the realm of descriptive statistics, the normal curve represents a peak model of central movement; namely, that the mean, mode, and median all occupy the same position on the distribution. The normal curve also represents the ideal unimodal, kurtosis neutral, and symmetrical distribution. In fact, the basis for the idea of kurtosis rests on the deviation of the tails of the distribution from the standard normal curve. Furthermore, the formula for standard deviation, the typical amount that values differ from the mean, is SD= Square root of SS divided by N; and can be used both as descriptive instrument and an inferential device. The standard deviation of a distribution of number can be used to describe the variation of the scores from the mean, but can further be used to conclude future probabilities of distributions. Going back to the normal curve, it has been estimated that 34% of scores fall within the mean and one standard deviation, and that 14% of scores fall between one and two deviations from the mean. While taking these known qualifications into account, it is possible to determine a score give the percentage given the score. In this way, the normal curve can be used as a benchmark for distribution description as well as an inferential instrument for the prediction and qualification of scores.[pic 1]