# Descriptive Statistics and Interpreting Statistics

**Descriptive statistics** are useful for describing the basic features of data, for example, the summary statistics for the scale variables and measures of the data. In a research study with large data, these statistics may help us to manage the data and present it in a summary table. For instance, in a cricket match, they can help us to manage records of the player and also help us to compare one player’s records with another player’s records.

**Types of Descriptive Statistics**

1. Measure of central tendency: The measure of central tendency measures the average value of the sample. In descriptive statistics, there are two types of averages: the first are the mathematical averages and the second are the positional averages.

The mathematical averages are of three types: arithmetic mean, geometric mean, and harmonic mean. The arithmetic mean is the most widely used measure for central tendency; it can be obtained by adding all the items of the series and dividing this total by the number of items. In descriptive statistics, the geometric mean is defined as the nth root of the products of all the n values of the variable. In descriptive statistics, the geometric mean is used when the items in the series are very large. The harmonic mean is defined as the reciprocal of the item. The harmonic mean is useful in finding the averages that involve speed, time, price and ratio.

There are two types of positional average: the median and the mode. The median is the average value of the series in which half the values are less than the median and half the values are greater than the median. The mode, the second positional average, shows a higher frequency in the series.

2. Measure of dispersion: In descriptive statistics, we can elaborate upon the data further by measuring the dispersion. Usually the range of the standard deviation and variance is used to measure the dispersion. In descriptive statistics, range is defined as the difference between the highest and the lowest value. The standard deviation and variance are usually used to measure the dispersion. Standard deviation is also called the root mean square deviation. Variance is also used to measure the dispersion, which can be simply derived from the square of the standard deviation. Visit our blog post on dispersion at this link for additional information.

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**Descriptive Statistics in SPSS**

As we’ve just described, descriptive statistics are used primarily to summarize the data. SPSS is statistical software that is used to calculate descriptive statistics. In SPSS, we have to perform the following steps:

- From the start menu, click on the “SPSS menu.”
- Select “descriptive statistics” from the analysis menu. After clicking the descriptive statistics menu, another menu will appear.
- From this window, select the variable for which we want to calculate the descriptive statistics and drag them into the variable window. Click on the option and select the descriptive statistics. After that, click on the “OK” button. The result window will appear and the descriptive statistics results table above will appear.

This table summarizes all of the raw data in the form of a table; these descriptive statistics are also used for comparison.

Your committee and the other professional readers of your dissertation will want to know the make-up of your sample and the responses to the questions in your instrument. Our statistics consultants will conduct these descriptive statistics for you, including a written explanation of the descriptive statistics, tables of the descriptive statistics, and figures of the descriptive statistics where appropriate, all in APA formatwith special attention to your institution’s requirements. Descriptive statistics are important for establishing the validity of your sample as a representation of the sampled population. Including these in your dissertation will allow comparison to other similar studies, while placing your results in perspective.

**Descriptive Statistics and Interpreting Statistics Resources**

Bartz, A. E. (1971). Basic descriptive statistics for education and the behavioral sciences (4th ed.). Oxford, UK: Burgess.

Bernstein, S., & Bernstein, R. (1999). Schaum’s outline of elements of statistics I: Descriptive statistics and probability. New York: McGraw-Hill.

Gotkin, L. G., & Goldstein, L. S. (1965). Descriptive statistics: A programmed textbook. New York: John Wiley & Sons.

Levitas, R., & Guy, W. (1996). Interpreting official statistics. New York: Routledge.

Li, J. C. R. (1957). In J. C. R. Li (Ed.), Introduction to statistical inference (pp. 3-13). Ann Arbor, MI: The Science Press.

McHugh, M. L., & Hudson-Barr, D. (2003). Descriptive statistics, part II: Most commonly used descriptive statistics. Journal for Specialists in Pediatric Nursing, 8(3), 111-116.

McPherson, G. (2001). Applying and interpreting statistics: A comprehensive guide (2nd ed.). New York: Springer-Verlag.

Morgan, G. A., Gliner, J. A., & Harmon, R. J. (1999). Measurement and descriptive statistics. Journal of the American Academy of Child & Adolescent Psychiatry, 38(10), 1313-1315.

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