succeedinyourstudies. This guide outlines three methods used to summarise the variability in a dataset. It will help you identify which measure is most appropriate to use for a particular set of data. Examples are also given
Overview. Discuss Common Measures of Variability. ? Range. ? Semi-Interquartile Range. ? Variance. ? Standard Deviation. Derive Computational Formulas for the. Standard Deviation and Variance
Measures of Variation -. Measures of Variation. Some Comments. • Range is the simplest, but is very sensitive to outliers. • Variance units are the square of the original units. • Interquartile range is mainly used with skewed data (or data with outliers). • We will use the standard deviation as a. f i i ft i hi measure of variation
Summarizing Data: Measures of Variation. One aspect of most sets of data is that the values are not all alike; indeed, the extent to which they are unalike, or vary among themselves, is of basic importance in statistics. Consider the following examples: In a hospital where each patient's pulse rate is taken three times a day,
Histograms are important tools for image processing. By doing statistics on the individual pixel values we can analyze an image, attempt to recognize features, or just make it “look better". center overall brightness of the image (mean pixel value) variation image contrast. 1
The variance and standard deviation are two measures of variability that indicate how much the scores are spread out around the p mean. • We use the mean as our reference point since it is at the center of the distribution. Page 8. The Sample Variance and the p. Sample Standard Deviation. Page 9. Sample Variance.
Measures of variation refer to a group of statistics that is intended to provide us with information on how a set of scores are distributed. An examination of measures of variation is a logical extension of any description of a data set using the measures of central tendency that we examined in the previous chapter. Consider a
Chapter 3: Measures of Variability. I. Measures of central tendency vs. Measures of variability a. Measures of central tendency (e.g., mean, median, mode) provide useful, but limited information. Information is insufficient in regards to the dispersion (i.e., variability) of scores of a distribution. b. Three measures of variability
Characteristics of. Standard Deviation? s is usually positive and NEVER negative s is 0 only when all data values are the same number the larger value for (s) the greater amount the data varies s can increase dramatically with the inclusion of outliers the units (minutes, feet, etc) are the same as the units of original values

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February 2018