1 / 12

Measures of Variation

This guide explores essential measures of variation in statistics, including sample range, variance, standard deviation, and interquartile range (IQR). The sample range reveals the difference between the largest and smallest observations, while variance and standard deviation quantify how much individual data points differ from the mean. The IQR focuses on the middle 50% of data, making it robust against outliers. Additionally, we cover how to create and interpret boxplots, which visually represent the distribution of the data and help in comparing variations across different samples.

francis-sargent
Télécharger la présentation

Measures of Variation

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Measures of Variation • Sample range • Sample variance • Sample standard deviation • Sample interquartile range

  2. Sample Range or, equivalently R = largest obs. - smallest obs. R = xmax - xmin

  3. Sample Variance

  4. Sample Standard Deviation

  5. What is a standard deviation? • it is the typical (standard) difference (deviation) of an observation from the mean • think of it as the average distance a data point is from the mean, although this is not strictly true

  6. Sample Interquartile Range or, equivalently IQR = third quartile - first quartile IQR = Q3 - Q1

  7. 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 measure of variation often in this course

  8. Boxplot - a 5 number summary • smallest observation (min) • Q1 • Q2 (median) • Q3 • largest observation (max)

  9. Boxplot Example - Table 4, p. 30 • smallest observation = 3.20 • Q1 = 43.645 • Q2 (median) = 60.345 • Q3 = 84.96 • largest observation = 124.27

  10. Creating a Boxplot • Create a scale covering the smallest to largest values • Mark the location of the five numbers • Draw a rectangle beginning at Q1 and ending at Q3 • Draw a line in the box representing Q2, the median • Draw lines from the ends of the box to the smallest and largest values • Some software packages that create boxplots include an algorithm to detect outliers. They will plot points considered to be outliers individually.

  11. Boxplot Example Min = 3.20 Max = 124.27 Q2 = 60.345 Q1 = 43.645 Q3 = 84.96 . . . . . 0 10 20 30 40 50 60 70 80 90 100 110 120 130

  12. Boxplot Interpretation • The box represents the middle 50% of the data, i.e., IQR = length of box • The difference of the ends of the whiskers is the range (if there are no outliers) • Outliers are marked by an * by most software packages. • Boxplots are useful for comparing two or more samples • Compare center (median line) • Compare variation (length of box or whiskers)

More Related