Lecture 4 Dispersion - Lecture-4 Measures of Variability The mean alone does not provide a complete or sufficient description of data In this section we

Lecture 4 Dispersion - Lecture-4 Measures of Variability...

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Lecture-4 Measures of Variability The mean alone does not provide a complete or sufficient description of data. In this section we present descriptive numbers that measures the variability or spread of the observations from the mean. In particular we include (i) Range (ii) Interquartile range (iii) Variance (iv) Standard deviation and (v) Coefficient of variation No two things are exactly alike. This is one of the basic principles of statistical quality control. Variation exists in all areas. The weather varies greatly from day to day, and even from hour to hour; grades on a test differ for students taking the same course with the same instructor, a person’s blood pressure, pulse, cholesterol level, and caloric intake will vary daily. While two data sets could have the same mean, the individual observations in one set could vary more from the mean than do the observations in the second set. Consider the following two sets of sample data: Sample A 1 2 1 36 Sample B 8 9 10 13 Although the mean is 10 for both samples, clearly, the data in sample A are further from 10 than are then data in sample B. We need descriptive numbers to measure this spread. Range Range is the difference between the largest and smallest observations. The greater the spread of the data from the center of the distribution, the larger the range will be. Since the range takes into account only the largest and smallest observations, it is susceptible to considerable distortion if there is an unusual extreme observation. Although the range measures the total spread of the data, the range may be an unsatisfactory measure of variability (spread) because outliers either very high or very low observations, influence it. One way to avoid this difficulty is to arrange the data in 1
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