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Lecture-4Measures of VariabilityThe mean alone does not provide a complete or sufficient description ofdata. In this section we present descriptive numbers that measures thevariability or spread of the observations from the mean. In particular weinclude(i)Range(ii)Interquartile range(iii)Variance(iv)Standard deviation and (v)Coefficient of variationNo two things are exactly alike. This is one of the basic principles ofstatistical quality control. Variation exists in all areas. The weather variesgreatly from day to day, and even from hour to hour; grades on a test differfor students taking the same course with the same instructor, a person’sblood pressure, pulse, cholesterol level, and caloric intake will vary daily. While two data sets could have the same mean, the individual observationsin one set could vary more from the mean than do the observations in thesecond set. Consider the following two sets of sample data: Sample A12136Sample B891013Although the mean is 10 for both samples, clearly, the data in sample A arefurther from 10 than are then data in sample B. We need descriptivenumbers to measure this spread. RangeRange is the difference between the largest and smallest observations. The greater the spread of the data from the center of the distribution, thelarger the range will be. Since the range takes into account only the largestand smallest observations, it is susceptible to considerable distortion if thereis an unusual extreme observation. Although the range measures the totalspread 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 in1