What are the roles of measure of dispersion in descriptive statistics? Following table gives the frequency distribution of thickness of computer chips (in nanometer) manufactured by two companies.

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Suresh Chand · Accepted Answer

Measure of dispression is a descriotive statistical measure used to measure the variation or spreed or scatter less in the data set. It gives additional information that enables to judge the reliability of measure of central tendency. The measure of dispersion is important because it determines the margin of error. You'll have when measuring the central tendency. Solution Part: For Company A: x f fx fx2 5 10 50 250 10 15 150 1500 15 24 360 5400 20 20 400 10000 25 18 450 11250 30 13 390 11700 N = 100 Σfx = 1800 Σfx2 = 40100 Now, (bar{x} = frac{sum fx}{N}) = (frac{1800}{100}) = 18 Standard deviation(σ) = (sqrt{frac{sum fx^2}{N} - left ( frac{sum fx}{N} right )^2}) = (sqrt{frac{40100 }{100} - left ( frac{1800}{100} right )^2}) = 8.77 And, Co-varience (c.v) = (frac{σ}{bar{x}} times 100%) = (frac{8.77}{18} times 100%) = 48.72% For Company b: x f fx fx2 5 12 60 300 10 18 180 1800 15 20 300 4500 20 22 440 8800 25 24 600 15000 30 4 120 3600 N = 100 Σfx = 1700 Σfx2 = 34000 Now, (bar{x} = frac{sum fx}{N}) = (frac{1700}{100}) = 17 Standard deviation(σ) = (sqrt{frac{sum fx^2}{N} - left ( frac{sum fx}{N} right )^2}) = (sqrt{frac{34000}{100} - left ( frac{1700}{100} right )^2}) = 7.14 And, Co-varience (c.v) = (frac{σ}{bar{x}} times 100%) = (frac{7.14}{17} times 100%) = 42% Since, the standard deviation and covarience of company B is less than that of company A. so, company B is considered more consistent in terms of thickness of computer chip.

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Thickness of computer chips		5	10	15	20	25	30
Number of chips	Company A	10	15	24	20	18	13
Number of chips	company B	12	18	20	22	24	4

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