Sturge's Rule.docx

2 Pages

Operations Management and Information System
Course Code
OMIS 2010
Alan Marshall

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1 Sturges’ Rule The derivation of Sturges’ Rule is not terribly complex, but not suitable for an introductory statistics course. One statement of the rule is to choose c such that: 2 c-1= n (1) This implies that every time the sample size doubles, we add one extra class to the frequency distribution. Taking natural logs of both sides of (1) yields: c – 1 = ln(n)/ln(2) c = 1 + ln(n)/ln(2) (2) The text gives us the formula: c = 1 + 3.3[log (10] (3) These are equivalent, but the textbook’s version (3) is not as convenient for many as many calculators provide natural logarithms but not logarithms base 10. The ratio ln(n)/log (n10= ln(10) = 2.302585. Dividing this by ln(2) = 0.693147 gives us 3.321928, 3.322 rounded to three decimal places. The curriculum for high school mathematics teaches Pascal’s Triangle extensively, as early as grade 9. There is a relationship between Pascal’s Triangle and Sturges’ Rule. Pascal's Triangle Row Sum 1 1 = 2 0 1 1 1 2 = 2 2 1 2 1 4 = 2 1 3 3 1 8 = 2 3 4 1 4 6 4 1
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