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Chapter

OMIS 2010 Chapter Notes -Frequency Distribution


Department
Operations Management and Information System
Course Code
OMIS 2010
Professor
Alan Marshall

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Sturges’ Rule1
The derivation of Sturges’ Rule is not terribly complex, but not suitable for an
introductory statistics course.2 One statement of the rule is to choose c such
that:
2c-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[log10(n)] (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)/log10(n) = 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.
Row
Sum
1 =
2
0
2 =
2
1
4 =
2
2
8 =
2
3
16 =
2
4
32 =
2
5
64 =
2
6
128 =
2
7
256 =
2
8
512 =
2
9
Pascal's Triangle
8
1
36
9
1
70
56
28
1
9
36
84
126
126
84
1
8
28
56
5
6
4
15
6
21
7
20
7
21
35
35
5
10
6
15
10
1
1
1
1
1
1
1
2
3
3
1
1
1
1
4
1
1
1
1
The sums across the rows of Pascal’s Triangle correspond to the powers of 2.
Therefore, the sum of each row is double the previous row’s sum. As well, each
1 © 2005, 2012 βeta Management Consultants and A. T. Marshall. Permission is granted for
use by the Schulich School of Business, York University for use in MGMT1050, Fall 2012.
2 However, it is related to the normal approximation of the binomial, covered in most
introductory business statistics texts.
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