School

York UniversityDepartment

Operations Management and Information SystemCourse Code

OMIS 2010Professor

Alan MarshallThis

**preview**shows half of the first page. to view the full**2 pages of the document.**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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