Question

1)What is Sturges’ formula, and what is it used for?

2)What is the formula for class width?

3)Consider a data set with 137 observations, with the smallest observation equal to 101.5 and the largest equal to 1564.7. How many class intervals will you use to create a frequency distribution for this data set? What class width will you use?

Answer 1

Solution:

Part 1) What is Sturges’ formula, and what is it used for?

Sturges’ formula is:

K = 1 + 3.322 Log(N)

it is used to find number of classes K.

Part 2) What is the formula for class width?

h = Class width is given by formula:

where L = Largest observation and S = Smallest observation

Part 3) Consider a data set with 137 observations, with the smallest observation equal to 101.5 and the largest equal to 1564.7. How many class intervals will you use to create a frequency distribution for this data set? What class width will you use?

N = 137

L = 1654.7

S = 101.5

We have to determine number of class intervals and class width.

Thus number of class intervals:

K = 1 + 3.322 * Log(N)

K = 1 + 3.322 * Log(137)

K = 1 + 3.322 * 2.136721

( Note: Use Excel or Scientific calculator to find Log(137) )

K = 1 + 7.0982

K = 8.0982

K = 8

Thus number of class intervals are = K = 8

and lass width:

Thus class width is