Mean - Step - Deviation Method
Step deviation method is a method of obtaining the mean of grouped data when the values are large. In statistics, there are three types of mean - arithmetic mean, geometric mean, and harmonic mean. When the values of the data are large and the deviation of the class marks have common factors, the step deviation method is used.
Definition
Step deviation method can be defined as the method used to obtain the mean of large values which is divisible by a common factor. These values of deviations are reduced to a smaller value by dividing all the values by a common factor. In other words, the step deviation method is used when the deviations of the class marks from the assumed mean are large and they all have a common factor. This method is also called a change of origin or scale method. The mean of grouped data is obtained by three different methods, direct method, assumed or short-cut method, and step deviation method. The step deviation method is considered as the extension of the assumed method as we use the deviation formula used in the assumed method.
Mean - Step - Deviation Method Formula
formula is:
Step Deviation of Mean =
where assumed mean
class size
midpoint of the class interval
frequency
Example: Find the mean of the following using the step-deviation method.
Class
Interval |
|
---|---|
10 - 25 | 2 |
25 - 40 | 3 |
40 - 55 | 7 |
55 - 70 | 6 |
70 - 85 | 6 |
85 - 100 | 6 |
Solution:
Class
Interval |
|
---|---|
10 - 25 | 2 |
25 - 40 | 3 |
40 - 55 | 7 |
55 - 70 | 6 |
70 - 85 | 6 |
85 - 100 | 6 |