Question

how to find mean with diviation method....explain with an example

Answer 1

Answer:

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. Let us learn more about the formula, the derivation of the step deviation method formula, and solve a few examples.

Definition of Step Deviation Method

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.

Step Deviation Method Formula

Before we go to the step deviation formula, let us quickly look at both the direct method and assumed or short-cut method formulas.

Estimated or Direct Mean = ∑x

i

f

i

/ ∑f

i

, where f

i

is the frequency and x

i

is the midpoint of the class interval.

Assumed Mean = A + ∑d

i

f

i

/ ∑f

i

, where A is the assumed mean, f

i

is the frequency, and deviation d

i

= x

i

- A.

Since this method is the extension of the assumed mean method, the formula is:

Step Deviation of Mean = A + h [∑u

i

f

i

/ ∑f

i

],

where,

A is the assumed mean

h is the class size

u

i

= d

i

/h

f

i

is the frequency

d

i

= x

i

- A

x

i

is the midpoint of the class interval

Answer 2

Answer:

The following steps are used to calculate the mean using this method:

1. Calculate the class marks of each class xi i.
2. Let A denote the assumed mean of the data.
3. Find ui i =(xi i −A)/h, where h is the class size.
4. Use the formula: A + h [∑ui i fi i / ∑fi i ]