# what is the differance between between direct mean method assumed mean methodand step deviation method.Because i can't understand where to use which method ? Please HELP

The following frequency distribution showing the marks obtained by 50  students in statistics at a certain college. Find the arithmetic mean using (1) Direct Method (2) Short-Cut Method (3) Step-Deviation.

 Marks Frequency

Solution:

 Direct Method Short-CutMethod Step-DeviationMethod Marks Total

Here x is the middle value of the marks as 20+29 divided by 2  = 24.5

Similarly we have got the values of x

Direct method is the method which will give an approx. value and in this we find the summation of the multiplication of frequency with the middle value (x) divided by the summation of frequency .

Mean =  =  = 54.9

Assumed mean method : in this method , firstly we get middle value i.e. x and then we assume a number i.e. A from the values of x , then we get D = x-A and then we find summation of the multiplication of deviated mean with the frequency

Then we use the formula

Mean = A +

= 54.5 +

= 54.9

Step deviation mean : in this method , we get the value of u by dividing  the deviated value(d) by the class interval(i.e.34.5 -  24,5 = 10) , then we find summation of multiplication of frequency and u

Then we use the formula

Mean =  A + *h

= 54.5 +

= 54.9

• -3

It's simple in direct method you have to multiply class marks and the given frequencies and divide the addition of the product by total number of frequency.

In Assumed mean method you have to assume a class mark and subtract from all class marks including the one which is assumed .Then multiply d by frequencies and divide the total of fidi by fi and add the resultant answer to the number which is assumed and you will get the the mean.

In step deviation you will follow the rules of assumed mean method upto calculating d and divide each by h(class width) and you will get u which you have to multiply with the given frequencies and divide the total fidi by fi.Then by using the formula A(Assumed number)+hu you will get mean.

when the method is specified use the same method .But when it is not specified use any method for you will get the same answer. But when the numbers are large for eg 350,250,475 avoid using direct method as it will become lengthy and hard to solve.

• 0

It's simple in direct method you have to multiply class marks and the given frequencies and divide the addition of the product by total number of frequency.

In Assumed mean method you have to assume a class mark and subtract from all class marks including the one which is assumed .Then multiply d by frequencies and divide the total of fidi by fi and add the resultant answer to the number which is assumed and you will get the the mean.

In step deviation you will follow the rules of assumed mean method upto calculating d and divide each by h(class width) and you will get u which you have to multiply with the given frequencies and divide the total fidi by fi.Then by using the formula A(Assumed number)+hu you will get mean.

when the method is specified use the same method .But when it is not specified use any method for you will get the same answer. But when the numbers are large for eg 350,250,475 avoid using direct method as it will become lengthy and hard to solve.

• 5
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