Overview of Mean Deviation for Grouped and Ungrouped Data

There can be possibly a large number of ways in which the grouped or ungrouped data can be spread around for an experiment. In that case, it becomes quite difficult to calculate the accurate outcome with great precision. If we are aware of the point over which most of the data is concentrated, then that point can be taken into account to find the accurate answer. And, that is how mean deviation is brought into effect, it measures the limit of variation of data.

Mean Deviation Frequency

A large data set is represented in the form of a graph or table representing the number of times that data has occurred, or the frequency of that data is known as the frequency distribution for that data set. 

It is to be noted that the unit of mean deviation will continue to remain the same as that of the data that is being stored in the data set. The frequency distributions that are involved in the mean deviation do not have any particular gap or hole in their data table and are hence referred to as rigid. 

The value of mean deviation for a frequency distribution depends on the value of all the data that is being stored in a certain class. Seeing as the values that are placed in a certain class happen to be specified, or follow a certain norm, the outcome is also known as the absolute mean. 

The mean deviation for a data set using frequency distribution provides us with the most suitable results as the actual data is being taken into consideration, not only the class of the data. This value can also be used to compare data if two or more classes or completely different tables.

How to Calculate Mean Deviation for Grouped and Ungrouped Data

For ungrouped data

The mean deviation for an ungrouped data can be given by utilising the following formula:

∑i = 1n ( | x i – M | ) / n

‘M’ in this formula stands for the mean of the ungrouped data. It can be found out by adding all the data available and dividing it all by the number of observations chosen.

For grouped data

The mean deviation for a group data can be given as:

∑f ( |X−X—| ) / ∑f

In this formula, the ‘x bar’ stands for the mean of that data taken. As the data obtained are grouped and have no gaps in their frequency distribution, it can give different values of frequency and still be effective. 

Mean Deviation for Continuous Frequency Distribution (with Regards to Grouped and ungrouped Data)

Grouped data

For this particular data type, class intervals or groups are arranged in a way that there is no gap between them and each class possesses its respective frequency. The selection of class intervals takes place in such a way that they should be either mutually exhaustive or exclusive.

The mean deviation formula for group data is:

Mean deviation = ∑f ( |X−X| ) / ∑f

Here ‘X’ stands for the men of that data set and is calculated by using the following formula:

∑fx / ∑f

In this formula, ‘x’ stands for the midpoints of various class intervals.

And, ‘f’ stands for the frequency of that particular data set.

Ungrouped data

In this type of data set, the data is represented in the form of rows and not in the tabular form. 

The mean deviation formula for ungrouped data is as follows:

Mean deviation = ∑|X−a| / n

∑|X−a| stands for the summation of all deviations for the value ‘a’

And, ‘n’ stands for the number of observations that are taken by an individual.

 As the data that we are choosing to act upon is chosen completely randomly, as it is a part of ungrouped data, it needs to be arranged temporarily. That way, we will get the answer as a value that is the closest to precision.

Conclusion

Mean deviation is a value that depends on the mean and median of that data. So, to find the mean deviation, one needs to be familiar with these terms. Using these it becomes easier to calculate the central value for a data frequency or the midpoint of that data. Hence, by the assortment of mean deviations in it, the data becomes more realistic and broad. And, that is how the importance of mean deviation is brought into effect in the concept of statistics.