Mean, Median & Mode Formula For Grouped Data

Mean, median, mode are the very popular terms in the statics which we study in the basic post matric level of the subject. These are basically the different kinds of the averages which are used at their suitable occasions or the purpose. 

Mean is the very first and the most popular average that we all use in our daily lives to figure out the average of the sequence of the numbers in any row. In order to calculate the mean we need to first sum up all the numbers of the row and then we simply need to divide the sum by the total frequency of the numbers. For instance if there are total 8 numbers then the sum needs to be divided by the 8 to figure out the mean.

Median on the other side is the other type of the average in which we just consider the value of the middle number in a whole lot number series. In order to calculate the mean you must first arrange the numbers in an ascending order and then take the mid value. 

At last the mod is the last and the least used type of the average yet it has some significant value. In mod we consider such number which has the most frequency of occurrence in other words the number, which takes place more times than any other number in the series of numbers.

Formula for Mean, Median, Mode

Well, yes we have the certain formulas in statistics to calculate the different kinds of the averages and the same thing is applicable in the mean/median/modes. If you want to calculate these respective averages, then here we are going to help you in that by our simple formulas. 

The grouped data is one such data which is different from the normal data, since here we have the grouped numbers of the data instead of the single numbers. 

Group data is generally seen as 5-10,10-15,15-20 and the series goes on, further we also have the frequency given of this group data in accordance to which they take place in the series. 

Now we have to simply calculate the mid value of the grouped data by dividing the sum of group data for the each sequence of the numbers. In the next column we multiply the mid value with the frequency numbers to calculate the ∑fx which is then divided by the total of frequency numbers. 

Mean Formula

Here is the simplified formula of mean for your consideration.

Examples:

Median Formula

Here below you can check out the median formula for the grouped data


Now, first of all we have to figure out the median class and for that we will apply the following formula 

Value of (n/2) observation

Here, we just need to put the value of frequency at the place of n and then calculate the concerned observation.Next you just need to check out that in which class the calculated observation is falling in order to figure out the median class.

Once the median class is determined then you can figure out the mean by putting the concerned values in the following formula

 

Mode Formula

Well, have the last average of mode and in the group data you first have to find out the mode class in order to determine the mode.

Example:

Here the mod class will simply be one which have the highest number of the frequency for instance if the class 20-30 has the highest frequency of 8 then we have 20-30 as our mode class. 

Once you have the mode class then you just have to solve the following formula by putting some values in order to get the mode

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