Reference and Education

# Mean- The formulations and details of the topic

The central tendency and one of the important significant topics of statistics is Mean. The mean for any set of data can be conveniently calculated by adding up all the values of the provided data and dividing by the number of observations. This is the explanation of the basic mean formula otherwise the same is different for different types of data, as in grouped and ungrouped data.

The data arranged as per the details of class intervals/groups is called grouped data while the random arrangements of the same fall under the category of ungrouped data.

## Statistical significance of the mean concept

It will be appropriate to call mean statistical data as it holds its importance in business and finance streams. The concepts of mean, median and mode are the base of statistics.

### Defining mean

The calculated centre or the average number of the data set. This is the statistical mean tendency that explains the respective data accurately. The same can be called a ratio of the sum of the observation to the number of the same.

The formula for finding the mean of a series is, The sum of the observation/ To calculate the mean of grouped data, the first step is to determine the midpoint of each interval or class. These midpoints must then be multiplied by the frequencies of the corresponding classes. The sum of the products divided by the total number of values will be the value of the mean you need.

To calculate the mean of grouped data, the first step is to determine the midpoint of each interval or class. These midpoints must then be multiplied by the frequencies of the corresponding classes. The sum of the products divided by the total number of values will be the value of the mean. To determine the same frequency distribution table makes the calculations simple and easy.

X̄ = Σfx/Σf is the basic concept. It should be noted that a list of n items is the set whose mean is to be calculated can be given by Mean= (x1, X2, X3…..xn)/n

Or, x̄ = Σfx/Σf

### Various methods of mean calculation for grouped data

1. Direct method: The simplest form of calculating the mean in the case of grouped data is the direct method. The steps of the same are mentioned below:

• Create a frequency distribution table with the columns headed class interval, corresponding class marks, frequency f1, the corresponding product of class marks and frequency.
• Substitute the respective values in the above-mentioned formula.

Assumed mean method: This method for mean calculation is used when the direct method gets stuck and isn’t working. As per this method, the below-mentioned steps are mandatory to be followed.

• Start with forming the frequency distribution table with five columns namely intervals, class marks (taking the middle value as assumed mean denoting it with ‘A’. Notifying the related deviations given by di=xi-Assumed mean. Frequencies, f1 and mean of di, using formula.
• Adding the final mean and assumed mean gives you the final mean value.

3. Step deviation method: The shifting of the origin or scaling method is the step deviation method. The step deviation method is used to lessen the calculations. The steps of application would be:

• Again, create a frequency distribution table as mentioned above.
• Find mean using the formula.
• Then add assumed mean to the product of class width.

Cuemath describes the types of mean namely, Arithmetic means, Geometric mean, Weighted mean and harmonic mean well. Mode formula is too well explained in the app. Mean, median and mode are the important concepts of statistics. Mode too is the measure of the central tendency for any type of data set that need to identify the central position of the data.

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