The Arithmetic Mean Of A Series

The observations based upon any test which happened, it can be an experiment for reading the changes in value, can be noted to vary between a range. The value for each experiment may not be identical. These values may be noted to be within a range of numbers. Thus, the range may not be useful for all the scenarios. Few observations work on the range, but not all. 

In the statistical domain, the observation can be any set of values regardless of the experiment. Few scenarios can be the height of people, marks of students, sales value per month, and many more. Therefore, it becomes abruptly difficult to get all the values and note them. Missing out values can make a serious issue. Hence, the concept leads to the origin of a new variable denoting this unique value such that it represents the overall observation. 

The arithmetic mean was introduced to be a value that can represent the overall data for the taken observation. Supporting the experiment, one can easily find the value representing the observed values as a whole. 

Arithmetic Mean of a series

Assume that a sample experiment takes place such that the observed values are in a given range. Suppose, a total of m readings were noted and analysed. Now, the readings can have different values, wherein few can be repeated. Now, the term, mean denotes the overall experiment as a whole. Thus, we can find the mean for the whole lot as one to represent. 

What is the mean? A simple question arises at this point. The answer to this question is the overall representation of data. Now, this is the definition we know from the above analysis. The mean is computed from the data by taking the average for each entry to the exact value. The Mean can be said to be the mid-value such that the total deviation is tending to zero from this unique represented value for the overall data. The calculation for this is similar to finding out the average for any set of values for any test. 

Now, when we find the average, we initially observe the values we have from the experiment. These different values can be added together to get a single value. This summation of the observation is taken into consideration for finding out the mean to represent as a whole. Now, this value is divided by the total number of observed values to get the average value for the experiment. This value represents the whole lot uniquely and this is known as the mean for any given data. The arithmetic mean represents the mean for the given arithmetic observations. 

The arithmetic mean can be evaluated for different series such as individual, discrete and continuous. 

For an individual series, the experiment had m readings, and the values can be unique or repeating depending on the type of experiment we had. Suppose, the different values are m1, m2, m3…. and so on. 

Now, the mean will represent the overall data from the experiment carried out. 

Thus, one can say that, 

Arithmetic Mean = m1+m2+m3+…..m

For a discrete series, the experiment had m readings, and the values are x and these values are noted with the frequencies f respectively, thus the arithmetic mean of a discrete series can be computed as, 

Arithmetic Mean = Σmfm

For continuous data, we compute the mid-value of each interval, and thus we compute the mean using the discrete series method. Thus, the mid value is computed as, 

Interval=lower limit + upper limit2

Now, the mean is computed using this interval value taken as frequencies for the respective values for the experiment. Thus the mean is computed for continuous series.

These formulas can be used on any set of observations for a sample experiment. Statistics uses this in different domains to carry out the representation of the central tendency. This is way far the most prominent formula for evaluating a value to represent the overall experiment as a whole. 

Conclusion

The arithmetic mean of different observations for any set of tests or experiments can be used to represent the whole as a one valued observation. This value can be part of the experimental observations or a unique value for the experiment. Depending on the number and value of the observations, the mean can have different values. 

Note that, if we add or subtract a value from the observation, the mean value deviates from the computed value.