Arithmetic Mean In Individual Series

The observations based upon any test or experiment can exhibit variations in value. The value for each experiment may not be identical. These values may be noted to be within a range of numbers. But, a range may not be useful for all the scenarios. A 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. A few examples can be the height of people, marks of students, sales value per month, and so on. Therefore, it becomes challenging to get all the values and repeat them each time. Missing out on these values can also cause a concern. 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 in Individual 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. The term denotes the overall experiment as a whole. 

What is the mean of any value? The overall average of a series of values is the mean. The mean is computed from the data by taking the average for each entry to the exact value. Thus, 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. The total 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 is known as the mean for any given data. The arithmetic mean represents the mean for the given arithmetic observations. 

For an individual series, the experiment can have m readings, and the values can be unique or repeated depending on the type of experiment. 

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

The formula can be used on any set of observations for a sample experiment representing an individual series. Statistics uses this in different domains to carry out the representation of the central tendency. This is, by far, the most prominent formula for evaluating a value to represent the overall experiment. 

Example

Suppose, in a company, there was a sample experiment conducted based on the number of working hours in a day for a set of workers. The observations noted were: 4, 8, 2, 7, 1, 3, 6, 5, 6, 3. For the given experiment, the working hours per day for each worker for the whole lot can be represented using the arithmetic mean. The above series is an individual series, and thus, from the formula, we can compute the arithmetic mean. 

The observation is for 10 workers of the company. Now, using the formula, we compute the summation of the values:

Summation = 4+8+2+7+1+3+6+5+6+3=45

Now, the mean of the given experiment can be computed as follows:

Mean=SummationNumber of observation=4510=4.5

Overall, the workers taken into consideration can be said to work for 4.5 hours daily. 

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.