Understanding the Democratic Power of the Arithmetic Mean": How to Calculate it
The central tendency is one of the fundamental concepts in statistics and the mean is the most widely used metric when it comes to the central tendency.
The mean usually referred to as the average, is exactly what it says. It is the average value of a dataset. Along with the mode and median, they provide a quick way of summarising and interpreting a dataset, using single values. In this article, we will explore the concept of the mean and learn how to calculate it.
Definition of the Mean
When you add up all the values of a dataset and divide it by the count, you get the mean. So, the arithmetic mean is defined as the sum of all the values in a dataset divided by the total number of values. The mean of a dataset is technically calculated as mean(X) = (x1 + x2 + x3 + ... + xn) / n, where n represents the number of counts of the dataset.
This formula holds for both population and sample data, except the notation used is different. For a population, the mean is denoted by the Greek letter μ (mu), while for a sample, it is denoted by the symbol x̄ (x-bar).
Calculation of the Mean
Here are the steps to follow:
add all the values in the observation.
Count the total number of values in the dataset.
Divide the total number by the count.
For example, suppose you researched the number of brushes purchased daily from a small shop and recorded the following outcome: {5, 8, 12, 7, 10}
Step 1: Sum up all the values: 5 + 8 + 12 + 7 + 10 = 42
Step 2: Count the total number of values: 5
Step 3: Divide the total number by the count: 42 / 5 = 8.4
Therefore, the mean of this dataset is 8.4.
Conclusion
The arithmetic mean, often simply called the "mean" or "average", is calculated by summing up all the values in a dataset and dividing by the total number of values. This gives the central value that incorporates and represents each data point equally - treating them all with equal "democratic" weight.
The formula for the arithmetic mean is:
mean(X) = (x1 + x2 + x3 + ... + xn) / n
Where x1, x2, x3, ...xn are the individual data values and n is the total number of data points.
To calculate:
add up all the data values (x1 + x2 + x3 + ... + xn)
Count the total number of data points (n)
Divide the sum by the total count (x1 + x2 + x3 + ... + xn) / n
For example, if the dataset is {5, 8, 12, 7, 10}:
Sum = 5 + 8 + 12 + 7 + 10 = 42
Total number of values = 5
Mean = 42 / 5 = 8.4
The mean treats all data points democratically by incorporating each value into the sum and dividing by the total count n. This provides the single, central "democratic" value around which the data is distributed.
For populations, the mean is denoted μ (mu). For samples, it is x̄ (x-bar).
However, the calculation method of summing values and dividing by the count is the same.
The mean succeeds at fairly representing the "voice" of all data points when summarizing the central tendency. This "democratic power" makes it one of the most widely used statistical measures
.