Arithmetic Mean

The arithmetic mean is the measure of the average calculated by adding up a set of numbers and then dividing it by the count of the numbers. For example, if the given numbers are 10, 16, 20, or 35, The average is calculated by dividing the sum of the numbers by their count: (10 + 16 + 20 + 35) ÷ 4 = 20.25. The arithmetic mean is 20.25. The important takeaways of the arithmetic mean are essential to understand. The arithmetic mean is calculated by dividing the total of the given numbers by their count.

Also, using the arithmetic mean in finance is not ideal because a single outlier can significantly affect the final result. For example: If you want to calculate the weekly expenses of your five friends. Four of them spend between $15 and $20 weekly, while the fifth friend spends $40 weekly. In finance, the geometric and harmonic means are among the most commonly used averages.

• The sum of deviations is always a zero. In simple words, when the mean value is subtracted from each data point, and the differences are added together, the result is zero. It can be mathematically expressed as: represent it as: 

• Outliers in a dataset can influence the arithmetic mean, leading to inaccuracies. This sensitivity to outliers can be taken as an advantage to detect the presence of outliers in datasets.

• Adding or subtracting a constant: When the same number is added to or subtracted from each value in a dataset, the mean shifts by that number.

• When you multiply or divide all the values by the same number, the mean is multiplied or divided by that number.
   

The geometric mean is widely used in finance as it accounts for probability, making it more precise for calculating investment returns. It works well for serially correlated data such as bond rates and stock returns. 

The arithmetic mean sums up the values and divides them by their count, whereas, the geometric mean multiplies them and calculates the nth root. The geometric mean will always be less than or equal to the arithmetic mean. 

For example, given a stock has a yearly return of 20%, – 8%, 10%, and 25% over four years:

Arithmetic Mean: (20 + (– 8) + 10 + 25)/ 4 = 11.75% per year

Geometric Mean: (1.20 × 0.92 ×  1.10 ×  1.25)¼ – 1 = 10.84 % per year.

To calculate the arithmetic mean, we use the formula:

x  = Σx/n

Here:

x represents the arithmetic mean, Σx is the sum of all values and n is the count of values.
 

Arithmetic Mean is significantly used in different fields to determine the average of quantities. Let’s look at a few applications of Arithmetic Mean:

Finance:

The arithmetic mean is often used in calculating the average income or expenses of employees.

Feature Scaling:

The arithmetic mean is used in mean centering for machine learning. It is performed by subtracting the average so that the mean becomes zero.

Model Quality Check:

We use the arithmetic mean in checking the model performance by applying absolute differences.

Hypothesis Testing:

It is applied in t-tests, where the means of two means are compared to determine whether they are significantly different.

Demographics:

The demographers apply the average mean to estimate the income, age, or population growth.