**Arithmetic Mean as the Centre of Gravity of the Distribution of Variables**

The arithmetic mean is a statistical measure that is commonly used to describe the central tendency of a dataset. It provides a single value that represents the "average" value of the variables in the dataset. In the context of the distribution of variables, the arithmetic mean can be thought of as the center of gravity.

The concept of center of gravity originates from physics, where it refers to the point at which the total weight of an object is considered to be concentrated. Similarly, in the case of the distribution of variables, the arithmetic mean represents the point around which the values of the variables are concentrated.

**Explanation:**

To understand this concept better, consider a set of data points representing the values of a variable. The arithmetic mean is calculated by summing up all the values and dividing the sum by the total number of values. This process essentially gives equal weight to each value in the dataset.

Now, visualize the dataset as a number line where each value is represented as a point. The arithmetic mean can be thought of as the point on the number line that balances the distribution of values. It is the point at which the sum of the distances of each value from the mean is minimized.

This concept can be further illustrated by considering the deviations of each value from the mean. Deviation refers to the difference between a value and the mean. If we sum up all the deviations of the values, we will get zero. This is because the positive deviations cancel out the negative deviations, resulting in a balance around the mean.

In this way, the arithmetic mean can be seen as the center of gravity of the distribution of variables, as it represents the point where the values are balanced. It provides a useful measure to describe the central tendency of the dataset and allows for comparisons between different datasets.

In conclusion, the arithmetic mean can be described as the center of gravity of the distribution of variables. It represents the point at which the values are balanced and provides a single value that summarizes the average value of the dataset.