What are the concepts of mean and midpoint?

What is Mean

The mean is generally known as the average of certain numbers. Mean or average of numbers is calculated by taking the sum of all the values and then dividing by the total number of values. The mean however is of two different types that include the arithmetic mean and geometric mean.

While mentioning the mean of a certain numbers the geometric mean is not what we are referring. As the geometric mean is a value of a number set calculates by taking their product. Since, when mean is being discussed the arithmetic mean is being referred. There are some online tools that help you to find mean value like mean calculator.

Arithmetic Mean

The arithmetic mean is a measure of central tendency, among the others including median and mode.

The average is what known as arithmetic mean. To measure and to represent the complete data with a single number, it is most popular and extensively utilized measure of central tendency.

It is a value that is calculated as first summing all the values together and dividing by total by the number of items. The arithmetic can be subdivided into two different types.

Types of Arithmetic Mean

• Simple Arithmetic Mean
• Weighted Arithmetic Mean

Properties of Arithmetic Mean

The deviation’s sum of the elements from the arithmetic mean is always zero i.e. ∑ (X–X) = 0.

The squared deviation’s sum from arithmetic mean’s values is smaller than the squared deviation’s sum of the items from any other values.

If the mean is replaced by each item in the series, the sum of these replacements should be the sum of the individual items.

How to Calculate Mean

The arithmetic mean can simply be calculated by taking the average of the given values. For taking the average add up all the provided values for taking the arithmetic mean and divide their sum by the total number of the values. However, to calculate the arithmetic mean of certain number values the general formula used is given as below.

Mean = Sum of the values / Total number of values

Midpoint

The midpoint or M is the point that is located exactly at the halfway between the two points A and B. The midpoint can only be found on a line segment a line or ray however can’t have a midpoint.

In order to exactly define the midpoint of a line segment we would say, the point in a segment that divides the segment into 2 congruent segments is a midpoint of a line segment. Moreover, the midpoint is the point present on a line segment that has the same distance between the two end points from it or is at half way distance.

Midpoint Formula

A method for finding the half way or midpoint between two co-ordinates in a graph is the midpoint formula. In a line segment with endpoints A and B, the midpoint is the same distance from A, B as discussed above.

When two points on a graph in the coordinate plane are known, the midpoint formula can be utilized in order to find the midpoint. Therefore, the midpoint M of the given 2 coordinates (x1, y1) and (x2, y2), is calculated as;

The thing that needs to be noted here is, that in the midpoint calculation the average value of both x- and y-coordinates is taken. Remembering the fact that average(mean) of both the congruent is taken makes the midpoint formula more easy to memorize. The two-number average is simply the sum of the two number values and then dividing by 2.

How to Calculate Midpoint

Simply using the midpoint formula, the midpoint of a line segment can be calculated effectively. Below is given the step by step solution to how to calculate the midpoint of a line segment.

Coordinates selection

First, choose a point to be (x1, y1) and another point to be (x2, y2). Generally, it does not make a difference which point is taken as x and which is y, however in rare situations, we required to identify the coordinates of the two points from the graph.

Putting the values

After that, put the values of each coordinates i.e. x1, y1, x2, and y2 into the formula ((x1+x2)/2, (y1+y2)/2), and then perform calculations according the formula.

Taking the Mean

As per the formula, the mean or average of each coordinates needs to be identified. For any two coordinates, we add them together and divide by two to obtain their average or mean. That is exactly what we are attempting in the midpoint formula.

Mean of coordinates is the Midpoint

As a result, the midpoint formula is considered as a method of determining the point that is the average of the x-terms and the y-terms.