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How to Find the Midpoint in Statistics?

TopPoint that splits the line segment into 2 portions of the same measure is known as midpoint. Out of several ways for tracing this point, there is one approach which is pretty simpler. In this approach, we measure the point by means of compass and a scale. We need to make a perpendicular bisector of the line segment, which creates two equal parts.

Geometrically, midpoint is found using the midpoint formula. It is a well-defined formula, which gets us the statistical value of this point. This method is applicable to all kinds of line geometries like upright or vertical, horizontal and slanting or diagonal.

So, the midpoint formula is provided as follows:
Suppose we have a Line Segment PQ with its endpoints coordinates as P(a, b), Q(c, d), then mid-point can be evaluated as:

$M (M_x, M_y)$ = $[\frac{a + c}{2}, \frac{b + d}{2}]$

In simple terminology, we can say that coordinates of midpoint are evaluated as Median of x - coordinates and y - coordinate respectively.

Let us consider an example to understand it better.

Example: Trace the midpoint of a line segment RS with endpoints as R (10, 4) and S (6, 8) using midpoint formula.

Solution: By substituting values of given coordinates in the midpoint formula, we can get midpoint as follows:
$M (M_x, M_y)$ = $[\frac{a + c}{2}, \frac{b + d}{2}]$

= $[\frac{10 + 6}{2}, \frac{4 + 8}{2}]$

= $[\frac{16}{2}, \frac{12}{2}]$

$M (M_x, M_y) = [8, 6]$
So, the midpoint of the line segment is located at the point (8, 6).