Both terms go in hand by hand. They are inseparable. Take them as a pair. If you are dealing with midpoint on one hand then you can’t ignore covariance.So clear the doubts about both of them. Otherwise, you will be in a serious problem. Well, maths is all about solving tricky problems.

What is a midpoint?

There are a lot of times when you need to find the midpoint. E.g you need to find the midpoint cutting the line. This is known as the midpoint. Distance is equal to both the endpoints. The segment is bisected with this midpoint. This concept is not very common but you need to remember it for future use.

Notation

M is used for the midpoint

Formula:

(a+c)/2,(b+d)/2

Example

Find the midpoint P between (–1, 2) and (3, –6).

First, I apply the Midpoint Formula; then, I’ll simplify:

So the answer is P = (1, –2).

How to find midpoint in geometry?

The midpoint of a Line Segment

1. Both x coordinates are added and then divided by 2.

2. The same happens with both of y coordinates.

Applications

It has one of the main applications in the field of geometry. So, In a practical field, one can see its vast usage in architecture and the field of fashion designing. None of the model or scale is completed without geometry which leads to the midpoint.

The engineering field is incomplete without this midpoint application as every other problem in it requires it. So, if you are going to choose engineering or physical sciences you better learn these concepts.

Sometimes data is large and requires time and energy. A lot of online midpoint calculators are available nowadays which will provide your answer within a few seconds.

Covariance

Co-variance is a very common term used in the fields of statistics and probability. If you are going to college and have opted for a mathematics major then co-variance is one of the main topics to cover. You cannot skip this one as it is a basic one when it comes to statistics.

Types

It has two types:

Negative and positive

Positive type

Positive covariance establishes when your one variable has a greater value as compared to the lesser variables.

Negative type

It’s the opposite of the first one. In this case, one group has higher values as compared to the lesser subset. Variables are considered as entities in this case. Like the physical ones.

 Understanding covariance

In other words, you can also take covariance like how the two variables mean to move together. Let’s take a look:

xi = It is the given x value in the data set

I’m = the mean of x values

I’m = mean of y values

n = total number of data points.

Formula

Following is the covariance formula derived from above information

Cov(x,y) = SUM [(xi – xm) * (yi – ym)] / (n – 1)

Example

Lets see one of the solved examples:

It is related to the company’s growth for a certain new product named as y. All figures are in percentages of y and a 4-quarterly sets are provided by the analysts of the company.Following is the given data set:

Q1: x = 2, y = 10

Q2: x = 3, y = 14

Q3: x = 2.7, y = 12

Q4: x = 3.2, y = 15

Q5: x = 4.1, y = 20

Covariance for the sum of products of xi and yi are calculated below:

Cov(x,y) = ((2 – 3) x (10 – 14.2) + (3 – 3) x (14 – 14.2) + … (4.1 – 3) x (20 – 14.2)) / 4 = (4.2 + 0 + 0.66 + 0.16 + 6.38) / 4 = 2.85

Conclusion 

You can also use the online covariance calculator if you find it difficult to do the covariance calculation by hand.

Image: R-chie overlapping covariance arc diagram by Daniel Lai, Jeff Proctor, Jing Yun and Irmtraud Meyer by dullhunk on 2012-07-12 09:21:32

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