Midpoint

The logic behind midpoint and covariance

Both are inter-related terms and you cannot separate them. If you need to know about one factor another one comes automatically. They are like a pair in the field of maths.

What is a midpoint?

When a middle line is divided into two equal segments starting from the center it is known as the midpoint. Distance is equal to both the endpoints. The segment is bisected with this midpoint. In elementary school training, these both are considered instrumental concepts. It is usually applied in the cartesian system and is a very common term. A midpoint calculator proves useful to calculate it quickly.

Formula:

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

It is one of the simplest formulae and has been in use for a long time.

How to find midpoint in geometry?

1. Add both "x" coordinates, divide them by 2

2. Add both "y" coordinates, divide by 2

Is y = 2x – 4.9 a bisector of the line segment with endpoints at (–1.8, 3.9) and

(8.2, –1.1)?

I can solve this by using just a graph and the answer seems like yes. But one should always keep this fact in mind while solving a problem. The graph or picture only suggests the answer and makes its picture. Only algebra will tell you the exact answer. So e.g if I have been provided with a problem of a midpoint and need to find it, I will first apply the midpoint formula.

After solving it, I will tell you if this point is on the line or not?

y = 2x – 4.9

y = 2(3.2) – 4.9 = 6.4 – 4.9 = 1.5

In this case, I want y=1.4 but this is a bisector which is indicated by the graph picture. On the other hand, when I performed all the calculations it was proven by algebra that it's not exactly a bisector. So, our answer will be no, it's not a bisector.

Calculation of midpoint becomes tough if the data is large and you don’t have enough time. In this case, one can use the online midpoint calculator. It will save both your time and energy. Now, let's move to the second main part which is known as covariance:

Covariance

In probability and statistics covariance is a very basic term. It is known as the joint variability calculation of two variables.

Types

It has two types:

Negative and positive

Positive type

If greater values for supposing one variable hold the greater value and if the same goes for the lesser variables we call it a positive covariance.

Negative type

If the variables show the opposite behavior then it is known as the negative one. It happens when the greater values correspond to the lesser values of another type.

A linear relationship between the variables is the sign of covariance. Covariance magnitude calculation is not told easily and requires a lot of time.

Understanding covariance

How the means of two variables move together is known as the covariance.

Analysts usually come with a set of data and a pair of x and y values. So, one can calculate covariance using five variables from the given data. Let us see them:

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

xm = the mean of x values

yi = the y value in the data set that corresponds with xi

ym = 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:

Company’s analyst has a five-quarter data set which shows the GDP growth in percentage and the new product line growth for company in percentages (y). 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

Mean value of x in this case is 3 and y value is equal to 14.2. 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

So, we say that quarterly GDP growth has a positive relationship with a company's new product growth.

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