Covariance and significant figures
While measuring any random values, distance or any time zone it is difficult to observe the measurements. And in this very context statistics has a very useful tool for us to observe the random values and their measurements called as Co-variance.
What is Co-variance?
Very similar to variance but much diverse as it can measure two random values together while variance measures only a single random value. In probability theory as well in statistics, covariance acts the same, i.e., possibly a positive or a negative covariance.
Positive and Negative Covariance
In terms of measuring the two random values at a time we must find out the corresponding behavior of both values toward each other. If the greater value one of the variables corresponds with the second greater value of the other variable, it shows a positive covariance. It shows if both the variables are corresponding toward the same values it gives a positive covariance.
On the other hand, the opposite value doesn’t correspond to the same value of both variables. If the larger value of a variable corresponds to the smaller one of the other variable it will give a negative covariance. In negative covariance both the variables show opposite behavior.
Linear relation between two variables
While talking about linear relationships, we usually refer to it as a degree to which two random variables have linear relations. And this relationship is shown by the signs of covariance, whether a positive covariance or a negative one. These signs of covariance shows the degree of their linear relationship.
Covariance, in other terms known as the expected values of two random variables which shows its correlation with each single variable. Hence these so-called expected values or the magnitude of the variables are not sure so the probability factor also builds a linear relationship between both variables.
Formula for covariance
As discussed earlier, covariance is the measurement of the number of variations happening in the two random variables. To measure the variations we have the following formula used for covariance
Cov (x, y) = E (X1 – X–)(Y1 – Y–)/ n-1
X1 = number of variable X
Y1 = number of variable Y
X– = average value of X
Y– = average value of Y
n = total number of variables
Above elaborately described signs show the process of calculation as well. Covariance calculator can be used online to solve the equations and queries.
A significant figure of a number is the digit which carries a meaningful contribution. The significant figures are the trails that contribute to the measurement techniques.
Almost every single digit is a significant figure and counted as a significant one except the zeros, that too in some certain conditions.
All the leading Zeros are not significant. As an example 0123, here we only have three significant figures that are 1, 2, and 3 while the leading digit 0 has no such significance.
The trailing zero which acts as a placeholder, i.e., 0.12 or 0.34 here the digit before the decimal has no significance.
While any zero placed in between any other digit or is contributing as a measuring unit is considered a significant figure. For example 10, 100, or 1011, as zero acts as a measuring digit here it is also counted as a significant figure.
In a broader scope, the number with greater significant figure is the leading digit with highest exponential position from the very left side which includes digits from 1 to 9. While on the other hand the least significant figure is the least exponential position from right, all in a decimal notation case.
For example; 1235 here 1 is the most significant digit while 5 is the least one. And if these digits have a zero in between somewhere, it will also be considered as a significant figure such as 1203.
To provide a more sophisticated scientific manner in order to achieve significant figures in all possible ways, a scientific rule is used known as Propagation of uncertainty. The sig fig calculator solves the long floating number equations and provides us the accurate result.
Rounding of numbers is also a method used to precise the significant figures. In this case we just round the digits into a precise but similar version. For example if we say 10.653801grams, it has 8 significant figures while rounding it in a precise version is 10.654 grams. This rounding of digits makes things much easier and precise to get any conclusion.A very common problem which students face is related to the long pdf files which are downloaded in order to complete the assignments. These long pdf files usually confuse the students and make it difficult for them to get it done. Split pdf can be used online by the students to cut pdf pages and save only those pages which are required and needed.