Answer

Verified

53.1k+ views

**Hint:**The correlation coefficient is a statistical measure of the strength in relationship between the relative movements of two variables, for the given variables x and y the formula become coefficient of correlation = $\dfrac{{Cov(x,y)}}{{{\sigma _X}{\sigma _Y}}}$

**Complete step by step solution:**

As in the question we have to find coefficient of correlation, for this

The correlation coefficient is a statistical measure of the strength in relationship between the relative movements of two variables. The values range in between $ - 1$ and $1$ if the calculated number is greater than $1$ or less than $ - 1$ means that there is an error in the correlation measurement. A correlation of $ - 1$ shows a perfect negative correlation, while a correlation of $1$ shows a perfect positive correlation. A correlation of $0$ shows no linear relationship between the movement of the two variables.

To calculate the product-moment correlation, one must first determine the covariance of the two variables in question. Next, one must calculate each variable's standard deviation. The correlation coefficient is determined by dividing the covariance by the product of the two variables' standard deviations.

So the relation is

Coefficient of correlation = $\dfrac{{Cov(x,y)}}{{{\sigma _X}{\sigma _Y}}}$

where

$Cov(x,y)$ is covariance of x and y that is \[8\]

${\sigma _X}$ is standard deviation of x that is $3$

${\sigma _y}$ is standard deviation of x that is $4$

Hence on putting the value of these ,

Coefficient of correlation = $\dfrac{8}{{3 \times 4}}$

Hence it is equal to the $\dfrac{2}{3}$

**Option A will be the correct answer.**

**Note:**Correlation coefficients are used to measure the strength of the relationship between two variables. Pearson correlation is the one most commonly used in statistics. This measures the strength and direction of a linear relationship between two variables that we use in this question.

Correlation coefficient values less than $0.8$ or greater than $ - 0.8$ are not considered significant.

Recently Updated Pages

In a family each daughter has the same number of brothers class 10 maths JEE_Main

If 81 is the discriminant of 2x2 + 5x k 0 then the class 10 maths JEE_Main

What is the value of cos 2Aleft 3 4cos 2A right2 + class 10 maths JEE_Main

If left dfracleft 2sinalpha rightleft 1 + cosalpha class 10 maths JEE_Main

The circumference of the base of a 24 m high conical class 10 maths JEE_Main

From the top of a hill h meters high the angles of class 10 maths JEE_Main

Other Pages

If a wire of resistance R is stretched to double of class 12 physics JEE_Main

when an object Is placed at a distance of 60 cm from class 12 physics JEE_Main

According to classical free electron theory A There class 11 physics JEE_Main

The resultant of vec A and vec B is perpendicular to class 11 physics JEE_Main

A count rate meter is used to measure the activity class 11 chemistry JEE_Main

The nitride ion in lithium nitride is composed of A class 11 chemistry JEE_Main