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Covariance (x,y) between x and y if x=15, y=40, xy=110, n=5 is
A.22
B.2
C.2
D.None of these

Answer
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Hint: In this question, we have to calculate the value of covariance (x,y) between x and y. We will use the formula for calculation of covariance. We simply put the required values into the formula and solve to get the desired result.
Formula used: cov(x,y)=xyn(xn)(yn)

Complete step-by-step answer:
This question is based on covariance. Covariance in statistics is the measurement of the relationship between two variables. For example, we know that when demand rises and as a result production of goods rises. Thus we can say demand and production have some relationship. This measurement of relationship is called covariance.
When we are given the summation of some terms, then the covariance between x and y, is given by the formula cov(x,y)=xyn(xn)(yn) Where n is the number of terms.
Consider the given question,
We are given, x=15, y=40, xy=110, n=5
We know that the covariance between two variable say xand y is given by the formula
cov(x,y)=xyn(xn)(yn) , Where n is the number of terms.
Putting the values, we get
cov(x,y)=1105(155)(405)
Using the BODMAS Rule, we will first divide.
On dividing 110 by 5 we get 22 , 15 by 5 we get 3 and 40 by 5 we get 8. Hence we have
 cov(x,y)=22(3)(8)
On multiplying, we get
cov(x,y)=2224
On solving, we get
cov(x,y)=2
Hence Option (C) is correct.
So, the correct answer is “Option C”.

Note: The general formula of covariance between two number is given by formula cov(x,y)=(xix)(yiy)n where xi is the data values of x, yiis the data values of y, xis the mean of dataxi and yis the mean of the data yi.
Covariance of the variable x with y is the same as the covariance of y with x. i.e. cov(x,y)=cov(y,x)
Covariance of the variable with itself is zero. i.e. cov(x,x)=0
Covariance may be positive, negative and zero also.
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