Question

Question 5
Given a random sample of four (x, y) pairs of data points:

(3.1,9) (3.5,13) (5,15) (4.6,11)

What is the covariance?

Answer 1

Given : a random sample of four (x, y) pairs of data points:

(3.1,9) (3.5,13) (5,15) (4.6,11)

To Find : What is the covariance

Solution:

(3.1,9) (3.5,13) (5,15) (4.6,11)

n = 4

x   = 3.1 ,   3.5  , 5 , 4.6

∑x  = 16.2

μx  = ∑x / n   = 16.2 /4  = 4.05

y = 9 , 13 , 15 , 11

∑y  = 48

μy  = ∑y / n   =48 /4  = 12

xi    xi-μx        yi      yi-μy   (xi-μx)(yi-μy)

3.1 -0.95 9 -3   2.85

3.5 -0.55 13 1  − 0.55

5 0.95 15 3  2.85

4.6 0.55 11 -1  − 0.55

_________________________

16.2                48               4.6

σ xy = ∑(xi-μx)(yi-μy) /n = 4.6/4  = 1.15

covariance  = 1.15

Learn More:

the covariance between the length and weight of five items is 6 and ...

https://brainly.in/question/9967416

if coefficient of correlation between x and y is 0.28 covariance ...

https://brainly.in/question/13877695