Statistics - Online Test

Mean (x) = (38+70+48+34+42+55+63+46+54+44)/10

               = 494/10

               = 49.4

X¯=(22+26+28+20+24+30)/6=25

1n∑i=1n(Xi−X¯)2=(9+1+9+25+1+25)/6=11.66

S.D=11.67−−−−√=3.42

[r=tan(π2−θ)]

here [θ=π2]

hence r = 0, therefore there is no linear correlation.

ρ=±bxy.byx−−−−−−√=±27.27−−−−√=±27

but sign of ρ$\rho$ is same as the sign of bxy,byx

therefore, ρ=27

we have x + 4y = 3 and 3x + y = 15 as the lines of regression of y on x and x on y respectively. 

therfore, for y = 3 the required line is x on y

so put y= 3 in 3x + y = 15

we get, x = 4

Let other two numbers be x and y 

Mean (x) = 4.4 = (1+2+6+x+y)/5

this gives (x+y)=13......(1) 

Also,       (x−y)=5 ........(2) 

Therefore from (1) and (2)

 x = 9 and  y = 4         

comparinf the given equation with ax + by + c= 0

a = -4, b =1 and c= -3

so ab < 0

hence, ρ=−ba∣∣ba∣∣=−ba−ba=1

so a perfect positive correlation.