Maharashtra State BoardHSC Arts 12th Board Exam
Advertisement Remove all ads

In the Following Data, One of the Values of Y is Missing. Arithmetic Means of X and Y Series Are 6 and 8 (A) Estimate the Missing Observation. (B) Calculate Correlation Coefficient. - Mathematics and Statistics

Advertisement Remove all ads
Advertisement Remove all ads
Advertisement Remove all ads
Sum

In the following data, one of the values of Y is missing. Arithmetic means of X and Y series are 6 and 8

X

6

2

10

4

8

Y

9

11

?

8

7

 (a) Estimate the missing observation.

 (b) Calculate correlation coefficient.

Advertisement Remove all ads

Solution

 
 
 

(a)First, we find the missing value of Y and let us denote it by a.

`barY=(SigmaY)/N=(9+11+a+8+7)/5=(35+a)/5`

`=>8=(35+a)/5=>40=35+a=>a=5`

Thus the completed series is 

X 6 2 10 4 8
Y 9 11 5 8 7

(b)Now we Find coefficient correlation

xi yi  xiyi `x_i^2` `y_i^2`
6 9 54 36 81
2 11 22 4 121
10 5 50 100 25
4 8 32 16 64
8 7 56 64 49
Σxi = 30 Σyi = 40  Σxiyi = 214 Σ`x_i^2`=220 Σ`y_i^2` = 340

 Here, n= 5, ΣX = 30, Σx2 = 40, ΣY=40, ΣY2 = 20 and Σxy = -26

Now,

`barX = (SigmaX)/n =30/5=6 " and "barY =(SigmaY)/n=40/5=8`

`:. r = (1/n Σ x iyi - barx bary)/(sqrt[[(Σxi^2)/n - barx^2] [(Σyi^2)/n - bary^2]`

`r = (1/5 xx 214 - 8 xx 6)/(sqrt(220/5 - 6^2) xx sqrt(340/5 - 8^2)`

`= (42.8 - 48)/((sqrt (44 - 36) xx sqrt(68 - 64))`

= `(-5.2)/(sqrt8 xx sqrt4)`

= `(-5.2)/(4sqrt2)`

r = -0.92

 

 
Concept: Statistics - Karl Pearson’s Coefficient of Correlation
  Is there an error in this question or solution?

APPEARS IN

Advertisement Remove all ads
Share
Notifications

View all notifications


      Forgot password?
View in app×