# 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

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.

#### 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 Σx_i^2=220 Σy_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
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