Coefficient of correlation between X and Y for 20 items is 0.3, mean of X is 15 and that of Y 20, standard deviation are 4 and 5 respectively. At the time of calculations one item 17 was wrongly copied instead of 27 in case of X-series and 35 instead of 30 in case of Y series. Find the correct coefficient of correlation.
Answers
Answer:
57
Step-by-step explanation:
divide multiply addition subtraction
The correct coefficient of correlation is 0.515
Given :
Coefficient of correlation between X and Y for 20 items is 0.3,
mean of X (x) = 15
mean of Y (y) = 20
standard deviation of x (p) = 4
standard deviation of y (q) = 5
number of items (n) = 20
To Find: the correct coefficient of correlation.
Solution:
According to the formula of correlation (r),
r = cov (x,y) / (p×q)
0.3 = cov(x,y) / (4×5)
cov (x,y) = 0.3 × 20 = 6
According to the formula of covariance,
Σxy/n - (x×y) = 6
Σxy/20 - (15 × 20) = 6
Σxy = 6120
Hence corrected covariance = 6120 - 17×35 + 27×30
= 6335
also, p²=16
⇒ Σx²/20 - 15² = 16
⇒ Σx² = 4280
and q² = 25
⇒ Σy²/20 - 20² = 16
⇒ Σy² = 8500
Again
Σx = nx - wrong x-value + correct x-value
= 20×15 - 17 + 27
= 310
Σy = ny - wrong y-value + correct y-value
= 20 ×20 - 35 + 30
= 395
Corrected Σx² = 4280 - 17² + 27²
= 5260
Corrected Σy² = 8500 - 35² + 30²
= 8175
So now the correct value of correlation coefficient is found using formula,
r = ( nΣxy - ΣxΣy) / √(((nΣx²) - (Σx)²)((nΣy²) - (Σy)²)))
= (20 × 6335 - 310×395) / √(((20×5260) - 310²) × ((20×8175) - 395²))
= 4250 / √(68022500)
= 0.515
Hence, the correct coefficient of correlation is 0.515
#SPJ2