Question

1a)The following distribution represents the number of minutes spent by a herd of cows in grazing

Minutes/week 0-99 100-199 200-299 300-399 400-499 500-599 600 & more

Number of cows 21 26 59 72 52 26 8

Determine the median.

b)If coveriance between X and Y is 18.8 and the variance of X and Y are 22.4 and 26.8 respectively. Find the coefficient of correlation between them.

Answer 1

Solution:

1.a). The median value for the number of cows:

Number of cows = 21 26 59 72 52 26 8

First sort the numbers in ascending order:

Number of cows sorted = 8 21 26 26 52 59 72

Median = $\frac{(n + 1)}{2}$

Where n = the number of values in the data set.

Median = $\frac{(7 + 1)}{2} = \frac{8}{2} = 4$

The 4^th value in the data set will be the median value. The 4^th value in the data set is 26

 

Median value = 26

 

b.). Coefficient correlation (X, Y):

$r_{X,Y} = \frac{S_{XY} }{(S_{X}S_{Y}) }$

Where:

·        r_XY = Correlation between X and Y

·        S_XY = Covariance between X and Y

·        S_X = Standard deviation of X

·        S_Y = Standard deviation of Y

Covariance between X and Y (S_XY) = 18.8

Standard deviation = Square root of variance

Variance of X = 22.4

Variance of Y = 26.8

Standard deviation of X = $\sqrt{22.4} = 4.7329$

Standard deviation of Y = $\sqrt{26.8} = 5.1769$

Coefficient correlation (r,_XY) = $\frac{18.8 }{(4.7329)(5.1769) } = \frac{18.8 }{24.5014 } = 0.7673$

Coefficient of correlation between X and Y = 0.7673