The following data show the midterm and final exam scores in an English writing class. Student 1 2 3 4 5 6 7 8 9 10 11 12 Midterm 81 95 91 98 84 86 88 92 99 91 99 81 Final 79 93 87 96 78 52 67 96 92 91 93 76 Find the sample covariance of the midterm and final exam scores (round off to first decimal place).

The co variance of the midterm and final exam scores is 58.76.

Step-by-step explanation:

The formula to compute the sample co variance is:

The values are computed in the table below.

Compute the co variance as follows:

Thus, the co variance of the midterm and final exam scores is 58.76.

solution:

the given function is ,

      =

the three roots of this quadratic function is , 0 ,8 and 10.all the roots are real and rational.

if a quadratic equation is of the form ,

sum of the roots = a + b +c= 0+8+10=18=  

product of roots taken two at a time = a b + b c+ c a = 0+80+0=80 =  

product of roots = a b c = 0=  

there are 11 doors in a hall starting from 0 to 11.the entry in the hall is permitted through gate number 0 and exit is allowed through only gate number 8 and 10.so, three roots(0,8,10) of quadratic function is given by entry and exit route of this hall.

the first one is x^2+2x+2

the second one is x^2+4

the last one is x^2-4x+8