Question

The average of 35 raw scores is 18. The average of first seventeen of them is 14 and that of last seventeen is 20. Find the eighteenth raw score.

Answer 1

Answer:

52 will be the 18th raw score

Answer 2

Step-by-step explanation:

let 35 raw scores be x1,x2,x3,......,x34,x35

average of 35 raw scores is 18

then [ (x1)+(x2)+(x3)+..….....+(x34)+(x35) ] / 35=18

[ (x1)+(x2)+(x3)+..….....+(x34)+(x35) ]=35(18)=630

(x1)+(x2)+.....+(x17)+(x18)+(x19)+...…....(x34)+(x35)=630......(1)

given average of first seventeen of them is 14

then

[ (x1)+(x2)+(x3)+......+(x17) ] / 17 =14

[ (x1)+(x2)+(x3)+......+(x17) ]=14(17)=238....(2)

given average of last seventeen is 20

then

[ (x19)+...…....(x34)+(x35) ] / 17 = 20

[ (x19)+...…....(x34)+(x35) ]=20(17)=340..…..(3)

from (1)st,(2)nd, and (3)rd equations we have to substitute the 2nd and 3rd equations values in 1st equation

then

238+(x18)+(340)=630

(x18)+578=630

x(18)=630-578=52

therefore,the eighteenth raw score is 52