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If x(1), x(2), ………,x(n) are n values of ...

If `x_(1), x_(2), ………,x_(n)` are `n` values of a variable `x` such that `sum(x_(i)-3) = 170` and `sum(x_(i)-6) = 50.`
Find the value of `n` and the mean of `n` values.

A

`8.25`

B

`6.25`

C

`7.25`

D

`4.25`

Text Solution

Verified by Experts

The correct Answer is:
C
We have,
`sum(x_(i)-3) = 170`
`rArr (x_(1)-3) +(x_(2)-3)+.....+(x_(n)-3) = 170`
`rArr (x_(1)+x_(2)+....+x_(n)) - (3+3+... "to n terms") = 170`
`rArr sumx_(i)-3n = 170 " " ...(1)`
Also, `sum(x_(i)-6) = 50`
`rArr sumx_(i)-6n = 50 " " ....(2)("as above")`
Subtracting eq. (2) from eq. (1), we get
`(sumx_(i) -3_(n)) -(sumx_(i)-6n) = 170-50`
`rArr 3n = 120 rArr n =40`
Put `n=40` in eq. (2), we get
`sumx_(i)-6 xx 40 = 50 rArr sumx_(i) = 290`
`therefore " Mean " bar(x) = (sumx_(i))/(n) = (290)/(40) = 7.25`
Hence, `n=40` and mean `=7.25`
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