f x1, x2..................xn are n values of a variable X. Such that
∑i = 1n(x1-2) = 110 and ∑i = 1n (x1-5) = 20.
Find the value of n and mean.
Answers
Step-by-step explanation :
( Please refer to attachment )
Questions might arrise in your mind -
Q. Why 110 = ∑ - 2n?
Ans. In ( x1 - 2 ) + ( x2 - 2 ) +.....+ ( xn - 2 ), there was 2 subtracted from each term.
Since there are n number of terms so - 2n is subtracted from Summation ( S ) or ∑
Q. What is Bar(X)?
Ans. Bar(X) is symbol of mean. Formula of Mean is,
Bar(X) = (1/n) ∑
Q. What ∑ stands for?
Ans. ∑ means Sigma used as symbol of Summation (S) to denote sum of n number of terms.
∑ = x1 + x2 +..... + xn
Answer:
5.67 IS THE ANSWER
Step-by-step explanation:
∑x
i
=x
1
+x
2
+...+x
n
So, ∑(x
i
−2)=(x
1
−2)+(x
2
−2)+...+(x
n
−2)
Also, ∑(x
i
−2)=110
⇒ (x
1
−2)+(x
2
−2)+...+(x
n
−2)=110
⇒ (x
1
+x
2
+..+x
n
)−2n=110
⇒ ∑x
i
−2n=110 ---- ( 1 )
Similarly,
∑(x
i
−5)=(x
1
−5)+(x
2
−5)+...+(x
n
−5)
Also, ∑(x
i
−5)=20
⇒ (x
1
−5)+(x
2
−5)+...+(x
n
−5)=20
⇒ (x
1
+x
2
+...+x
n
)−5n=20
⇒ ∑x
i
−5n=20 ---- ( 2 )
Subtracting ( 1 ) from ( 2 ) we get,
⇒ ∑x
i
−5n−(∑x
i
−2n)=20−110
⇒ −3n=−90
∴ n=30
⇒ ∑x
i
−5(30)=20
⇒ ∑x
i
=20+150
∴ ∑x
i
=170
⇒ Mean=
n
∑x
i
=
30
170
=5.67