Read the information given below carefully and answer the question that follows:
(A) The mean of 20 observations is 17. On checking, it was found that two observations were wrongly copied as 3 and 6. If the wrong observations are replaced by correct values 8 and 9, then the correct mean will be 16.4.
(B) The ratio of $4^{3.5} : 2^5$ is same as 4 : 1
(C) The ratio of 1.5 : 2.5 can also be written as 3 : 5
(D) If: 2A = 3B = 4C, then, A : B : C is equal to 6 : 4 : 3
Choose the correct option:
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → (A) is incorrect but (B), (C) and (D) are correct
(A) Mean of 20 observations = 17
So, wrong total = 20×17=340
Wrongly copied values = 3 and 6
Correct values = 8 and 9
Correction in total:
(8+9)−(3+6) = 17−9 = 8
New total = 340+8=348
Correct mean:348/20 = 17.4 . hence, statement A is incorrect.
(B) = $4^{3.5} : 2^5$
$4^{3.5}$ =$(2^2)^{3.5}$ = $2^7$
So ratio: $2^7$ :$2^5$ = $2^2$:1 = 4: 1
Statement (B) is correct
(C) 1.5 : 2.5= 15/10 : 25/10 = 15 : 25 = 3 : 5
Statement (C) is correct
(D) 2A=3B=4C
Let common value = k
A= k/2, B =k/3 and C = k/4
A:B:C = 1/2 : 1/3 : 1/4 = 6 : 4 : 3
Statement (D) is correct