Question

Which of the following statements is true for a symmetric distribution?
(A) (Q3 - M) = (M -0.)
(B) (Q3+M)=(M+Q1)
(C) (Q2-Q3)=(Q3-Q1)
(D) Q3+Q1 > 2M​

Answer 1

C) is the correct option

Answer 2

Given : a symmetric distribution

To Find :  Which of the following statements is true

(A) (Q3 - M) = (M -Q1)

(B) (Q3+M)=(M+Q1)

(C) (Q2-Q3)=(Q3-Q1)

(D) Q3+Q1 > 2M​

Solution:

a symmetric distribution

Q3 - Q2  =   Q2 - Q1

Q2=  Median

Q3 - M = M - Q1

Hence (A) (Q3 - M) = (M -Q1)  is correct

Q3 - M = M - Q1

=> Q1 + Q3 = 2M  

Lets take example

Q1 = 5    Q2 = 7    Q3  = 9

(Q3 - M) = (M -Q1)

 9 - 7 =  7 - 5  = 2

(Q3+M)=(M+Q1)

 9 + 7  ≠ 7 + 5

(Q2-Q3)=(Q3-Q1)

7 - 9  ≠  9 - 5

Q3+Q1 > 2M​

9 + 5 = 2 (7)

Hence (A) (Q3 - M) = (M -Q1)  is correct

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