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Observe the following statements : (A)...

Observe the following statements :
(A) : The median of 100 items is 52. The value of the largest item is 100. It was later found that it actually 110. Therefore the true median is 52.
(R ) : The median is not effected by the extreme observations.

A

both A, R are true and `R rArr A`

B

both A, R are true and `R cancelrArr A`

C

A is true, R is false

D

A is false, R is true

Text Solution

AI Generated Solution

The correct Answer is:
To solve the question, we need to analyze the statements given and determine their validity. ### Step 1: Analyze Statement (A) Statement (A) claims that the median of 100 items is 52, and after discovering that the largest item was incorrectly recorded as 100 instead of 110, the true median remains 52. - The median is the middle value of a data set when arranged in ascending order. For an even number of observations (like 100), the median is the average of the two middle numbers. - In this case, since the median is stated to be 52, it indicates that the 50th and 51st items (when arranged in order) average to 52. - Changing the largest item from 100 to 110 does not affect the middle values (50th and 51st) because they are not extreme values. **Conclusion for (A)**: The statement is true. ### Step 2: Analyze Statement (R) Statement (R) states that the median is not affected by extreme observations. - This is a general property of the median. It is resistant to outliers or extreme values, meaning that even if the largest or smallest values change significantly, the median can remain unchanged as long as the changes do not affect the middle values. **Conclusion for (R)**: The statement is true. ### Step 3: Determine the Relationship Between (A) and (R) Now that we have established that both statements (A) and (R) are true, we need to assess if (R) is a reason for (A). - Since (R) explains why (A) holds true (the median remains unaffected by the change in the largest value), we can conclude that (R) is indeed a reason for (A). ### Final Conclusion Both statements (A) and (R) are true, and (R) is a reason for (A). Therefore, the correct answer is: **Both A and R are true and R is a reason for A.**
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