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Solution


Q.

Assertion (A): If the median and mode of a frequency distribution are 50 and 60, respectively, then its mean is 45.

Reason (R): Mean, median and mode of a frequency distribution are related as:

Mode = 3 (Median) − 2 (Mean)
1 Both, Assertion (A) and Reason (R) are true and Reason (R) is correct explanation of Assertion (A).  
2 Both, Assertion (A) and Reason (R) are true but Reason (R) is not correct explanation for Assertion (A)  
3 Assertion (A) is true but Reason (R) is false.  
4 Assertion (A) is false but Reason (R) is true.  

Ans.

(1)

Given, median and mode of a frequency distribution are 50 and 60, respectively.

The empirical relationship between mean, mode and median is:
Mode = 3 × Median − 2 × Mean

∴ 60 = 3 × 50 − 2 (Mean)

⇒ Mean = (150 − 60) / 2 = 90 / 2 = 45

Therefore, both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).