The question consists of two statements, namely, Assertion (A) and Reason (R). Choose the correct option.


Assertion (A)



Reason (R)



The mean of 15 numbers is 25. If 6 is subtracted from each number, the mean of new numbers is 19.



Mode = 3(median) – 2(mean).


Let suppose 15 numbers are = n1, n2, …….. , n15



Given mean = 25


25 =


⇒ n1 + n2 + …… + n15 = 25 × 15


⇒ n1 + n2 + …… + n15 = 375 … [equation (i)]


After subtracting 6 from each number the mean = 19


So, we have,


(n1 – 6), (n2 – 6), …….. (n15 – 6)





From equation (i)



⇒ Mean = 25 – 6 = 19


It means assertion (A) is true,


Reason (R) ⇒ by empirical formula which is,


Mode = 3(median) – 2(mean) is true.


But Reason (R) is not correct explanation of assertion (A).

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