Question

Question consists of two statements, namely, Assertion (A) and Reason (R). For selecting the correct answer, use the following code: 

(a) Both Assertion (A) and reason (R) are true and Reason (R) is a correct explanation of Assertion (A). 

(b) Both Assertion (A) and reason (R) are true and Reason (R) is not a correct explanation of Assertion (A). 

(c) Assertion (A) is true and Reason (R) is false. 

(d) Assertion (A) is false and Reason (R) is true.

Assertion (A)	Reason (R)
Consider the following frequency distribution: Class interval 3 – 6 6 – 9 9 – 12 12 – 15 15 – 18 18 – 21 Frequency 2 5 21 23 10 12 The mode of the above data is 12.4.	The value of the variable which occurs most often is the mode.

The correct answer is: (a) / (b) / (c) / (d)

Answer 1

(b) Both assertion (A) and reason (R) are true, but reason (R) is not a correct explanation of assertion (A). 

Clearly, reason (R) is true. 

The maximum frequency is 23 and the modal class is 12 – 15. 

Now, x_k = 12, f_k = 23, f_k-1= 21, f_k+1 = 23 and h = 3

∴ Mode = \(\{12+3\times\frac{(23-21)}{(2\times23-21-10)}\}\)

= \((12+3\times\frac{2}{15})\)

= (12 +0.4) 

= 12 

∴ Assertion (A) is true. 

However, reason (R) is not a correct explanation of assertion (A).