Question

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.

Options

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

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

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

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

Answer 1

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

Explanation:

Reason (R) is clearly true.

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

∴ x_k = 12, f_k = 23, f_{k – 1} = 21, f_{k + 1} = 10 and h = 3.

∴ Mode = `{12 + 3 xx ((23 - 21))/((2 xx 23 - 21 - 10))}`

= `(12 + 3 xx 2/15)`

= 12.4

∴ Assertion (A) is true.

But, Reason (R) is not a correct explanation of Assertion (A).