Question

**Assertion (A):** Consider the following data: | Class | Frequency | | :--- | :--- | | 65 – 85 | 4 | | 85 – 105 | 5 | | 105 – 125 | 13 | | 125 – 145 | 20 | | 145 – 165 | 14 | | 165 – 185 | 7 | | 185 – 205 | 4 | The difference of the upper limit of the median class and the lower limit of the modal class is 20. **Reason (R):** The median class and modal class of grouped data are always different.

Accepted Answer

C. Total frequency $N = 67 \implies N/2 = 33.5$. Cumulative frequencies are 4, 9, 22, 42, 56, 63, 67. - Median class is 125 – 145 (upper limit $= 145$). - Modal class (maximum frequency 20) is 125 – 145 (lower limit $= 125$). Difference $= 145 - 125 = 20$. Hence Assertion (A) is true. However, Reason (R) is false because median class and modal class can be the same (as seen in this example).

Assertion-Reason: Median class and Modal class

Explanation

Practise this under board exam conditions

Class	Frequency
65 – 85	4
85 – 105	5
105 – 125	13
125 – 145	20
145 – 165	14
165 – 185	7
185 – 205	4