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Mathematics

Assertion (A) : The difference in class marks of the modal class and the median class of the following frequency distribution table is 0.

Class intervalFrequency
20-301
30-403
40-502
50-606
60-704

Reason (R) : Modal class and median class are always the same for a given frequency distribution.

  1. Both A and R are correct, and R is the correct explanation for A.

  2. Both A and R are correct, and R is not the correct explanation for A.

  3. A is true, but R is false.

  4. Both A and R are true.

Statistics

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Answer

Cumulative frequency distribution table :

Class intervalClass markFrequencyCumulative frequency
20-302511
30-403534
40-504526
50-6055612
60-7065416

Median = 162\dfrac{16}{2} = 8th term.

The 8th term lies in the class 50-60.

∴ Median class = 50-60

Also, frequency of class 50-60 is highest.

∴ Modal class = 50-60.

∴ Assertion (A) is true.

Modal class and median class are not always the same for a given frequency distribution.

∴ Reason (R) is false.

Hence, Option 3 is the correct option.

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