Question

C.I.	0 - 10	10 - 20	20 - 30
Frequency	15	25	b
Cumulative frequency	15	a	50

Assertion (A): a = 15 + 25 = 40;
b = 50 − a

Reason (R): a + 15 = 25
and b = 50 − 10

Options

• A is true, R is false.

• A is false, R is true.

• Both A and R are true and R is the correct reason for A.

• Both A and R are true and R is the incorrect reason for A.

Answer 1

A is true, R is false.

Explanation:

Cumulative frequency is the accumulated sum of frequencies up to a specific class interval. For example, the cumulative frequency for the 10–20 class interval incorporates frequencies from all previous intervals as well. Consequently, the cumulative frequency for the 10–20 interval is calculated by adding the frequencies of the 0–10 and 10–20 intervals together.

The cumulative frequency for the 10–20 interval is the sum of the frequencies for the 0–10 and 10–20 intervals:

a = 15 + 25 = 40

The cumulative frequency for the 20–30 interval is 50, which includes all previous frequencies. Therefore, the frequency for the 20–30 interval is:

b = 50 − a = 50 − 40 = 10

∴ A is true, R is false.