Identify the continuous variables. (A) Number of tails obtained in hundred…

A variable is classified as continuous when it can take any value, including fractional or decimal values, within a given range and is typically obtained by measuring with an instrument. A variable is classified as discrete when it can take only distinct, countable values - usually whole-number counts, though sometimes other fixed-size increments - and is typically obtained by counting occurrences or applying a scoring rule.

• Number of tails obtained in hundred tosses of a coin: this comes from counting outcomes, so it can only be a whole number such as 0, 1, or 2, up to 100 — a discrete variable.

• Weight of students in a school: this comes from measuring on a weighing scale, so it can be any value such as 52.3 kg or 52.36 kg — a continuous variable.

• Marks scored by students in an objective type examination: each response contributes one of a fixed set of possible increments (for example, a mark for a correct answer or a penalty for an incorrect one), so the total falls on a finite, countable set of values rather than varying continuously — a discrete variable.

• Height of plants in an agricultural field: this comes from measuring with a scale or tape, so it can be any value such as 15.2 cm or 15.23 cm — a continuous variable.

An independent check: ask whether a meaningful value can exist between two consecutive readings. Between a weight of 52 kg and 53 kg, values such as 52.4 kg or 52.47 kg are meaningful, confirming weight is continuous; between a tail count of 40 and 41, no in-between value such as "40.5 tails" is meaningful, confirming the tail count is discrete. The same reasoning applies to height (continuous) and exam marks (discrete).

Weight of students and height of plants are therefore the continuous variables, while the number of tails and the exam marks are discrete — matching the option that pairs weight and height only.