Discrete Metric
A discrete metric is a metric that is countable and can be listed, that is a metric that takes specified number of values. The values are always distinct and separate values. They are never infinite numbers meaning the number is either a natural number or a real number.
Examples:
If X is assumed be the year that any student selected in a classroom at random was born, this value can be 1990, 1995, 2005. X is said to be discrete since the numbers are countable and all can be listed.
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The time that women finish a 100m dash 2016 Olympics to the nearest hundreds is discrete metric since the time can be listed for instance 9:57 p.m. or 10:20 a.m. and unlike when it is not stated to the nearest hundreds and the exact time is required. This can take values such as 9:57123456 p.m. or even 10:201544 a.m. which can always not be listed since one does not know the exact time.
Continuous Metric
A continuous metric is a metric that is not broken and is always whole and with no interruption. It takes any values in the range given even if it is infinite numbers of possibilities. These numbers are numbers that are not natural numbers or real numbers.
Example:
If Y is assumed to be the exact mass of a random animal selected in a museum, one cannot be certain of the exact number of animals in the museum and consequently cannot list all the masses of the animals accurately. Their masses can range from 0kg to 2000kg or even more and any animal can have any mass in that range. For instance an animal weighing a gazelle may weigh 30.4568kg among while a lion may weigh 199.8765kg and so forth. The numbers are not discrete since in this case we cannot count or list them as they may fall within any scale.
