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A simple definition of variable, which you have seen in the last chapter, does not tell you how it varies. Different variables vary differently and depending on the way they vary, they are broadly classified into two types:
  1. Continuous and
  2. Discrete.
A continuous variable can take any numerical value. It may take integral values (1, 2, 3, 4, ...), fractional values (1/2, 2/3, 3/4, ...), and values that are not exact fractions ( =1.414, =1.732, ... , =2.645).

For example, the weight of a student, as he/she grows say from 30 kg to 50 kg, would take all the values in between them. It can take values that are whole numbers like 40kg, 50kg, 48kg, 35kg. It can also take fractional values like 40.85 kg, 46.34 kg and 49.99kg etc. that are not whole numbers. Thus the variable “weight” is capable of manifesting in every conceivable value and its values can also be broken down into infinite gradations. Other examples of a continuous variable are height, time, distance, etc. A discrete variable can take only certain values, but not like a continuous variable. The value of discrete variable changes only by finite “jumps”. It “jumps” from one value to another but does not take any intermediate value between them.

For example, a variable like the “number of bags in a shop”, for different shops, would assume values that are only whole numbers. It cannot take any fractional value like 0.5 because “half of a bag” is absurd. Therefore it cannot take a value like 26.5 between 26 and 27. Instead its value could have been either 26 or 27. What we observe is that as its value changes from 26 to 27, the values in between them the fractions are not taken by it. But do not have the impression that a discrete variable cannot take any fractional value. Suppose X is a variable that takes values like 1/3, 1/14, 1/22, 1/35, ... Is it a discrete variable? Yes, because though X takes fractional values.

It cannot take any value between two adjacent fractional values. It changes or “jumps” from 1/14 to 1/22 and from 1/22 to 1/35. But cannot take a value in between 1/14 and 1/22 or between 1/22 and 1/35. Already we have mentioned that example 4 is the frequency distribution of marks in statistics of 100 students as shown in Table 3.1. It shows how the marks of 100 students are grouped into classes. You will be wondering as to how we got it from the raw data of Table 3.1. But, before we address this question, you must know what a frequency distribution is.

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