RANGE
DEFINITION
Range is the difference between the largest and smallest values in a set of observations. Range gives an indication of how spread out, the values are.
CALCULATOR

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Range:
FORMULA AND DERIVATION
For a given set of observations $$x_1,x_2\dots \dots \dots x_n$$, the range is defined as follows:-
$Range={\mathop{\mathrm{max}}_{i} \left(x_i\right)\ }-{\mathop{\mathrm{min}}_{i} \left(x_i\right)\ }$
In simple terms,
$Range=largest\ value-smallest\ value$
EXAMPLES
Example 1

Following is the data on the marks of 10 students in an exam:-
$$\mathrm{98,\ 42,\ 27,\ 92,\ 11,\ 3,\ 68,\ 87,\ 74,\ 76.}$$

Here,
$$Largest\ value=98$$
$$Smallest\ value=3$$
$Range=98-3=95\ marks\$
Example 2

Consider the following marks of 100 students:-

Marks Number of Students
$$0-20$$ $$12$$
$$20-40$$ $$2$$
$$40-60$$ $$8$$
$$60-80$$ $$72$$
$$80-100$$ $$6$$

In this case, the smallest value could be 0 and the largest value could be 100. Therefore, we consider the range to be $$100-0=100$$ .
In case of a grouped frequency distribution, as above, we will not have sufficient knowledge about the exact values included in each class interval, and therefore, the range will include all possible values available in the frequency distribution.