### Theory:

Consider the following example:

Ram has gone out walking every day. In the first two weeks, he has walked the following distances on each of the days.

$$4$$, $$5$$, $$7$$, $$2$$, $$6$$, $$7$$, $$5$$, $$4$$, $$7$$, $$6$$, $$4$$, $$3$$, $$5$$ and $$4$$ miles respectively.

Construct a frequency distribution table and find the range of the data collected.

Step $$1$$: Let us arrange the numbers in ascending or descending order.

$$2$$, $$3$$, $$4$$, $$4$$, $$4$$, $$4$$, $$5$$, $$5$$, $$5$$, $$6$$,$$6$$, $$7$$, $$7$$, $$7$$

Step $$2$$: Let us construct a frequency distribution table of the ordered data.

 Distance(in miles) Frequency $$2$$ $$1$$ $$3$$ $$1$$ $$4$$ $$4$$ $$5$$ $$3$$ $$6$$ $$2$$ $$7$$ $$3$$

Step $$3$$: Find the range of the data.

From the tabular column, the highest value is $$7$$, and the lowest value is $$2$$.

$$\text{Range} = \text{Highest value} - \text{Lowest value}$$

$$= 7 - 2$$

$$= 5$$

The range of the given set of data is $$5$$.