Theory:

Histograms are one way of graphically representing a grouped data or continuous data.
 
Histograms are made of a set of rectangles. The \(X\)-axis will have the different ranges of continuous data, and \(Y\)-axis will have the frequency.
 
Let us learn how to draw histograms.
 
Click here to see how to draw a histogram if the class intervals are equal.
 
Now, we shall see how to draw a histogram if the class intervals are not equal.
Example:
Draw a histogram for the below given data:
 
Number of treesHeight(in m)
\(25 - 30\)\(12\)
\(30 - 40\)
\(20\)
\(40 - 60\)\(30\)
\(60 - 65\)\(10\)
\(65 - 70\)\(29\)
\(70 - 75\)\(16\)
\(75 - 80\)\(24\)
 
Solution:
 
Step \(1\): Since the class intervals are not equal, let us select the with minimum class size. From the given, \(25 - 30\) has the minimum class size, which is \(5\).
 
Step \(2\): Let us modify all the class intervals having the class size as \(5\).
 
For example: Consider the interval \(30 - 40\) having class size \(10\) and frequency \(20\). When the class size is changed to \(5\), then the new frequency will be \(\frac{20}{10} \times 5 = 10\)
 
Step \(3\): Let us form the new frequency table.
 
Number of treesHeight (in m)(frequency)Class sizeNew frequency(in m)
\(25 - 30\)\(12\)\(5\)\(\frac{12}{5} \times 5 = 12\)
\(30 - 40\)\(20\)\(10\)\(\frac{20}{10} \times 5 = 10\)
\(40 - 60\)\(30\)\(20\)\(\frac{30}{20} \times 5 = 7.5\)
\(60 - 65\)\(10\)\(5\)\(\frac{10}{5} \times 5 = 10\)
\(65 - 70\)\(29\)\(5\)\(\frac{29}{5} \times 5 = 29\)
\(70 - 75\)\(16\)\(5\)\(\frac{16}{5} \times 5 = 16\)
\(75 - 80\)\(24\)\(5\)\(\frac{24}{5} \times 5 = 24\)
 
Step \(4\): Now, we shall draw the histogram for the above data.
 
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