The median of the histogram is given as follows,
The width of the each bar is 30.
The total area of the histogram is
[tex]\begin{gathered} \text{Total area = 30}\times35+30\times45+30\times25+30\times20 \\ \text{Total area = 1,050+1,350+750+600} \\ \text{Total area = 3,750} \end{gathered}[/tex]
The median will be
[tex]\begin{gathered} Median\text{ = }\frac{3,750}{2} \\ \text{Median = 1,875} \end{gathered}[/tex]
The area of the first class is
[tex]30\times35=1,050[/tex]
The area of the second class is
[tex]30\times45=1,350[/tex]
The difference between the median and the area of the first class is
[tex]1,875-1,050=825[/tex]
The median is, therefore, larger than the first class but within the second class.
The depth within the second class median is located
[tex]\frac{375}{45}=8.34[/tex]
The median best estimate is
[tex]30+8.34=38.34[/tex]
Therefore, the range of the median class interval between 31 and 60 minutes will be 38.24 minutes.
