Question

Please help me with calculating the range of the median daily exercise time by using the histogram.

Answer 1

The median of the histogram is given as follows,

The width of the each bar is 30.

The total area of the histogram is

`\begin{gathered} \text{Total area = 30}*35+30*45+30*25+30*20 \\ \text{Total area = 1,050+1,350+750+600} \\ \text{Total area = 3,750} \end{gathered}`

The median will be

`\begin{gathered} Median\text{ = }(3,750)/(2) \\ \text{Median = 1,875} \end{gathered}`

The area of the first class is

`30*35=1,050`

The area of the second class is

`30*45=1,350`

The difference between the median and the area of the first class is

`1,875-1,050=825`

The median is, therefore, larger than the first class but within the second class.

The depth within the second class median is located

`(375)/(45)=8.34`

The median best estimate is

`30+8.34=38.34`

Therefore, the range of the median class interval between 31 and 60 minutes will be 38.24 minutes.