Solution
Santos takes the train into the city five days a week for work.
For one work week, he kept track of how many minutes long each train ride was:
48, 51, 48, 48, 50
To find the mean of ungrouped data, the formula is
[tex]\bar{x}=\frac{\sum_{x}}{n}[/tex]n is the number of data given.
Where n = 5
Substitute the data into the formula above
[tex]\begin{gathered} \bar{x}=\frac{48+51+48+48+50}{5} \\ \bar{x}=\frac{245}{5}=49\text{ minutes} \end{gathered}[/tex]Hence, the mean is 49
To find the median, we arrange the given data in ascending number and pick the middle number as shown below
[tex]48,48,48,50,51[/tex]Hence, the median is 48
To find the range, the formula
[tex]Range=Biggest\text{ number}-Smallest\text{ number}[/tex]The smallest number is 48
The largest number is 51
Substitute into the formula above
[tex]\begin{gathered} Range=51-48=3 \\ Range=3 \end{gathered}[/tex]Hence, the range is 3
To find the midrange, the formula is
[tex]Midrange=\frac{Biggest\text{ number+Smallest number}}{2}[/tex]Substitute the values into the formula above
[tex]\begin{gathered} M\imaginaryI drange=\frac{B\imaginaryI ggest\text{number+Smallestnumber}}{2} \\ M\mathrm{i}drange=\frac{51+48}{2}=\frac{99}{2}=49.5 \end{gathered}[/tex]Hence, the midrange is 49.5
Thus, the answer is Mean, 49: Median, 48: Range, 3; Midrange, 49.5
