Question

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 50Calculate the mean, median, range, and midrange of the train ride times for the week.

Answer 1

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

`\bar{x}=(\sum_(x))/(n)`

n is the number of data given.

Where n = 5

Substitute the data into the formula above

`\begin{gathered} \bar{x}=(48+51+48+48+50)/(5) \\ \bar{x}=(245)/(5)=49\text{ minutes} \end{gathered}`

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

`48,48,48,50,51`

Hence, the median is 48

To find the range, the formula

`Range=Biggest\text{ number}-Smallest\text{ number}`

The smallest number is 48

The largest number is 51

Substitute into the formula above

`\begin{gathered} Range=51-48=3 \\ Range=3 \end{gathered}`

Hence, the range is 3

To find the midrange, the formula is

`Midrange=\frac{Biggest\text{ number+Smallest number}}{2}`

Substitute the values into the formula above

`\begin{gathered} M\imaginaryI drange=\frac{B\imaginaryI ggest\text{number+Smallestnumber}}{2} \\ M\mathrm{i}drange=(51+48)/(2)=(99)/(2)=49.5 \end{gathered}`

Hence, the midrange is 49.5

Thus, the answer is Mean, 49: Median, 48: Range, 3; Midrange, 49.5