Question

The 8 students in Mrs. Evans Class were asked how many minutes it takesthem to get to school in the morning. Here is what they answered:10, 11, 8, 14, 16, 13,9, 5Find the mean and median travel times for these students.If necessary, round your answers to the nearest tenth.

Answer 1

The data set represents the time in minutes that takes 8 students of the class to get to school in the morning.

`\mleft\lbrace10,11,8,14,16,13,9,5\mright\rbrace`

1) To calculate the mean of the data set you have to add all observations and divide it by the number of observations, following the formula:

`\bar{X}=(\sum^8_(n\mathop=1)(x_i))/(n)`

X[bar] is the mean

xi represents the i-observation

n is the total observations

`\begin{gathered} \bar{X}=(10+11+8+14+16+13+9+5)/(8) \\ \bar{X}=(86)/(8) \\ \bar{X}=10.75 \end{gathered}`

The mean value of the data set is 10.75 minutes, this means that the average commute time to school for the students of Mts Evans class is 10.8 minutes.

2) The median is the value of the sample that divides it into two halves. To determine the median of the data set, the first step is to calculate its position. To calculate the position of the median for n even sample you have to use the following formula:

`\text{PosMe}=(n)/(2)`

Our sample size is n=8, so the position of the median is:

`\text{PosMe}=(8)/(2)=4`

This value indicates that the median is the 4th observation of the data set.

The next step is to order the data set from least to greatest and then localize the fourth observation:

`\mleft\lbrace5,8,9,10,11,13,14,16\mright\rbrace`

Counting from the left, the 4th observation is 10 minutes.

So the median of the data set is Me=10 minutes