Question

What happens to the median? what happens to the mean?do they increase, decrease, or stay the same ?

Answer 1

The number of observation in the data is n = 8. So median value is equal to average of number at postion n/2 and n/2 + 1.

The number at position n/2 is 1015 and at position (n/2 + 1) is 1025.

Determine the average value of 1015 and 1025.

`\begin{gathered} \text{Median = }(1015+1025)/(2) \\ =(2040)/(2) \\ =1020 \end{gathered}`

So median value is 1020.

If the rent $1100 changes by $1060, then median value does not change as median is obtained by average of fourth and fifth position number which does not include the number 1100.

Thus median remain same.

Determine the mean of monthly rents.

`\begin{gathered} \text{Mean}=(820+910+945+1015+1025+1085+1100+1100)/(8) \\ =(8000)/(8) \\ =1000 \end{gathered}`

Determine the mean when rent 1100 to 1060.

`\begin{gathered} \text{Mean =}(820+910+945+1015+1025+1085+1060+1060)/(8)\text{ } \\ =(7920)/(8) \\ =990 \end{gathered}`

Determine the change in mean value.

`1000-990=10`

Thus mean decrease by $10.