$*4)$ The following is a collection of $50$ apartment rent prices in a Rochester, New York neighborhood in dollars from the lowest price of $$1100$ a month to the highest price of $$4000$ a month:

$\backslash$table$[[1100,1100,1100,1100,1200,1200,1300,1300,1400,1500],[1500,1600,1800,1800,1800,1900,1900,1900,1900,1900],[2000,2000,2000,2000,2000,2100,2100,2100,2200,2200],[2200,2300,2300,2400,2400,2400,2500,2600,2900,2900],[2900,2900,3100,3100,3100,3100,3100,3100,3200,4000]]$

a$)$ Find the range and mode of this collection of data. If the data is multimodal, list them all.

b$)$ Find the upper and lower fences for this data. Are any of these prices outliers? If so$,$ state which ones.

c$)$ The mean and standard deviation of the Rochester neighborhood rent prices are $$1852$ and $$321\mathrm{.}61$ respectively. Meanwhile, the mean and standard deviation of rent of a Binghamton neighborhood are $$2088$ $$172\mathrm{.}07$ respectively. Is a $$2400$ a month apartment for rent more relatively expensive in Rochester, or in Binghamton? Explain your answer