Question

the company wants to add a jacket to the lineup so the median cost is $50. how much should the jacket cost? is this the only option to make the median $50? if not, what other price could the jacket be? explain your answer.

Explanation:

Step1: Arrange current prices in ascending order

$40,40,50,100$

Step2: Consider two - case scenarios for adding a new value

If we have an even number of data points after adding a new jacket price, the median is the average of the two middle - values. Let the new price be $x$.
Case 1: If $x\leq40$, the data set in ascending order is $x,40,40,50,100$. The median is the third - value, which is $40
eq50$.
Case 2: If $40 < x<50$, the data set in ascending order is $40,40,x,50,100$. The median is $x$. So, if $x = 50$, it meets the requirement.
Case 3: If $x\geq50$, the data set in ascending order is $40,40,50,x,100$. The median is $50$. So any price $x\geq50$ will make the median $50$.

Answer:

The jacket should cost at least $50$. Any price $x\geq50$ will make the median of the cost of jackets equal to $50$. This is because when we arrange the prices in ascending order, if $x\geq50$, the middle value (for an odd number of data - points after adding $x$) or the average of the two middle values (if we consider a more complex scenario with multiple new items added in the future) will be $50$.