tristan records the number of customers who visit the store each hour on a saturday. his data representing…

tristan records the number of customers who visit the store each hour on a saturday. his data representing the first seven hours are 15, 23, 12, 28, 20, 18, and 23. how many customers visited the store during the eighth hour if the median number of customers per hour did not change?

tristan records the number of customers who visit the store each hour on a saturday. his data representing the first seven hours are 15, 23, 12, 28, 20, 18, and 23. how many customers visited the store during the eighth hour if the median number of customers per hour did not change?

Answer

Explanation:

Step1: Sort the original seven - hour data

Sort the data (15,23,12,28,20,18,23) in ascending order: (12,15,18,20,23,23,28). For (n = 7) (odd number of data points), the median is the (\left(\frac{n + 1}{2}\right))th value. (\frac{7+1}{2}=4)th value. So the median of the seven - hour data is (20).

Step2: Consider the eight - hour data

When we add an eighth data point (x), (n=8) (even number of data points). The median of an even - numbered data set is the average of the (\frac{n}{2})th and (\left(\frac{n}{2}+1\right))th values. We want the median to still be (20). Let's sort the combined data (original seven sorted values (12,15,18,20,23,23,28) and the new value (x)) in ascending order. The median of eight data points is (\frac{4\mathrm{th}\text{ value}+5\mathrm{th}\text{ value}}{2}). If the median is (20), we need to make sure that when we sort the eight - data set, the average of the 4th and 5th values is (20). If (x\leq20), the sorted data set is (12,15,18,x,20,23,23,28). The median is (\frac{x + 20}{2}). Set (\frac{x+20}{2}=20), then (x + 20=40), (x = 20). If (x\geq20), the sorted data set is (12,15,18,20,x,23,23,28). The median is (\frac{20 + x}{2}). Set (\frac{20+x}{2}=20), then (x=20).

Answer:

(20)