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? 16 19 20 23

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? 16 19 20 23

Answer

Answer:

C. 20

Explanation:

Step1: Arrange initial data in order

$12,15,18,20,23,23,28$

Step2: Find initial median

Since $n = 7$ (odd), median is the $\left(\frac{7 + 1}{2}\right)$-th value, which is the 4 -th value. So the initial median is 20.

Step3: Analyze effect of new value on median

When $n=8$ (even), the median is the average of the $\frac{n}{2}$-th and $\left(\frac{n}{2}+1\right)$-th ordered values. If the new value is 20, the ordered data set with 8 values will still have the average of the middle - two values as 20. So the median remains 20.