Question

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 1

We have first, the 7 hrs observations, so arranging them in ascending order, to find median:
12, 15, 18, 20, 23, 23, 28
Now, number of observations n = 7, which is odd
So, median for odd n is given by
Median = (n + 1)th / 2 position
Median = (7 + 1)th / 2 position
Median = 4th position in our arranged data

4th position = 20
So, median = 20
Now, for 8th observation, we need a value, such that the median remains 20.
Median for n=8, which is even = 
Median = [ (n/2)th + (n/2 + 1)th ] /2
20 = [ 4th + 5th ] / 2
40 = 4th + 5th
So, in our 8 observations data, the 4th + 5th observations should be equal to 40, but in previous data, we had 4th observation as 20 and 5th as 23, so the eighth hour number should be our 5th observation now. So,

5th = 40 - 20
5th = 20
Therefore, 20 people visited the store in 8th hr.