The number of lattes sold daily for two coffee shops is shown in the table:

Lattes

12

52

57

33

51

15

46

45

Based on the data, what is the difference between the median of the data, including the possible outlier (s) and excluding the possible outlier (s) ?

48.5

23

8.4

3

Option 4 (3)

Step-by-step explanation:

The first step involved in calculating the median it to list the observations in the ascending order. This gives:

12 15 33 45 46 51 52 57.

The second step is to identify the middle number (in case the observations are in odd numbers) or numbers (in case the observations are in even numbers) after the ascending order step has been done. It can be observed that the middle numbers in this data set are 45 and 46. Since there are two numbers, so their average will be the median of this data set. Therefore, the median is 45.5.

It can be observed that that there are 2 outliers in the data set: 12 and 15. Once removed, the data set will be:

33 45 46 51 52 57.

The middle numbers are 46 and 51 and the mean of the two middle numbers is 48.5.

Therefore, the difference between the median of the data, including the possible outliers and excluding the possible outliers is given by 48.5 - 45.5 = 3. Therefore, Option 4 is the correct answer!