Let's first write down the values that we have in number form.
2,3,4,4,5,5,5,6,6,6,7,7,7
b. The median is the middle number of the data set
2,3,4,4,5,5,5,6,6,6,7,7,7
Since 5 is the middle number, 5 is the median
Answer=5
c. the mean can be calculated by adding all of the numbers, and then dividing by the number of numbers.
Mean=(sum of all numbers)/(number of numbers)
Sum of all number=2+3+4+4+5+5+5+6+6+6+7+7+7=67
There are 13 numbers in the data set
Mean=67/13=5.15
Answer=5.15
c. if a data point of 20 were to be added to the data set. The median would only increase from 5 to 5.5
2,3,4,4,5,5,5,6,6,6,7,7,7,20 (5+6)/2=11/2=5.5
The mean would increase the most from 5.15 to 6.2
Mean=(2+3+4+4+5+5+5+6+6+6+7+7+7+20)/14=6.2
In general, outlying numbers in a data set have a greater effect on the mean than the median.
