Mini Lecture: Mode, Median, Mean

The 411 for a successful

data analysis.

THE MODE• The most common number

• The most frequently occurring number

THE MODE• In a bar graph, the mode is the

highest bar.

• In a line plot, the mode is the highest column.

THE MODE

• It is possible to have more than one mode. This occurs if there is a tie.

THE MODEEXAMPLE DATA SET

3, 8, 9, 12, 3, 10, 15, 9

In this example, the mode is 3 and 9 because both occur the most times.

(twice)

THE MODE

• It is possible to have no mode.

• This occurs when all of the data entries occur the same number of times.

THE MODEEXAMPLE DATA SET

4, 7, 2, 9, 12, 3

All of the numbers occur one time, so there is no mode.

THE MEDIAN• This is the middle number.

• Half of the data entries are higher than the median.

• Half of the data entries are lower than this number.

THE MEDIAN

• Before attempting to determine the median, you must put the data entries in numerical order!

THE MEDIAN

I REPEAT, YOU MUST PUT THE ENTRIES IN NUMERICAL

ORDER!!

THE MEDIANTo find the median:

• Simply mark off a number from each end of the data set until you are left with one number remaining.

• This is to insure you have marked off the same amount of numbers above and below the median.

THE MEDIANBUT WAIT . . .

TROUBLE LIES AHEAD. . .

• If the number of data entries is EVEN, you will mark off all of the numbers.

THE MEDIANThe Solution:

1. Mark off the entries as before, but stop when there are two numbers remaining.

2. Find the halfway point between the two numbers - the mean.

THE MEDIANEXAMPLE DATA SET

8, 3, 9, 12, 4, 4, 6, 10, 5

The median is 6. Did you remember to put the entries in numerical

order?

THE MEDIAN3, 4, 4, 5, 6, 8, 9, 10, 12

Notice that there are four entries higher than 6 and four entries lower

than 6.

THE MEDIANOne More Example…

8, 3, 9, 12, 4, 4, 6, 10, 5, 11

After putting the numbers in order, one gets…

3, 4, 4, 5, 6, 8, 9, 10, 11, 12

THE MEDIANThis time there are two middle

numbers - 6 and 8.

The median is the halfway point between these two numbers . . . .

7 !!!!

THE MEAN

This number represents fairness.

THE MEANIf you collected all of the data,

golf balls in this case, put them in a big pile, and then

made sure everyone received the same amount; this

amount would be the mean.

THE MEAN•But you don’t have that many

golf balls, and you don’t want to have to do that every time.

•So, there is an easier way…

THE MEAN1. Add all of the entries in the data

set.

2. Take that sum and divide by the number of entries in the data set.

P.S. It is okay to get decimal numbers.

THE MEANEXAMPLE DATA SET

8, 3, 9, 11, 4, 12, 6, 10, 7, 5

The mean is 7.5.

THE MEAN1. The sum of the data set is 75.

2. There are 10 entries. 75 / 10 = 7.5