http://www.ck12.org Chapter 15. Concepts of Statistics
Example B
Compute the mean, median and mode for the following numbers.
3, 5, 1, 6, 8, 4, 5, 2, 7, 8, 4, 2, 1, 3, 4, 6, 7, 9, 4, 3, 2
Solution:
Mean:The sum of all these numbers is 94 and there are 21 numbers total so the mean is^9421 ≈ 4 .4762.
Median:When you order the numbers from least to greatest you get:
1, 1, 2, 2, 2, 3, 3, 3, 4, 4, 4, 4, 5, 5, 6, 6, 7, 7, 8, 8, 9
The 11thnumber has ten numbers to the right and ten numbers to the left so it is the median. The median is the
number 4.
Mode:the most frequently occurring number is the number 4.
Note: it is common practice to round to 4 decimals in AP Statistics.
Example C
You write a computer code to produce a random number between 0 and 10 with equal probability. Unfortunately,
you suspect your code doesn’t work perfectly because in your first few attempts at running the code, it produces the
following numbers:
1, 9, 1, 1, 9, 2, 9, 1, 9, 9, 9, 2, 2
How would you argue using mean, median, or mode that this code is probably not producing a random number
between 0 and 10 with equal probability?
Solution:This question is very similar to questions you will see when you study statistical inference.
First you would note that the mean of the data is 4.9231. If the data was truly random then the mean would probably
be right around the number 5 which it is. This is not strong evidence to suggest that the random number generating
code is broken.
Next you would note that the median of the data is 2. This should make you suspect that something is wrong. You
would expect that the median is of random numbers between 0 and 10 to be somewhere around 5.
Lastly, you would note that the mode of the data is 9. By itself this is not strong data to suggest anything. Every
sample will have to have at least one mode. What should make you suspicious, however, is the fact that only two
other numbers were produced and were almost as frequent as the number 9. You would expect a greater variety of
numbers to be produced.
Concept Problem Revisited
In order to decide which measure of central tendency to use, it is a good idea to calculate and interpret all three of
the numbers.
For example, if someone asked you how many people can sit in the typical car, it would make more sense to use
mode than to use mean. With mode, you could find out that a five person car is the most frequent car driven and
determine that the answer to the question is 5. If you calculate the mean for the number of seats in all cars, you will
end up with a decimal like 5.4, which makes less sense in this context.
On the other hand, if you were finding the central heights of NBA players, using mean might make a lot more sense
than mode.
Vocabulary
Themeanis the arithmetic average of the data.
Themedianis the number in the middle of a data set. When the data has an odd number of counts, the median is