Three primary statistics are used to describe a variable’scentral tendency, defined as the average behavior of the variable.You can use these statistics, known as the mean, the median, andthe mode, to draw meaningful conclusions about a variable’s pastbehavior and to predict its future behavior.

An investor is considering a stock with the following returnsover the past 12 years:

Year	Annual Return
1	8%
2	12
3	14
4	8
5	6
6	6
7	9
8	5
9	5
10	4
11	6
12	7

Mean

The mean, also known as the arithmetic mean, tells the_________ value a variable is expected to take. The mean adds up allthe observations and divides by the number of observations, asshown in the following formula:

? or x? ? or x?

= =

?i = 1nxin?i = 1nxin

The mean (or average) return for this stock over the past 12years is _________.

For notational purposes, x??x¯ represents a ________ mean, while µ represents a ___________ mean.However, they are calculated the same way.

Median

The median indicates the ___________ observationin a data set. The median tells us that half the data set liesabove the median and the other half lies below it.

If you list all your observations in numerical order, the medianwould be the middle observation. For data sets with an odd numberof observations, identifying the median is easy. However, for datasets with an even number of items, there is no “middle.” In thatcase, you average the two middle observations to find themedian.

Now, present the stock return data in ascending order: 4%, 5%,5%, 6%, 6%, 6%, 7%, 8%, 8%, 9%, 12%, 14%

This data set has 12 observations, so average observations 6 and__________ to find the median, which is _________

When the median and mean are similar, you can conclude that thedata is relatively symmetrical. Depending on the distribution'sshape, the data may be normally or uniformly distributed. However,if the median is significantly less than or greater than the mean,that suggests that several extremely high or low observations,called __________ must be affecting the results, andthat the distribution is skewed.

Are there any outliers in this sample of data?________

Mode

The mode indicates the _______ observation. In thestock return data, the mode is ______ because itoccurs 3 times.

The mode does not necessarily indicate the center of a data set,but if the data is roughly symmetrical, the mode will be close tothe mean and median.

Check Your Understanding

Your college football team has 15 linebackers listed on theroster. The weights of these 15 players, in pounds, are shownbelow:

238	219	233
203	208	236
248	227	220
208	227	225
227	215	241

What is the weight of the average linebacker?

The ________ is ________ pounds.

What weight is most common amongst the linebackers?

The ________ is ________ pounds.

What is the average weight of the linebackers?

The _________ is _________ pounds.