Using
the Mean and Median
Purpose
Both
the mean and the median are commonly used to describe what would be a “typical”
value in a set of data.This exercise
is to help you determine the kinds of data sets for which the values of
these statistics really reflect a “typical” data value.
Scenario
You are interviewing for a position at R.E. Enterprises, Inc., a company
founded by a former Statistics professor who has left academia for the
big bucks in private industry. Of key interest to you is the annual
salary earned by a typical employee of this company. While you were
waiting for R.E. to show up for the interview, you couldn’t help but notice
a paper on the CEO’s desk listing the salaries of all 5 employees of the
Production Division of the company, along with the salaries of all 5 employees
of the Corporate Division.
1. The
5 salaries of the Production Division are as shown below (in thousands). Make
a dot plot of the data. Then
compute the mean and median and decide whether these statistics reflect
the “typical” salary for this division. 36
38 40
42 44
dot plot:______________________________
mean = ________ typical?
_______
median = _______ typical?
________ 2. The
salaries for the Corporate Division are: 20 20 24 26 210 Repeat
the above for these data.
dot plot: ______________________________
mean = ________ typical?
________
median = ________ typical?
_________ 3. Which
Division has a higher mean salary? ___________ Which
has a higher median salary? ____________
If you can apply for a position in only one division, which would you choose?
____________ 4. A
statistic is said to be “resistant” to outliers ifits
value is not affected too much by a small percentage ofextreme
values in the data set. Which
statistic do you think is considered to be resistant – the mean or the
median?