Outliers

Have you ever heard the idiom "out of the ball park."   This idiom is used when you find something out of range,  unreasonably, or inconsistent.   The phrase came from the idea that some baseballs are hit within the field area, but, some balls are hit out of the stadium ... beyond the normal expectations.

The following are examples of things that are "out of the ball park:"     Say you have $26 to buy something, but, you can only find the thing for $178.   That thing is "out of the ball park," it is out of your range for purchase.   Say you want to go to a New York restaurant for dinner.  Your are in California.   This might make going to diner in New York "out of the ball park," if you want to have dinner in the next hour. Say you have $150 to buy a plane ticket to your favorite vacation spot, but, you find all the tickets are about $500.  Your desire to buy the tickets at the cost of $150 is "out of the ball park," an unreasonable expectation. You have seen a Music CD, that you want, sold for $15, $14.25, $16.75, and $95.23.   The place you saw the CD for sale at $95.23 was selling the CD at a price that was "out of the ball park,"  it is not with the range of prices typical of the CD. Someone offers to buy you a car for about $7000.   You see cars you like for $5167, $7312, $6023 and a sports car at $85,000.   When you looked at the sports car (at $85,000), you were looking at a car that was "out of the ball park" for the purchase. In math, we have a special name for things that are well out of the normal,  or anticipated value for something.   We call something that is out of the ball park, an "OUTLIER."  When you look at a list of things, there can be more than one outlier.   Unfortunately, there is no accurate way to identify when something is out of the ball park.  Everyone has their own method.   Use  your gut feelings and see if you can identify things that are outliers.   The following sets of number give you a chance of recognizing outliers: 12, 61, 15, 17, 10 ................. 61 is the outlier. 0, 75, 82, 62, 69, 321 ....... 0 and 321 are the outliers. It is important to recognize outliers.   If we do not recognize outliers, information can be affected during statistical examination.   For example, in the following example the outliers would unreasonably skew the results. What is the student mean if the students earned the following grades on a quiz: 100, 100, 96, 96, 96, 100, 93, 93, 10, 27.   Answer: 81.     However, throwing out the outliers in the previous list, we have 100, 100, 96,96, 96,100,93,93 and an mean of about 97 (96.75).   A mean of 97 is far more representative of the result for the majority of the students.

Identify the outliers in the following sets of numbers:
1.   16, 20, 23, 19, 17, 25, 83	Answer Outlier is 83.
2.   40, 50, 30, 60, 3	Answer Outlier is 3.
3.   86, 23, 74, 79, 90, 76, 82, 10	Answer Outliers are 10 and 23.
4.   167000, 170000, 200500, 168000, 500000	Answer Outlier is 500000.