16+Creating+box+and+whisker+plots+and+finding+outliers


 * Box and Whisker Plots**

Hello, today I will be walking you through how to do a box and whisker plot problem. Okay, well first you want to read the problem thoroughly and gather all of your numerical data. Next you must take your numerical data and put it in order from least to greatest. Then you must find the median of your data. If you have an even amount of numbers then you will have to average the two numbers in the middle. You can do this by adding the two numbers and dividing by two. If the data set is odd then you will be fine because you will not have to average the number in the middle. Once you have your median you can put it next to Q2. Q2 represents the median of the entire data set in the 5# summary. Your 5# summary should be labeled from top to bottom: Min, Q1, Q2, Q3, and Max. So, now that you have your median, next you will have to find Q1 and Q3. To find these you must divide your entire data set right down the middle creating two separate data sets. You should put a line down the middle, it will make it easier for you. These two separate data sets should have an even amount of numbers in it. After this you must find the median of the two data sets. The median of the first data set (data set left of the line) is Q1. The median of the second data set (data set right of the line) is Q3. Next you must find your min and max, don’t worry this simple. Just look at your entire data set and find the lowest number, which will be your minimum and find your largest number, which will be your maximum. After this is done you must find your inter quartile range or IQR. You do this by: Q3-Q1. After you’ve found your IQR you must find your lower fence and higher fence. You can find these fences by the following formulas. Lower fence: Q1-(1.5xIQR)/Higher fence: Q3+(1.5xIQR). These fences will indicate whether or not there are outliers. Before you can indicate whether or not there are outliers you must create your box and whisker plot. Create a scale that you think will be accurate. A good way of doing this is by looking at your max and min. If your min is 0 and your max is 15, it would be a good idea to scale by 2.5. Then you graph the min, the Q1, Q2, Q3, and Max. After this you must use the numbers you got from your fence formulas. Put the fence numbers into the graph. If there are any numbers that are lower than the lower fence then it is an outlier. If there are any numbers that are higher than the higher fence then it is an outlier. That’s all there is to doing box and whisker plot problems folks. Have a good summer FST.


 * Rules and other important information you must know before you begin constructing a Box with Whiskers on it :)**

median (2nd quartile) = 80
 * Write the data in numerical order. Find the first quartile, the median, the third quartile, the minimum (smallest value) and the maximum (largest value). These are referred to as a five statistical summary.

first quartile = 70

third quartile = 90

minimum = 65

maximum = 100 || || http://www.regentsprep.org/regents/math/algebra/AD3/boxwhisk.htm
 * Place a circle beneath each of these values in relation to their location on an equally spaced number line. || [[image:http://www.regentsprep.org/regents/math/algebra/AD3/quartiles2.gif width="239" height="108" align="center"]] ||
 * Draw a box with ends through the points for the first and third quartiles. Then draw a vertical line through the box at the median point. Now, draw the whiskers (or lines) from each end of the box to these minimum and maximum values. || [[image:http://www.regentsprep.org/regents/math/algebra/AD3/quartiles3.gif width="272" height="107" align="center"]] ||


 * BUT WHAT ABOUT OUTLIERS!?!?!?!?!?!?!?**

**Find the outliers, if any, for the following data set:** **10.2, 14.1, 14.4. 14.4, 14.4, 14.5, 14.5, 14.6, 14.7, 14.7, 14.7, 14.9, 15.1, 15.9, 16.4**

To find out if there are any outliers, I first have to find the IQR. T hen Q 2  = 14.6. There are seven data points on either side of the median, so Q 1  is the fourth value in the list and Q  3  is the twelfth: Q  1  = 14.4 and Q  3  = 14.9. Then IQR = 14.9 – 14.4 = 0.5. Outliers will be any points below Q 1  – 1.5×IQR = 14.4 – 0.75 = 13.65 or above Q  3 + 1.5×IQR = 14.9 + 0.75 = 15.65.


 * Now that you have an understanding of Box and Whisker Plots, try these related problems.**

1. Draw a box–and–whisker plot for the given set of temperatures. 2. Find any outliers for the given set of temperatures. Answer: There are no outliers in this data set. 3. Find the median, upper quartile, lower quartile, and interquartile range for the given set of temperatures.

http://www.purplemath.com/modules/boxwhisk3.htm
 * Visit the following websites for more help on Box and Whisker Plots:**

http://ellerbruch.nmu.edu/cs255/jnord/boxplot.html

http://www.purplemath.com/modules/boxwhisk.htm www.ihateRaj.com