Get out your notes we previously took on Box and Whisker Plots.

How to make a Box and Whisker Plot

Our first step is to put them in order from least to greatest. Here we have 17 numbers: 10, 8, 2, 15, 9, 10, 7, 2, 6, 6, 5, 12, 13, 7, 7 ,7, 12 Our first step is to put them in order from least to greatest.

Here they are in order! 2, 2, 5, 6, 6, 7, 7, 7, 7, 8, 9, 10, 10, 12, 12, 13, 15 Putting the numbers in order makes it easier to do every other part!

2, 2, 5, 6, 6, 7, 7, 7, 7, 8, 9, 10, 10, 12, 12, 13, 15 First we need to find the median. Remember the median is the MIDDLE of our data set. Median: 7

2, 2, 5, 6, 6, 7, 7, 7, 7, 8, 9, 10, 10, 12, 12, 13, 15 Notice that the median splits the data into two “halves.” Now we just need to find the ‘median’ of each of these two halves. We do NOT include the actual median when doing this.

2, 2, 5, 6, 6, 7, 7, 7, 7, 8, 9, 10, 10, 12, 12, 13, 15 We need to find the ‘median’ of the half of the data set that is made up of numbers less than the median. Not including the actual median! This number is actually called the lower quartile (or the first quartile). Lower quartile: 6

2, 2, 5, 6, 6, 7, 7, 7, 7, 8, 9, 10, 10, 12, 12, 13, 15 Now we need to find the ‘median’ of the half of the data set that is made up of numbers greater than the median. Still not including the actual median. This number is actually called the upper quartile (or the third quartile). Upper quartile: 11

2, 2, 5, 6, 6, 7, 7, 7, 7, 8, 9, 10, 10, 12, 12, 13, 15 The last two numbers are the easiest to get. One is called the lower extreme (or the minimum). It is the lowest number in the data set. Lower extreme: 2 One is called the upper extreme (or the maximum). It is the largest number in the data set. Upper extreme: 15

2, 2, 5, 6, 6, 7, 7, 7, 7, 8, 9, 10, 10, 12, 12, 13, 15 We have now found the 5 numbers we need to create a Box and Whisker Plot All together, these numbers are called the Five Number Summary.

Five Number Summary: Lower extreme (min): 2 Lower quartile (Q1): 6 Median: 7 Upper quartile (Q3): 11 Upper extreme (max): 15

Creating the Box and Whisker Plot Above a number line, put a line for each number in our five number summary. Connect the upper and lower quartiles, making a box. This is the “box” part of the plot. From the box draw a line to the upper and lower extremes. This is the “whisker” part of the plot.

The finished product: Normally box and whisker plots are horizontal but they can occasionally be seen this way also.

Steps to create a Box and Whisker Plot Order the data from least to greatest Find each number in the five number summary Plot the five number summary on a number line Draw the box around the upper and lower quartiles Extend the whiskers from the box to the extremes

Finding Outliers

Outliers: An outlier is an observation that lies outside the overall pattern of a distribution. Usually, the presence of an outlier indicates some sort of problem. This means we need to know how to find them!!!

Definition of an outlier An outlier is a point which falls more than 1.5 times the interquartile range above the third quartile or below the first quartile. So in order to find out if there are outliers we first need to know what the interquartile range is an how to find it.

Interquartile Range (IQR) What is the interquartile range? When looking at data sets, the range is the difference between the maximum and the minimum. So the interquartile range is the difference between the upper and lower quartiles. Using our data set from earlier, the interquartile range is 11 - 6 = 5

Finding outliers: An outlier is a point that is 1.5 times the IQR away from the upper or lower quartile. 1.5 times our IQR from earlier is 1.5(5) = 7.5 So outliers in our data set are 7.5 away from either 6 or 11 To find this just take 6 - 7.5 = -1.5 or 7.5 + 11 = 18.5 Since no data points are less than -1.5 or greater than 18.5 we have no outliers in this particular data set What would some outliers to our data set be?