Exercise 3 Page 317

We are asked to create a dot plot and determine if the extreme value is an outlier. First, let's draw the dot plot.

Now, let's review what makes a data point x an outlier. Data is an outlier if one of two conditions are met.

1. If x is less than 1.5 times the interquartile range below the first quartile: x< Q_1 -1.5(IQR)
2. If x is greater than 1.5 times the interquartile range above the third quartile: x> Q_3+1.5(IQR)

   Now, we can enter the data into the L₁ list in our graphing calculator.

   
   

   Having entered everything into lists, we use 1-Var Stats feature to find the key information about the spread of the data. Note that you have to scroll down to get to the relevant information.

   
   
   We found that for the given data set, Q_1=81, Q_3=90, and the IQR (Q_3-Q_1) is 9. Let's substitute those values into the inequalities from above and see what values we get. Let's start with the first quartile.
   x

   SubstituteII

   Q_1= 81, IQR= 9

   x< 81-1.5( 9)

   Multiply

   Multiply

   x<81-13.5

   SubTerms

   Subtract terms

   x<67.5

   Now let's do the same process with the third quartile.

   x>Q_3+1.5(IQR)

   SubstituteII

   Q_3= 90, IQR= 9

   x> 90+1.5( 9)

   Multiply

   Multiply

   x>90+13.5

   AddTerms

   Add terms

   x>113.5

   Any data point that is greater than 113.5, or less than 67.5, is an outlier. None of the values in the given set are outliers because they all fall within the range of 113.5>x>67.5.