the lengths, in feet, of various bridges are 88, 251,275,354,and 1,121. Name any outliers in the data set

Question

this is a homework question about measures of variation, and im very confused.

Answer 1

OK, Christa, I hope I can still help!

 

To find outliers, we use Q₁ - 1.5(IQR) and Q₃ + 1.5(IQR)

 

What the heck do those mean??  Q₁ is the mean of the first half of our data that lies below the overall mean, Q₃ is the mean of the second half of our data that lies above the overall mean, and IQR is the difference between the two.

 

You already have the data in numerical order.  The middle number, the mean, is 275.  

 

So, Q1 = (88 + 251)/2 = 169.5.

Q₃ = (354 + 1121)/2 = 737.5.

IQR = 737.5 - 169.5 = 568

 

Let's plug all those in.  169.5 - 1.5(568) = -682.5

737.5 + 1.5(568) = 1589.5

 

So, any numbers below -682.5 or above 1589.5 are outliers.  None of our numbers match, so there are no outliers.

 

Hope this helps!