Box Plots and Outliers

Box Plots and Outliers

Box Plot

We need 5 numbers, called the 5 number summary:

1. minimum value

2. Q1

3. median

4. Q3

5. maximum value

Harry Potter Data

The 5 number summary is:

Minimum 70.9

Q1 78.9

Median 81.35

Q3 84.45

Maximum 86.2

Drawing the plot free hand

• Use a scaled line to draw the box plot• Approximate locations of the values.

• We say this is SKEWED LEFT since the longer tail is on the left side.

Using the TI

• Put the data into the list

• Press y = ; make sure that there is nothing in the 10 equations

• Press 2nd key, y =

• There are 3 statistical plots.

• Press #1

• Turn the plot ON

• Select the 2nd box plot

• Make the x list L1

• Press Zoom

• Press Enter on #9

• The Box plot will appear

• Press TRACE to see values; use right or left arrow keys to move around.

Inter-quartile Range

• The inter-quartile range (IQR) is the value of Q3 – Q1

Outliers

• An outlier is an unusual score, relative to the data set. It will influence the mean and the standard deviation.

• A data set might have no outliers, one outlier, or several outliers.

• Two types: Mild and Extreme

Mild Outliers

Look for data values (x) that are either:

1.

2.

Q1 - 3 IQR x <Q1-1.5 IQR

Q3 + 1.5 IQR < x Q3 + 3 IQR

Extreme Outliers

Look for values that are either:

1.

2.

x < Q1 - 3 IQR

x > Q3 + 3 IQR

Harry Potter data - checking

Example: Ages of actresses at the time they first won the Oscar

50 44 35 80 26 28 41

21 61 38 49 33 74 30

33 41 31 35 41 42 37

26 34 34 35 26 61 60

34 24 30 37 31 27 39

34 26 25 33

5 number summary for actresses

• Min = 21

• Q1 = 30

• Med = 34

• Q3 = 41

• Max = 80

Actresses

• Check for outliers. Identify type.

Box plot with outliers

• When we select the 1st box plot on the TI, it allows us to see outliers. Select the mark that is visible for you.

• Zoom #9 results in:

• Trace and go to the right twice.

• The 50 is the last data value that is not an outlier.

Comparison of Boxplots and histograms