Box Plots and Outliers Box Plot We need

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Box Plots and Outliers

Box Plots and Outliers

Box Plot We need 5 numbers, called the 5 number summary: 1. minimum value

Box Plot We need 5 numbers, called the 5 number summary: 1. minimum value 2. Q 1 3. median 4. Q 3 5. maximum value

Harry Potter Data The 5 number summary is: Minimum Q 1 Median Q 3

Harry Potter Data The 5 number summary is: Minimum Q 1 Median Q 3 Maximum 70. 9 78. 9 81. 35 84. 45 86. 2

Drawing the plot free hand • Use a scaled line to draw the box

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 =

Using the TI • Put the data into the list • Press y = ; make sure that there is nothing in the 10 equations

 • Press 2 nd key, y = • There are 3 statistical plots.

• Press 2 nd key, y = • There are 3 statistical plots. • Press #1

 • Turn the plot ON • Select the 2 nd box plot •

• Turn the plot ON • Select the 2 nd box plot • Make the x list L 1

 • Press Zoom • Press Enter on #9

• Press Zoom • Press Enter on #9

 • The Box plot will appear

• The Box plot will appear

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

• 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 Q 3 –

Inter-quartile Range • The inter-quartile range (IQR) is the value of Q 3 – Q 1

Outliers • An outlier is an unusual score, relative to the data set. It

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.

Mild Outliers Look for data values (x) that are either: 1. 2.

Extreme Outliers Look for values that are either: 1. 2.

Extreme Outliers Look for values that are either: 1. 2.

Harry Potter data - checking

Harry Potter data - checking

Example: Ages of actresses at the time they first won the Oscar 50 44

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 Q 1 =

5 number summary for actresses • • • Min = 21 Q 1 = 30 Med = 34 Q 3 = 41 Max = 80

Actresses • Check for outliers. Identify type.

Actresses • Check for outliers. Identify type.

Box plot with outliers • When we select the 1 st box plot on

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

 • Zoom #9 results in:

• Zoom #9 results in:

 • Trace and go to the right twice. • The 50 is the

• Trace and go to the right twice. • The 50 is the last data value that is not an outlier.

Comparison of Boxplots and histograms

Comparison of Boxplots and histograms