Graphing Quantitative Data: Techniques and Visualization Strategies

Graphing Quantitative Data CHAPTER 3

3 Graphs for Quantitative Data Advantage Type of Graph Dot Plot Retains individual data Histogram Displays shape Box Plot Displays center & spread

Shape Symmetric Right Skewed Uniform Left Skewed

Other Attributes for Shape Outliers (Unusual data compared with the other data) Modes (# of Humps) Unimodal (One hump) Bimodal (Two humps) Multimodal (Many humps)

Center Depends on Shape If Skewed: If Symmetric: Use mean (average) Use median ? =?1+ ?2+ This value will have half the data values below it and half above it ? This value is pulled in the direction of outliers *We let the calculator calculate this!

Spread Depends on Shape If Skewed: If Symmetric: Use Standard Deviation (SD) Use Interquartile Range (IQR) ??? = ?3 ?1 ?1 ?2+(?2 ?)2+ ? 1 ? = *The calculator can calculate the 5 # Summary but you should memorize the IQR formula! *We let the calculator calculate this!

Kentucky Derby Winning Times Dot Plot o Retains Individual o Lable Both Axes o Scale on Both Axes o Title o Shows Shape o Shows Modes o Shows Outliers

Earthquake Magnitudes Histogram o Stores Data in Bins o Lable Both Axes o Scale on Both Axes o Title o Shows Shape o Shows Modes o Shows Outliers

Earthquake Magnitudes Max Right Fence Box Plot o Lable Axis Q3 Center = Median Q1 o Scale on Axis o Title o Shows Center o Shows Spread Left Fence Min

Big Picture Earthquake Magnitude Always graph both using same scale to get big picture of shape, center, and spread

L1 # of Pets for each student Enter Quantitative Data 0 0 1 1 1 1 2 2 2 2 2 3 3 4 5 STAT EDIT Highlight L1 CLEAR ENTER Enter data values

? = 1.933333333 ??= 1.387014608 To Calculate Statistics STAT 5# Summary ???? = 0 ?1 = 1 ??? = 2 ?3 =3 ???? = 5 CALC 1-VAR STAT Depending on your calculator ENTER OR List: L1 FreqList: blank Calculate

# of Pets 6 To Graph Histogram 5 STAT PLOT 4 PLOT 1 # of Students ENTER on ON 3 Type: Choose Histogram Xlist: L1 2 FreqList: 1 1 WINDOW Xmin=0 Ymin=0 0 Xmax=6 Ymax=6 0 1 2 3 4 5 Xscl=1 Yscl=1 # of Pets GRAPH *You can TRACE the values

# of Pets To Graph Box Plot 6 5 STAT PLOT MaxX=5 PLOT 1 4 ENTER on ON Type: Choose Box Plot # of Pets 3 Xlist: L1 Q3=3 FreqList: 1 WINDOW 2 Med=2 Xmin=0 Ymin=0 Xmax=6 Ymax=6 1 Q1=1 Xscl=1 Yscl=1 GRAPH 0 MinX=0 *You can TRACE the values

# of Pets for each student Enter Quantitative Data 0 0 1 1 1 1 2 2 2 2 2 3 3 4 5 STAT It is easier to enter this data as a frequency table instead because of the repeating data values EDIT Highlight L1 CLEAR L1 # of Pets 0 1 2 3 4 5 L2 Frequency 2 4 5 2 1 1 ENTER Highlight L2 CLEAR ENTER Enter data values

? = 1.933333333 ??= 1.387014608 To Calculate Statistics STAT 5# Summary ???? = 0 ?1 = 1 ??? = 2 ?3 =3 ???? = 5 CALC 1-VAR STAT Depending on your calculator L1, L2 ENTER OR List: L1 FreqList: L2 Calculate

# of Pets 6 To Graph Histogram 5 STAT PLOT 4 PLOT 1 # of Students ENTER on ON 3 Type: Choose Histogram Xlist: L1 2 FreqList: L2 1 WINDOW Xmin=0 Ymin=0 0 Xmax=6 Ymax=6 0 1 2 3 4 5 Xscl=1 Yscl=1 # of Pets GRAPH

# of Pets To Graph Box Plot 6 5 STAT PLOT MaxX=5 PLOT 1 4 ENTER on ON Type: Choose Box Plot # of Pets 3 Xlist: L1 Q3=3 FreqList: L2 WINDOW 2 Med=2 Xmin=0 Ymin=0 Xmax=6 Ymax=6 1 Q1=1 Xscl=1 Yscl=1 GRAPH 0 MinX=0

New Example In 2018-2019 season, there were nine defensive players on the Orlando Solar Bears hockey team. The number of total minutes each player had spent in the penalty box during the season were 4, 6, 6, 10, 10, 12, 22, 41, and 122. (Yes, Mike Monfredo really had 122 penalty minutes so far in that season!) Calculate the statistics and graph both a histogram and box plot.

Solution In 2018-2019 season, there were nine defensive players on the Orlando Solar Bears hockey team. The number of total minutes each player had spent in the penalty box during the season were 4, 6, 6, 10, 10, 12, 22, 41, and 122. (Yes, Mike Monfredo really had 122 penalty minutes so far in that season!) ? = 25.9 ??= 37.8 4, 6, 10, 31.5, 122 Penalty Min 5 0 10 30 50 70 90 110 130 Calculate the statistics and graph both a histogram and box plot.

Solution In 2018-2019 season, there were nine defensive players on the Orlando Solar Bears hockey team. The number of total minutes each player had spent in the penalty box during the season were 4, 6, 6, 10, 10, 12, 22, 41, and 122. (Yes, Mike Monfredo really had 122 penalty minutes so far in that season!) ? = 25.9 ??= 37.8 4, 6, 10, 31.5, 122 Penalty Min 5 0 Calculate the statistics and graph both a histogram and box plot. 10 30 50 70 90 110 130 Now describe the shape, center, and spread

Solution In 2018-2019 season, there were nine defensive players on the Orlando Solar Bears hockey team. The number of total minutes each player had spent in the penalty box during the season were 4, 6, 6, 10, 10, 12, 22, 41, and 122. (Yes, Mike Monfredo really had 122 penalty minutes so far in that season!) ? = 25.9 ??= 37.8 4, 6, 10, 31.5, 122 Penalty Min 5 0 Calculate the statistics and graph both a histogram and box plot. Describe the shape, center, and spread 10 30 50 70 90 110 130 Shape: Right Skewed, Unimodal One outlier at 122 Center = Median = 10 Spread = IQR = Q3 Q1 = 31.5 - 6 = 25.5

How do we know about outliers? We need to calculate the left fence and the right fence. Left fence = ?1 1.5 ??? Left fence = 6 1.5(25.5) = -32.25 Do we have any data values smaller than -32.25? Nope! So no outliers on left side! Right fence = ?3 + 1.5 ??? Left fence = 31.5 + 1.5(25.5) = 69.75 Do we have any data values larger than 69.75? Yep! So 122 is an outlier on the right side! *Notice the Box Plot on the previous slide, the tail goes to 41 which is the last data value that is not an outlier. * You should memorize the left and right fence formulas!

Homework Complete Quiz Chapter 1-2 Complete HW Chapter 3 Read Cinderella PP