Download Section 2.3 Day 2

Section 2.3
Day 2
5-Number Summaries,
Outliers, and Boxplots
5-Number Summary
If you include the minimum and
maximum values of the data set
along with the median and quartiles,
you get the 5-number summary.
AKA 5-point summary
5-Number Summary
Find 5-number summary.
Find 5-number summary….don’t forget key!
3I2 represents 32 mph
Find 5-number summary….n=18
3I2 represents 32 mph
5-Number Summary
Graphical display of a 5-number summary is
a boxplot or box-and-whiskers plot
How do we construct a
boxplot?
1. Plot the 5 points
1. Plot the 5 points
2. Draw box from Q1 to Q3
1. Plot the 5 points
2. Draw box from Q1 to Q3
3. Draw vertical line at median
1. Plot the 5 points
2. Draw box from Q1 to Q3
3. Draw vertical line at median
4. Extend whiskers to min and
max values
1. Plot the 5 points
2. Draw box from Q1 to Q3
3. Draw vertical line at median
4. Extend whiskers to min and
max values
5. Label graph (context)
Outliers
What are outliers?
Outliers
Recall outliers in a set of data are any
values that differ significantly from
the other values.
For this data, are there any outliers?
Formula for Outliers
A value is an outlier if it lies more than
1.5 times the IQR from the nearest
quartile.
Formula for Outliers
A value is an outlier if it lies more than 1.5
times the IQR from the nearest quartile.
Thus, a value is an outlier if it is
< Q1 – 1.5(IQR)
or
> Q3 + 1.5(IQR)
For this data, are there any outliers?
IQR = Q3 – Q1 = 42 – 30 = 12
Lower end:Q1 – 1.5(IQR) = 30 – 1.5(12) = 12
Upper end:Q3 + 1.5(IQR) = 42 + 1.5(12) = 60
Modified Boxplot
Modified boxplot is like a basic boxplot
except the whiskers only go as far as the
largest and smallest nonoutliers
(sometimes called adjacent values).
Any outliers appear as individual dots or
other symbols.
Modified Boxplot
Modified boxplot is like a basic boxplot
except the whiskers only go as far as the
largest and smallest nonoutliers
(sometimes called adjacent values).
Any outliers appear as individual dots or
other symbols.
Boxplots
Useful when plotting a single quantitative
variable and
• you want to compare shapes, centers, and
spreads of two or more distributions
• you don’t need to see individual values,
even approximately
• you don’t need to see more than the
5-number summary but would like outliers
to be clearly indicated
Graphing Calculator
You can use graphing calculator to find
5-number summary and draw boxplot.
Use data from Display 2.46 on page 61
Graphing Calculator
You can use graphing calculator to find
5-number summary and draw boxplot.
Use data from Display 2.46 on page 61
Press “STAT”
Select 1:Edit
Enter the data elements in list
Note: no need to reorder data first
Graphing Calculator is Your Friend!
Your calculator will compute the summary
statistics for a set of data.
After entering data in list:
Press “STAT”
Arrow right to “CALC”
Select “1: 1-Var Stats”
1-Var Stats L1
Enter
1-Var Stats
Display 2.46 on page 61
1-Var Stats
Draw Boxplot
2nd
STAT PLOT
1: Plot 1 …on
Type: select modified boxplot symbol
Xlist: L1
Freq: 1
Mark:
Graph
Draw Boxplot
If you can not see the boxplot,
press “Zoom”
Select 9: ZoomStat
Standard Deviation
Differences from the mean, x – x, are called
deviations.
Standard Deviation
Differences from the mean, x – x, are called
deviations.
Mean is balance point of distribution so the
set of deviations from the mean will always
sum to zero.
∑(x – x ) = 0
Standard Deviation
Formula for standard deviation, s, is:
Standard Deviation
Formula for standard deviation, s, is:
Dividing by n - 1 gives a slightly larger value
than dividing by n. This is useful because
otherwise the standard deviation of the
sample would tend to be smaller than the
standard deviation of the population the
sample came from.
Computing Standard Deviation
Computing Standard Deviation
Use 1-Var Stats.
Symbol for standard deviation is sx
Summary from Frequency Table
Summary from Frequency Table
Page 68
Summary from Frequency Table
Enter “values” in List 1
Enter “frequency” in List 2
“STAT”, “CALC”, “1: 1-Var Stats”
1-Var Stats L1, L2
Enter
Important Note
When homework says to use the
formulas to compute something,
you may use your calculator
Questions?