This document discusses exploratory data analysis techniques including boxplots and five-number summaries. It explains how to organize and graph data using histograms, frequency polygons, stem-and-leaf plots, and box-and-whisker plots. The five important values used in a boxplot are the minimum, first quartile, median, third quartile, and maximum. An example constructs a boxplot for a stockbroker's daily client numbers over 11 days.

2.  To use the techniques of exploratory data
analysis, including boxplots and five-number
summaries, to discover various aspects of
data.

3.  Organizes data using frequency distribution
 Graphic Representation: Histogram,
Frequency Polygon, Ogives
 Purpose: confirm various conjectures about
the nature of the data.

4.  Organizes data using stem and leaf plot
 Measure of central tendency used: median
 Measure of variation: IQR (Q3 – Q1)
 Graphic Representation: Box-and-Whisker
Plot
 Purpose: To examine data to find out what
information can be discovered about the data
such as the center and the spread.

5.  Five important values used:
1. MinimumValue
2. Q1
3. Median
4. Q3
5. MaximumValue

6.  A boxplot is a graph of a data set obtained by
1. Drawing a horizontal line from the minimum
value to Q1
2. Drawing a horizontal line from Q3 to the
maximum value
3. Drawing a box whose vertical sides pass through
Q1 and Q3 with a vertical line inside the box
passing through Q2(the median)

7.  A stockbroker recorded the number of clients she saw
each day over an 11-day period. The data are shown.
Construct a boxplot for the data.
 33, 38, 43, 30, 29, 40, 51, 27, 42, 23, 31
1. Order: 23, 27, 29, 30, 31, 33, 38, 40, 42, 43, 51
2. Find median, Q1 and Q3:
▪ 33, 29, 42
3. Draw scale for data on x-axis
4. Locate the 5 numbers
5. Draw a box around Q1 and Q3, draw vertical line through the
median, connect maximum and minimum values

8.  If median is near center, distribution is appx
symmetric.
 If median falls left of center, distribution is
positively skewed.
 If median falls right of center, distribution is
negatively skewed.

9.  If lines are appx same length, distribution is
appx symmetric.
 If right line is larger than the left, distribution
is positively skewed.
 If left line is larger than the right, distribution
is negatively skewed.

10.  A resistant statistic is one that is not affected by
an extremely skewed distribution.
 Examples: summary stats (median and IQR)
 A nonresistant statistic is one that is affected by
an extremely skewed distribution.
 Examples: mean, standard deviation
 When distribution is skewed or contains outliers,
median & IQR more accurately summarize the
data.

11.  p. 157-158 #1, 5, 7-10, 13, 15