3-5: Exploratory Data Analysis  Exploratory Data Analysis (EDA) data can be organized using a stem and leaf (as opposed to a frequency distribution)  The measure of central tendency used is the median.  The measure of variation used is the interquartile range (IQR = Q 3 -Q 1 ).  Data is represented graphically in a boxplot (also known as Box and Whisker Plot).  Use resistant statistics – statistics relatively less affected by outliers  Boxplot – a graph of a data set obtained by drawing :  a horizontal line from the minimum data value to Q 1  a horizontal line from Q 3 to the maximum data value  a box whose vertical sides pass through Q 1 and Q 3,  a vertical line inside the box passing through the median (Q 2 ).

 Five Number Summary – the five specific values used to construct a boxplot.  Minimum, the lowest value in a data set  Q 1  The median  Q 3  Maximum, the highest value in a data set Section 3-5

Determining the Five Number Summary Section 3-5  A stockbroker recorded the number of clients she saw each day over an 11-day period. 33, 38, 43, 30, 29, 40, 51, 27, 42, 23, 31  Arrange the data in order  Find the median  Find Q 1.  Find Q 3.

Creating a Boxplot Section 3-5  Draw an appropriate scale on a number line that contains values that span your five number summary  Plot your five number summary above the number line.  Draw a horizontal line from your minimum to Q 1.  Draw a horizontal line from Q 3 to your maximum.  Draw a box from Q 1 to Q 3.  Draw a vertical line through your median.

How To Read a Boxplot Section 3-5  The median  If the median is near the center of the box, the distribution is symmetric.  If the median is to the left of the center of the box, the distribution is positively skewed.  If the median is to the right of the center of the box, the distribution is negatively skewed.  The lines (or “whiskers”)  If the lines are about the same length, the distribution is symmetric.  If the right line is larger, the distribution is positively skewed.  If the left line is larger, the distribution is negatively skewed.

Boxplot of Two Data Sets Section 3-5  A dietician is interested in comparing the sodium content of real cheese with the sodium content of a cheese substitute. The data for the two random samples are shown. Compare the distributions using boxplots. Real CheeseCheese Substitute

Homework  Pg 157: 1-3, 7-10, 12 Section 3-5