1. 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 ).

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

3. 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.

4. 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.

5. 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.

6. 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 310 420 45 40 220 240 180 90 270 180 250 290 130 260 340 310

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