1. 1.2 Displaying Quantitative Data with Graphs

2.  Each data value is shown as a dot above its location on the number line 1.Draw a horizontal axis (a number line) and label it with the variable name 2.Scale the axis- start by looking at the minimum and maximum values of the variable 3.Mark a dot above the location on the horizontal axis corresponding to each data value Dotplot

4. Dotplot with number of siblings

5.  Look at overall pattern and departure  Describe overall pattern by its shape, center, and spread  Important kind of departure is an outlier, an individual value that falls outside the overall pattern How to examine the distribution of a quantitative variable

6.  Concentrate on main features:  Major peaks, not minor ups and downs  Clusters of values and obvious gaps  Potential outliers not just the smallest and largest observations  Look for rough symmetry or clear skewness. Describing Shape

7.  A distribution is roughly SYMMETRIC if the right and left sides if the graph are approximate mirror images of one another.  A distribution is RIGHT SKEWED/SKEWED TO THE RIGHT if the right side of the graph (containing the half of the observations with larger values is much longer than the left side  A distribution is LEFT SKEWED/SKEWED TO THE LEFT if the left side of the graph is much longer than the right side Symmetric, Right Skewed, and Left Skewed

8.  The direction of skewness is the direction of the long tail not the direction where most observations are clustered. Skewness

9. Symmetric, Right Skewed, and Left Skewed

10. Symmetric, Right-Skewed, or Left- Skewed

11.  Unimodal- there is a single peak; one mode  Bimodal- there are two peaks; two modes  Multimodal- more than two peaks Mode

12.  Describe the shape of the distribution-most common value/ where a cluster of values takes place  Describe the center of the distribution-midpoint  Describe the spread (range of values)  Identify any potential outliers-items that clearly stand out. Brothers and Sisters

13. Household size

14.  Separate each observation into a stem consisting of all but the final digit and a leaf, the final digit.  Write the stems in a vertical line at the right of the column  Do not skip stems!  Write each leaf in the row to the right of the stem  Arrange the leaves in increasing order  Provide a key that explains context of what the stem and leaves mean Stem plot /Stem and Leaf Plot

15.  Splitting stems  Back to back stems Stem Plot/ Stem and Leaf Plot

16. How many pairs of shoes does a typical teenager have?

17.  Divide data into classes of equal width  Make sure you specify classes so that each individual falls into exactly one class  Find the count (frequency) or percent (relative frequency) of individuals in each class  Label and scale your axes and draw the histogram  Horizontal axis- variable whose distributor you are displaying  Vertical axis-contains the scale of counts or percents Histograms

18.  Make sure you choose classes that are all the same width  Each bar represents a class with no horizontal space between the classes unless a class is empty.  No right choice of the classes in a histogram. Five classes is a good minimum Histograms

19. Foreign Born Residents

20. Foreign Born Residence

21. Foreign Born Residents

22. Histograms on the Calculator

23. Histograms on Calculator

25. Don’t confuse histograms and bar graphs Histograms  Distribution of quantitative variable  The horizontal axis is marked in units  No space between bars Bar Graphs  Display the distribution of a categorical variable.  The horizontal axis identifies categories or quantities  Blank spaces between bars

26.  Doesn’t make it a meaningful display of data. Just because a graph looks nice…