1.2 Displaying Quantitative Data with Graphs

 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

Dotplot with number of siblings

 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

 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

 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

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

Symmetric, Right Skewed, and Left Skewed

Symmetric, Right-Skewed, or Left- Skewed

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

 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

Household size

 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

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

How many pairs of shoes does a typical teenager have?

 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

 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

Foreign Born Residents

Foreign Born Residence

Foreign Born Residents

Histograms on the Calculator

Histograms on Calculator

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

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