1. Statistics Section 1.2

2.   Dotplots are among the simplest graphs to construct and interpret. Dotplots

3.  Remember your SOCS  Shape : The dotplot is slightly skewed right (with the “tail” to the right of the peak)  Outlier: There are no apparent outliers. (We’ll learn more formal ways of determining their presence soon)  Center: The center of the plot (containing 39 values) is the 20 th value, or Median, which is 6. If the shape is Symmetric, the mean is another appropriate measure of center.  Spread: The range of the data is 14 with most values in the lower end. The interquartile range is 5 (from 4-9) which shows fairly low variability.

4.   Following is a stemplot of how many pairs of shoes owned by a random sample of 20 males.  Some tips for making stemplots:  Stemplots do not do well for large data sets  There is no magic number of stems, but 5 is a good base.  If the number of leaves is too large, you may split stems – but if you do so, you must split ALL stems  Sometimes rounding large numbers will make your stemplot easier to interpret.  All leaves are only one digit. Stemplots 04555677778 10000124 22 358 Key: 0|4represents amale with 4pairs of shoes

5.  Check your understanding… 68 7 88 979 1008 1115566 12012223444457888999 1301233333444899 1402666 1523 168 Here is a stemplot of the percents of residents aged 65 and older in 50 states and the District of Columbia. Key: 6|8 represents 6.8% 1.The low outlier is Alaska. What percent of Alaska residents are 65 or older? 2.Ignoring the outlier, what is the shape of the distribution? 3.The center of the distribution is close to…

6.   Perhaps the most common display of Quantitative data is a Histogram.  Let’s create a histogram using data on foreign born residents of the United States. Histograms State% % % % Alabama2.8Indiana4.2Nebraska5.6Rhode Island12.6 Alaska7.0Iowa3.8Nevada19.1South Carolina4.1 Arizona15.1Kansas6.3New Hampshire5.4South Dakota2.2 Arkansas3.8Kentucky2.7New Jersey20.1Tennessee3.9 California27.2Louisiana2.9New Mexico10.1Texas15.9 Colorado10.3Maine3.2New York21.6Utah8.3 Connecticut12.9Maryland12.2North Carolina6.9Vermont3.9 Delaware8.1Massachusetts14.1North Dakota2.1Virginia10.1 Florida18.9Michigan5.9Ohio3.6Washington12.4 Georgia9.2Minnesota6.6Oklahoma4.9West Virginia1.2 Hawaii16.3Mississippi1.8Oregon9.7Wisconsin4.4 Idaho5.6Missouri3.3Pennsylvania5.1Wyoming1.2 Illinois5.6Montana1.9

7.  1. Divide the data into classes of equal width. Aim for around 6 classes. a.In this case, the data ranges from 1.2 to 27.2, so counting by 5s seems appropriate. b.We also need to decide what to do if a data point is exactly on the “border.” In this case we’ll go 0-4.99, 5-9.99, etc. 2.Find the count (frequency) or percent (relative frequency) of individuals in each class. 3. Label your axes and draw the Histogram. a.The horizontal axis should be the variable studied, while the vertical axis should indicate counts or percents. Steps to Make a Histogram

8.  Describing the Histogram: SOCS Shape: The distribution is skewed right and unimodal. Most states have fewer than 10% of foreign-born residents, but several states have much higher percents. Center: From the graph, we see the midpoint would fall in the 5-9.9% class. Spread: The percent of foreign born residents in the states varies from less than 5% to more than 25% Outliers: There are no obvious outliers.

9.   Your calculator will make a histogram for you  Look at page 36-37 (21) for step by step instructions.  When making a graph for a test, be sure to transfer the graph from your calculator to the actual test.  Also LABEL and SCALE your axes!! On the Calculator…

10.   Don’t confuse Histograms and Bar Graphs.  Basics: Histogram bars touch – Bar Graphs don’t  Histograms display quantitative variables – Bar graphs display categorical variables.  Use percents instead of counts on the vertical axis when comparing distributions with different numbers of observations.  Comparing reading levels by comparing the first 400 words of a book and the first 100 words of an article would need to be displayed by percents for an accurate comparison.  Just because a graph looks nice doesn’t mean it’s a meaningful display of data. Using Histograms Wisely