1. Chapter 1: Exploring Data Sec. 1.2: Displaying Quantitative Data with Graphs, cont.

2. Histograms Histogram - a graph of the distribution of one quantitative variable where nearby values are grouped together. How to make a histogram: 1) Divide the range of data into classes of equal width. 2) Find the count (frequency) or percent (relative frequency) of individuals in each class. 3) Label and scale your axes and draw the histogram. The height of the bar equals its frequency. Adjacent bars should touch, unless a class contains no individuals. How to make a histogram: 1) Divide the range of data into classes of equal width. 2) Find the count (frequency) or percent (relative frequency) of individuals in each class. 3) Label and scale your axes and draw the histogram. The height of the bar equals its frequency. Adjacent bars should touch, unless a class contains no individuals.

3. Example, p. 33 - 34 This table presents data on the percent of residents from each state who were born outside of the U.S. Start by deciding on a width for each class: Identify the smallest and largest values. Think of a range that contains both. 0 - 30 Pick a number that divides the range evenly. 5

4. Example, p. 33 - 34 This table presents data on the percent of residents from each state who were born outside of the U.S. Next, make a frequency table: Frequency Table ClassCount Total 0 to < 5 5 to < 10 10 to < 15 15 to < 20 20 to < 25 25 to < 30 20 13 9 5 2 1 50

5. Example, p. 33 - 34 Next, make a histogram: Frequency Table ClassCount Total 0 to < 5 5 to < 10 10 to < 15 15 to < 20 20 to < 25 25 to < 30 20 13 9 5 2 1 50 Percent of foreign-born residents Number of States 0 5 10 15 20 25 30 20 18 16 14 12 10 8 6 4 2 0

6. Count vs. Percent

7. Describing Histograms S hape – skewed right and unimodal. O utliers – No obvious observations outside the overall pattern. C enter – Would fall somewhere between 5 to 9.9%. S pread – Varies from less than 5% to over 25%. (Could also go back to original data: 1.2% to 27.2%) Example on p. 35 ***Same example as before, but they’ve changed the class width to be 2.5.***

8. Using Histograms Wisely Here are several cautions based on common mistakes students make when using histograms. Cautions! 1) Don’t confuse histograms and bar graphs. 2) Don’t use counts (in a frequency table) or percents (in a relative frequency table) as data. 3) Use percents instead of counts on the vertical axis when comparing distributions with different numbers of observations. 4) Just because a graph looks nice, it’s not necessarily a meaningful display of data. Cautions! 1) Don’t confuse histograms and bar graphs. 2) Don’t use counts (in a frequency table) or percents (in a relative frequency table) as data. 3) Use percents instead of counts on the vertical axis when comparing distributions with different numbers of observations. 4) Just because a graph looks nice, it’s not necessarily a meaningful display of data.

9. Histograms on the TI-calculator  Push STAT.  Push ENTER.

10. Histograms on the TI-calculator 96 67 89 64 83 84 65 6.56 56 116 36 610 78 4.59 77  Enter data. (All in the L1 column.)  After you have entered one observation, press ENTER to go to the next line.  Push 2 nd and QUIT (MODE).  Press 2 nd STAT PLOT (Y=).

11. Histograms on the TI-calculator  Push ENTER.  Make sure Plot 1 is On – Highlight On and press ENTER.  Select the Histogram under Type.  Make sure your Xlist matches the list you entered your data.  Push GRAPH.  For a better picture, press ZOOM 9:ZoomStat.

12. Histograms on the TI-calculator  Push TRACE.  This allows you to see what the range is for each class and the number that fall in that class.  If you want to change the class width: Press WINDOW and change settings.

13. Histograms on the HP Prime 96 67 89 64 83 84 65 6.56 56 116 36 610 78 4.59 77  Push Apps.  Highlight or press Statistics 1 Var  Enter data.

14. Histograms on the HP Prime  Push Plot.  To Zoom in, Press Menu  Press Zoom  Select 3 In

15. Histograms on the HP Prime  To change window, push 2 nd, Plot.  Push Plot.

16. Histograms on the HP Prime  If you want to Trace, press Menu and check to see that there is a dot beside Trace.  Press Menu again.

17. The Practice of Statistics, 5 th Edition17 MAKE and INTERPRET dotplots and stemplots of quantitative data DESCRIBE the overall pattern of a distribution IDENTIFY the shape of a distribution MAKE and INTERPRET histograms of quantitative data COMPARE distributions of quantitative data Data Analysis: Making Sense of Data

18. Homework – Due Monday  P. 44 – 45 #52 & 57