1. Chapter 3 Lesson 3.2, 3.3a Graphical Methods for Describing Data 3.2: Stem-and-Leaf Plots 3.3a: Histograms

2. Stem-and-Leaf Displays When to Use Univariate numerical data How to construct –Select one or more of the leading digits for the stem –List the possible stem values in a vertical column –Record the leaf for each observation beside each corresponding stem value –Indicate the units for stems and leaves in a key Each number is split into two parts: Stem – consists of the first digit(s) Leaf - consists of the final digit Use for small to moderate sized data sets. Doesn ’ t work well for large data sets. Be sure to list every stem from the smallest to the largest value Can also create comparative stem-and-leaf displays

3. The following data are price per ounce for various brands of different brands of dandruff shampoo at a local grocery store. 0.320.210.290.540.170.280.360.23 Create a stem-and-leaf display with this data. StemLeaf 1 2 3 4 5 What would an appropriate stem be? List the stems vertically For the observation of “ 0.32 ”, write the 2 behind the “ 3 ” stem. 2 Continue recording each leaf with the corresponding stem 19 4 7 8 6 3 Key: Stem: Tenths Leaf: Hundredths

4. The Census Bureau projects the median age in 2030 for the 50 states and Washington D.C. A stem-and-leaf display is shown below. Notice that you really cannot see a distinctive shape for this distribution due to the long list of leaves We can split the stems in order to better see the shape of the distribution. Notice that now you can see the shape of this distribution. We use L for lower leaf values (0-4) and H for higher leaf values (5-9).

5. The following is data on the percentage of primary-school-aged children who are enrolled in school for 19 countries in Northern Africa and for 23 countries in Central African. Northern Africa 54.6 34.348.977.859.688.597.492.583.9 98.891.697.896.192.294.998.686.696.9 88.9 Central Africa 58.334.635.545.438.663.853.961.969.9 43.085.063.458.461.940.973.934.874.4 97.461.066.779.6 Create a comparative stem- and-leaf display. What is an appropriate stem? Let ’ s truncate the leaves to the unit place. “ 4.6 ” becomes “ 5 ”

6. How Many Pairs of Shoes Do You Own?

7. Histograms When to UseUnivariate numerical data How to constructDiscrete data ― Draw a horizontal scale and mark it with the possible values for the variable ― Draw a vertical scale and mark it with frequency or relative frequency ― Above each possible value, draw a rectangle centered at that value with a height corresponding to its frequency or relative frequency Constructed differently for discrete versus continuous data For comparative histograms – use two separate graphs with the same scale on the horizontal axis

8. Queen honey bees mate shortly after they become adults. During a mating flight, the queen usually takes several partners, collecting sperm that she will store and use throughout the rest of her life. A study on honey bees provided the following data on the number of partners for 30 queen bees. 1224667878 11 835671019 7 6 975474678 10 Create a histogram for the number of partners of the queen bees.

9. First draw a horizontal axis, scaled with the possible values of the variable of interest. Next draw a vertical axis, scaled with frequency or relative frequency. Draw a rectangle above each value with a height corresponding to the frequency. Suppose we use relative frequency instead of frequency on the vertical axis. What do you notice about the shapes of these two histograms?

10. Histograms When to UseUnivariate numerical data How to constructContinuous data ― Mark the boundaries of the class intervals on the horizontal axis ― Draw a vertical scale and mark it with frequency or relative frequency ― Draw a rectangle directly above each class interval with a height corresponding to its frequency or relative frequency This is the type of histogram that most students are familiar with.

11. A study examined the length of hours spent watching TV per day for a sample of children age 1 and for a sample of children age 3. Below are comparative histograms. Children Age 1Children Age 3 Notice the common scale on the horizontal axis TI-Tip: How to Make a Histogram

12. Homework Pg.113: #3.17, 3.21 Pg.134: #3.25 Reading Notes 3.3