Chapter 4. Displaying Quantitative Data. Copyright 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley

Dealing With a Lot of Numbers Summarizing the data will help us when we look at large sets of quantitative data. Without summaries of the data, it s hard to grasp what the data tell us. The best thing to do is to make a picture Copyright 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 4-3

Your Assignment Working with your group, you have 15 min to fill in as many blanks as you can. Do this from memory, past notes, or the textbook. Copyright 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 4-4

A bar chart or pie chart is often used to display categorical data. These types of displays, however, are not appropriate for quantitative data. Quantitative data is often displayed using either a histogram, dot plot, or a stem-and-leaf plot. Copyright 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 4-5

In a histogram, the interval corresponding to the width of each bar is called a bin. A histogram displays the bin counts as the height of the bars (like a bar chart). Unlike a bar chart, however, the bars in a histogram touch one another. An empty space between bars represents a gap in data values. If a value falls on the border between two consecutive bars, it is placed in the bin on the right. Copyright 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 4-6

Relative Frequency Histogram A relative frequency histogram displays the proportion of cases in each bin instead of the count. Histograms are useful when working with large sets of data, and they can easily be constructed using a graphing calculator. A disadvantage of histograms is that they do not show individual values. Be sure to choose an appropriate bin width when constructing a histogram. As a general rule of thumb, your histogram should contain about 7-10 bars. Copyright 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 4-10

Stem-and-Leaf Displays A stem-and-leaf plot is similar to a histogram, but it shows individual values rather than bars. It may be necessary to split stems if the range of data values is small. Copyright 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 4-11

Outlier Outlier Outlier To verify that these are really outliers, we d have to calculate the IQR and then find Q3 + IQR*1.5. No time today though :*( Copyright 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 4-13

A back to back stem-and-leaf plot can be useful when comparing two distributions. Number of Pairs of Shoes Owned Male Female 0 Don t need to do until AP Stats. 1 2 3 4 5 Copyright 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 4-15

The stems of the stem-and-leaf plot correspond to the bins of a histogram. You may only use one digit for the leaves. Round or truncate your values if necessary. (See next slide for example of truncating.) Stem-and-leaf plots are useful when working with sets of data that are small to moderate in size, and when you want to display individual values. Copyright 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 4-16

Create a stem plot for the SAT test data below. 630 640 720 830 950 200 630 620 640 910 520 760 730 800 640 610 590 580 590 570 750 630 Don t want to use 0 as the leaf bc they are all zero and I d have to have stems from 20 95! Yuck! Key: So let s truncate the 0 s and then include that in the key! Copyright 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley