Analyzing One-Variable Data

1. 1 Analyzing One-Variable Data Lesson 1.5 Displaying Quantitative Data: Histograms

2. Displaying Quantitative Data: Histograms • Make histograms of quantitative data. • Interpret histograms. • Compare distributions of quantitative data with histograms.

3. Displaying Quantitative Data: Histograms You can use a dotplot or stemplot to display quantitative data. Both graphs show every individual data value. For large data sets, this can make it difficult to see the overall pattern in the graph. We often get a cleaner picture of the distribution by grouping nearby values together. Doing so allows us to make a new type of graph: a histogram. Histogram A histogram shows each interval as a bar. The heights of the bars show the frequencies or relative frequencies of values in each interval.

4. Displaying Quantitative Data: Histograms (a) Dotplot and (b) histogram of the duration (in minutes) of 220 eruptions of the Old Faithful geyser.

5. Displaying Quantitative Data: Histograms How to Make a Histogram Choose equal-width intervals that span the data. Five intervals is a good minimum. Make a table that shows the frequency (count) or relative frequency (percent or proportion) of individuals in each interval. Draw and label the axes. Put the name of the quantitative variable under the horizontal axis. To the left of the vertical axis, indicate if the graph shows the frequency or relative frequency of individuals in each interval. Scale the axes. Place equally spaced tick marks at the smallest value in each interval along the horizontal axis. On the vertical axis, start at 0 and place equally spaced tick marks until you exceed the largest frequency or relative frequency in any interval. Draw bars above the intervals. Make the bars equal in width and leave no gaps between them. The height of each bar corresponds to the frequency or relative frequency of individuals in that interval. An interval with no data values will appear as a bar of height 0 on the graph.

6. Displaying Quantitative Data: Histograms The choice of intervals in a histogram can affect the appearance of a distribution. The figure below shows two different histograms of the foreign-resident data. • The one on the left uses the intervals of width 5 from the previous example. • The one on the right uses intervals half as wide: 0 to <2.5, 2.5 to <5, and so on. Histograms with more intervals show more detail but may have a less clear overall pattern.

7. Displaying Quantitative Data: Histograms What are we actually doing when we make a histogram?

8. Displaying Quantitative Data: Histograms Histograms can be used to compare the distribution of a quantitative variable in two or more groups. • It’s a good idea to use relative frequencies (percents or proportions) when comparing, especially if the groups have different sizes. • Be sure to use the same intervals when making comparative histograms so the graphs can be drawn using a common horizontal axis scale. Is it true that students who graduate from high school earn more money than students who do not graduate from high school?

9. LESSON APP 1.5 How old are U.S. presidents? The table gives the ages of the first 44 U.S. presidents when they took office. • Make a frequency histogram of the data using intervals of width 4 starting at age 40. • Describe the shape of the distribution. • What percent of presidents took office before the age of 60?

10. Displaying Quantitative Data: Histograms • Make histograms of quantitative data. • Interpret histograms. • Compare distributions of quantitative data with histograms.