1.1 Displaying Distributions with Graphs, Continued

Transcription

1 1.1 Displaying Distributions with Graphs, Continued Ulrich Hoensch Thursday, January 10, 2013

2 Histograms Constructing a frequency table involves breaking the range of values of a quantitative variable into classes. A histogram displays only the count or percent of the observations that fall into each class. The bars in a histogram are contiguous; that is, they touch at the ends. The classes should always have equal width.

3 Example 5 If we choose the classes 75 IQ score < 85, 85 IQ score < 95,..., 145 IQ score < 155, we obtain the following frequency table and histogram.

4 Example 5, Frequency Table and Histogram

5 Examining Distributions Major peaks of a distributions are called modes; if there is only one major peak, then the distribution is unimodal. Distributions may be symmetrical, or skewed. A distribution is skewed to the right if the right tail (corresponding to larger values) is much longer than the left tail (corresponding to smaller values). A distribution is skewed to the left if the left tail is much longer than the right tail. An outlier is an individual value that falls outside the overall pattern. Identifying outliers is a matter of judgement based on the nature of the data.

6 Example 6: Length of Words in Shakespeare s Plays The distribution is unimodal, skewed to the right and has no outliers.

7 Example 7: Breaking Strengths of Semiconductor Wires The distribution is unimodal, roughly symmetrical and has two outliers on the left corresponding to wires that were not attached to the semiconductor; and one outlier to the right which represents a measurement error.

8 Time Plots

9 Example 8: Yearly Discharge of the Mississippi River

10 Example 8: Yearly Discharge of the Mississippi River The histogram on the left fails to show the trend of the variable over time. The time plot on the right includes a trend line.

11 Creating Histograms Using Excel The data are given in column A. We choose the cutoffs for the classes to be 11, 14, 17,..., 53, 56. Enter all but the lowest and highest cutoff in a column of the Excel sheet. This gives us the bin range used to generate the frequency table.

12 Creating Histograms Using Excel Now, click Data Analysis under the Data tab. Then, select Histogram and click OK. If the data analysis option is not available, the Analysis ToolPak must be added in. See the class web page for instructions on how to do this.

13 Creating Histograms Using Excel Enter the data range as the Input Range, enter the Bin Range, and select the output to be in a free cell in the worksheet.

14 Creating Histograms Using Excel Click OK. The output is a frequency count for the classes.

15 Creating Histograms Using Excel Now, we need to generate a frequency distribution that is usable as the input for a bar chart. To this end, we compute the class midpoints of each class, and arrange them in a column. Immediately to the right of each midpoint, we type the class frequency (this is most easily done by copying the frequency column above).

16 Creating Histograms Using Excel Next, create a bar graph as explained in the Bar Graphs Using Excel tutorial. The result should look somewhat like this:

17 Creating Histograms Using Excel The bars do not touch. To correct this, click on any one of the bars, right-click, and select Format Data Series... in the context menu.

18 Creating Histograms Using Excel Set the gap to 0%, and under the Border Color menu, select Solid line, and set the color to black.

19 Creating Histograms Using Excel The following histogram results.

20 Creating Histograms Using Excel In this case, it might be a good idea to decrease the font size on the horizontal axis a bit. Click on the panel, then right-click and set the font down to 8 pt. This is the final result.

21 Creating Time Plots Using Excel We start by selecting a basic 2-D line plot.

22 Creating Time Plots Using Excel Click Select Data, select the data in the second column, including the label Discharge.

23 Creating Time Plots Using Excel Press the Edit button and select the data in the first column, without the label Year.

24 Creating Time Plots Using Excel Click OK and OK again. Optionally, remove the label Discharge on the right and edit the caption.