# SECTION 2-1: OVERVIEW SECTION 2-2: FREQUENCY DISTRIBUTIONS

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5 Chapter 2 Describing, Exploring and Comparing Data 23 sure you save your work, using a file name that will be indicative of the material contained in the Excel workbook. You will find you use many of the data sets more than once, and can utilize different worksheets within a file to separate the different work you do with the same data. 2) You can also practice your skills by using Excel to complete exercises 5 through 8 and 13 through 20 from section 2-2 Basic Skills and Concepts in your text book. SECTION 2-3: PICTURES OF DATA CREATING A HISTOGRAM There are two situations you may find yourself in when asked to create a histogram: 1) You may only have the original data, in which case you can use the Data Analysis, Histogram feature in Excel; or 2) You may have an existing frequency distribution, in which case you can use the Chart Wizard. CREATING A HISTOGRAM DIRECTLY FROM A DATA SET 1) Using the instructions from section 2-2 if necessary, repeat the steps to create a frequency distribution for the data on Cotinine Levels in Smokers. Remember, you will select Tools, Data Analysis and Histogram. In addition make sure that the box beside Chart Output is checked. If you saved your previous work, you can have the output placed underneath your original work. 2) Click on OK. You will see the information below in your worksheet. Note: Excel uses bin numbers that are the upper class limits, but they are typically printed in the center of the histogram bars. This is deceptive. Usually values in the middle of the bars are interpreted to be the class midpoint values. Make sure you modify your histogram as outlined below to rectify this situation. MODIFYING THE HISTOGRAM You will need to modify the histogram some to make it look the way you want it to. In particular, you will want to remove the extra column on the histogram entitled More, change your values on the horizontal axis to either reflect class midpoints, or to show the classes, close the gap between the bars, re-name the

8 26 Chapter 2 Describing, Exploring and Comparing Data 1) With the Chart Area selected, left click in this region, and then click on Chart Options. 2) In the Chart Title and Category (X) Axis boxes, type in more appropriate names for the graph and the values on the horizontal axis. Your dialog screen should look similar to the one shown below. Then click OK. OR, alternatively: 1) Select the title or the axis name you want to change by clicking on it. Your title or axis name will have a selection box around it. 2) To change the name, simply begin typing the new name you wish to use. Notice the text is typed up at the top of the worksheet, and the title in the box is changed once you press Enter. 3) To delete a title, simply click on it to create the "handles," and then press Delete. If you delete a title, and later want to re-create it, select the Chart Area, right click, then click on Chart Options and click on the Titles tab. Resizing a Region 1) Select the region you want to resize. Specifically, let s resize the entire Chart Area. 2) Notice the black "handles" on the selection box. a) By clicking and dragging on the corner handles, you can resize the region in both directions. b) By clicking and dragging on the side handles, you can stretch or shrink the region horizontally. c) By clicking on the middle handles at the top or bottom, you can stretch or shrink the region vertically. 3) Move your cursor to the black box in the lower right hand corner. Your cursor should change to a double headed arrow. Left click, and holding the mouse down, drag this corner diagonally across your screen to resize the chart in both directions.

11 Chapter 2 Describing, Exploring and Comparing Data 29 you wish to select. Your dialog box should look like the following: 10) Click on Next. 11) In Step 4 of 4 - Chart Location, determine whether you want your chart in a new worksheet (recommended option) or inserted in an existing worksheet. Then click on Finish. 12) You should now see a basic relative frequency histogram like the one shown below. Clearly, you will again want to modify the histogram by changing the gap width to 0, resizing the picture, realigning your horizontal axis labels, etc. See the previous instructions in this section to make appropriate modifications to your relative frequency histogram. Cotinine Levels of Smokers Relative Frequency 40% 30% 20% 10% 0% Cotinine Levels CREATING A FREQUENCY POLYGON Once we have the frequency distribution for our data, we may choose to represent it graphically as a frequency polygon rather than a histogram. Since frequency polygons display points above the class midpoints, we first need to enter a new column for these values. 1) If you already have your frequency distribution for the Cotinine Levels of Smokers entered in a worksheet, you can simply add a column showing the class midpoints. This column can be entered directly next to the relative frequencies, or can be entered elsewhere on your worksheet. We have chosen to insert a column between the column containing the classes, and the column containing the relative

13 Chapter 2 Describing, Exploring and Comparing Data 31 Complaints Against Phone Carriers Frequency Rates and Services 4473 Marketing 1007 International Calling 766 Access Charges 614 Operator Services 534 Slamming Cramming ) We first need to sort the data in order of decreasing frequency. Click on any one cell containing a value in the Frequency column. Do NOT select the entire column! 3) Click on Data in the menu bar, and then click on Sort. Make sure that the Sort by box shows Frequency. Click inside the circle next to Descending. Your dialog box should look like the following: 4) Click on OK. Your data should now be sorted from highest to lowest. You should see that the table labels were rearranged so that they stayed matched with the appropriate data value. Your table should look like the following: 5) Click on Insert, then click on Chart, and click on Column. Follow through the 4 linked steps in the Chart Wizard. Remember, when you enter a range, you should do so by selecting the appropriate cells in your worksheet. Notice

19 Chapter 2 Describing, Exploring and Comparing Data 37 Interpreting the Output in the Descriptive Output Table Below is a brief description of each of the measures included in Descriptive Statistics. Mean: The arithmetic average of the numbers in your data set. Standard Error: This is computed by using the formula S/ n where S is the sample standard deviation and n is the number of observations. Median: This is the data value that splits the distribution in half. To determine the value of the median, the observations are first arranged in either ascending or descending order. If the number of observations is even, the median is found by taking the arithmetic average of the two middle values. If the number of observations is odd, then the median is the middle observation. Mode: This is the observation value associated with the highest frequency. Caution: Three situations are possible regarding the mode: 1) If all values occur only once in a distribution, Excel will return #N/A. 2) If a variable has only one mode, Excel will return that value. 3) If a variable has more than one mode, Excel will still return only one value. The value used will be the one associated with the modal value that occurs first in the data set. To check the accuracy of the mode, it would be wise to create a frequency distribution. Standard Deviation: This is computed using the formula: S = ( X X) n 1 Sample Variance: This is the standard deviation squared. Kurtosis: This number describes a distribution with respect to its flatness of peakedness as compared to a normal distribution. A negative value characterizes a relatively flat distribution. A positive value characterizes a relatively peaked distribution. Skewness: This number characterizes the asymmetry of a distribution. Negative skew indicates that the longer tail extends in the direction of low values in the distribution. Positive skew indicates that the longer tail extends in the direction of the high values. Range: The minimum value is subtracted from the maximum value. Minimum: The lowest value occurring in the data set. Maximum: The highest value occurring in the data set. Sum: The sum of the values in the data set. Count: The number of values in the data set. CREATING PARTICULAR SAMPLE STATISTICS USING THE FUNCTION WIZARD If you just want to know particular values, without producing the entire table of Descriptive Statistics, you can use the Function wizard, and select just the options that you want to use. 1) Decide which values you want to compute. We will compute the Mean, Median, Mode and Midrange as shown in Table 2-8 of your book.

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