100 Standard Deviation 2.4 ACTIVITY APPLET You can find the interactive applet for this activity at MyLab Statistics. 100 CHAPTER 2 Descriptive Statistics The Standard deviation applet is designed to allow you to investigate interactively the standard deviation as a measure of spread for a data set. You can generate a data set by entering a Sample size and clicking Simulate; you can generate data values by clicking Add point or by clicking above the horizontal axis. The mean of the points is shown as a green arrow and the median is shown as a red arrow. A blue line segment covering the range from one standard deviation below the mean to one standard deviation above the mean is shown below the horizontal axis. Numeric values for the standard deviation and the other summary statistics are shown in the table at the right. Remove a data value by dragging the corresponding point outside the axis range. Remove all the data values and their corresponding points from the data set by clicking Reset. Sample size: Mean/Median versus Standard Deviation Summary Statistics: Mean Median 0 Simulate 2 0 4 x 6 8 Std. dev. Add point Reset Info EXPLORE Step 1 Specify a Sample size. Step 2 Click Simulate. Step 3 Add and remove various points to and from the plot. Step 4 Remove all the points from the plot. DRAW CONCLUSIONS 1. Plot 10 points that have a mean of about 5 and a standard deviation of about 1. Write the estimates of the values of the points. Plot a point with a value of 15. What happens to the mean and standard deviation? Plot a point with a value of 20. What happens to the mean and standard deviation? 2. How can you plot eight points so that the points have the greatest possible standard deviation? Use the applet to plot the set of points and then use the formula for standard deviation to confirm the value given in the applet. How can you plot eight points so that the points have the least possible standard deviation? Explain. APPLET
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