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Recall from the previous sections that the variance from my sample of the number of meals Debbie grilled per month was 6. In comparison, the units of the variance for the grill example would be 6. The frequency of these potty breaks must keep Debbie very busy. When this is the case, the empirical rule sounds like a decree from the emperor tells us that approximately 68 percent of the data values will be within one standard deviation from the mean. According to the empirical rule, For example, suppose that the average exam if a distribution follows a bellscore for my large statistics class is 88 points shape—a symmetrical curve and the standard deviation is 4.
In our example, two standard deviations equal 8. According to Figure 5. Two standard deviations around the mean. In this case, I would expect all the exam scores to be between 76 and Number of Students Three standard deviations around the mean. U At least The following table shows the number of home runs hit by the top 40 players in Major League Baseball during the season. Number of Home Runs from Top 40 Players in 57 38 33 29 52 38 32 29 49 37 31 29 46 37 31 28 43 35 31 28 42 34 30 28 42 34 30 28 41 34 30 28 39 33 29 27 39 33 29 27 Source: www.
The following histogram shows that this distribution is neither bell-shape nor symmetrical, so we cannot apply the empirical rule see Figure 5. The mean for this distribution is The following table summarizes various intervals around the mean with the percentage of values within those intervals. From the data set, we can observe that 95 percent actually fall between The same explanation holds true for three and four standard deviations around the mean. This technique includes quartile and interquartile measurements. Approximately 25 percent of the data points will fall below the first quartile, Q1.
Approximately 50 percent of the data points will fall below the second quartile, Q2. And, you guessed it, 75 percent should fall below the third quartile, Q3. This is Q2. This is Q1. This is Q3. These are extreme values whose accuracy is questioned and can cause unwanted distortions in statistical results. Therefore, the value 10 would be an outlier in this data set. Use the exact same steps to calculate these measures as those used to calculate measures of central tendency shown in Chapter 4.