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Hannah noted the height of each student in her class and found that the mean height of the students is 56 inches, with a standard deviation of 1.2 inches. The height of one of the students, James, is 59 inches. What is the z-score for James' height?  2.5  -2.5  3.6  -3.6 RATIONALE Recall that the z-score can be calculated with the following formula: The given value is 59 inches, the mean is 56 inches, and the standard deviation is 1.2 inches. Plug these values in to get the following z-score: This also tells us that 59 is 2.5 z-scores or standard deviations above the mean. CONCEPT Standard Scores and Z-Scores 2 Which of the following is NOT a step used in calculating standard deviation?  Subtracting the value of each data set from the mean.  Dividing the sum of each value by the total number of values plus 1.  Calculating the mean of the data set.  Squaring the difference of x - u. RATIONALE Recall the standard deviation . So there is no addition of 1 to any values. CONCEPT Standard Deviation 3 In which of these cases should the median be used?  When the data has small variance  When the data has extreme values  When the data has nominal values  When data has no outliers RATIONALE Since the mean uses the actual values in the data, it is most affected by outliers and skewness. So, we only want to use the mean when the data is symmetric as a measure of centrality. When the data is skewed or has extreme values, the median is a better measure since it is not as sensitive to these values. CONCEPT Measures of Center 4 The average daily rainfall for the past week in the town of Hope Cove is normally distributed, with a mean rainfall of 2.1 inches and a standard deviation of 0.2 inches. If the distribution is normal, what percent of data lies between 1.9 inches and 2.3 inches of rainfall?  95%  34%  99.7%  68% RATIONALE Recall that if the data is normal, then the 68-95-99.7 rule applies which states that 68% of all data points fall within one standard deviation of the mean, 95% of all data points fall within two standard deviations of the mean, and 99.7% of all data points fall within three standard deviations of the mean. 1.9 inches and 2.3 inches are both 0.2 inches from the mean of 2.1 inches, which is the same as one standard deviation in either direction. This tells us that 68% of the data should lie between 1.9 inches to 2.3 inches. CONCEPT 68-95-99.7 Rule 5 Ralph records the time it takes for each of his classmates to run around the track one time. As he analyzes the data on the graph, he notices very little variation between his classmates’ times. Which component of data analysis is Ralph observing?  The overall spread of the data  The center of the data set  An outlier in the data set  The overall shape of the data RATIONALE Since Ralph is looking at the variation of data, this is examining the spread of the data. CONCEPT Data Analysis 6 Sara wonders what percentage of her students answered at least half of the quiz questions incorrectly. The relative cumulative frequency of students who earned a score of 21 or higher on the quiz is __________.  18%  68%  16%  32% RATIONALE To get the relative cumulative frequency of 21 or greater, we need to first find the cumulative number of 21 or more. We simply add up any bin that has the number 21 or more, such as the bin that shows scores of 21-25, 26-30, 31-35, and 36-40. This would be: To calculate relative cumulative frequency, we wi

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