Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
AP Statistics z-scores and transforming data Notes 2.1b One way to measure location is to calculate the standardized score or z-score. z x mean xx standard deviation sx Example The following are test scores on Mr. Pryor’s first Statistics Test. 79, 81, 80, 77, 73, 83, 74, 93, 78, 80, 75, 97, 73, 77, 63, 86, 90, 79, 85, 83, 89, 84, 82, 97, 92 A. Calculate the mean, standard deviation and 5-number summary for the test grades. B. Calculate and interpret the z-score for the score 93? C. Calculate and interpret the z-score for the score73? Transforming Data Effect of adding (or subtracting) a constant Adding the same positive number a to (subtracting a from) each observation adds a to (subtracts a from) measures of center and location (mean, median, quartiles, percentiles), but does not change the shape of the distribution or measures of spread (range, IQR, standard deviation) Effect of multiplying (or dividing) by a constant Multiplying (or dividing) each observation by the same positive number b multiplies (divides) measures of center and location (mean, median, quartiles, percentiles) by b, multiplies (divides) measures of spread (range, IQR, standard deviation) by b, but does not change the shape of the distribution Example D. If Mr. Pryor adds 5 to each student’s score, calculate the mean, standard deviation and 5-number summary for the transformed test grades. E. If Mr. Pryor multiplied each student’s score by 1.1, calculate the mean, standard deviation and 5-number summary for the test grades. F. If Mr. Pryor multiplied each student’s score by .9 then added 10, calculate the mean, standard deviation and 5number summary for the test grades. G. Suppose Mr. Pryor standardized the student’s scores, what would be the shape, center, and spread of the new distribution?