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College Prep. Stats. Sections 3.1 – 3.3 Quiz Review Name: _____________________________________ 1. Which measures of center are resistant (not affected by outliers)? 2. Which measures of spread are resistant? 3. Find the a) mean, b) median, c) mode, d) midrange, e) range, f) standard deviation, g) variance, and h) coefficient of variation for the following sample data: 24, 27, 28, 32, 24, 27, 24, 28, 28, 28, 32, 37, 34, 40, 41, 24, 28 4. The mean test score on a Biology test was 84 with a standard deviation of 3.5. Jeremy got a 77. How many standard deviations away from the mean is this? 5. For what types of data sets can you use Chebyshev’s Theorem? 6. Draw and label a picture that is skewed to the right. Is the tail on the right or left? 7. The scores of 40 students are summarized in the frequency distribution below. Find the mean score using: Test Scores 56 – 61 Students/ Frequency (f) 13 62 – 67 7 68 – 73 9 74 – 79 2 80 – 85 4 86 – 91 4 92 – 97 1 = x fx = x2 fx2 = 8. Using the table from number 7, what is the standard deviation of the frequency distribution? Use: 9. Speed limits in Illinois are listed below (effective January 1, 2014). Use the range rule of thumb, ≈ deviation of those speed limits. 25 30 35 40 45 65 s 𝑟𝑎𝑛𝑔𝑒 4 n ( fx 2 ) ( fx) 2 n(n 1) to estimate the standard 10. Using the Empirical Rule, answer the following questions: a) What percentage of data falls within 1 standard deviation of the mean? b) What percentage of data falls within 2 standard deviations of the mean? c) What percentage of data falls within 3 standard deviations of the mean? 11. To earn a “B” in Geometry, Abby must get a grade average of at least 80%. Abby’s test scores are 85%, 90%, and 75%. Her final exam score counts as three test scores in the average. Abby got a grade of 78% on the final exam. What was her final grade average? Did she get a “B”? Use 𝑥 x = Σ(𝑤∙𝑥) Σ𝑤 xw w = = 12. The ages of the members of a gym have a mean of 48 years and a standard deviation of 11 years. Using Chebyshev’s theorem 1 (1 − 2), what percent of members are within 2 standard deviations away from the mean? What are the maximum and minimum ages 𝐾 that are within 2 standard deviations of the mean? 13. In a right tail distribution, where does the median fall according to the mean? 14. In a left tail distribution, where does the median fall according to the mean?