Math 116 Chapter 3: Finding Measures of Center and Variation - Prof. Maria Aronne, Exams of Statistics

Download Math 116 Chapter 3: Finding Measures of Center and Variation - Prof. Maria Aronne and more Exams Statistics in PDF only on Docsity! Math 116 - Chapter 3 review Name___________________________________ Find all the measures of the center and variation of the following data set. Round your answer to one more decimal place than the original data. Show your work. 1) Jeanne is currently taking college zoology. The instructor often gives quizzes. On the past five quizzes, Jeanne got the following scores: 1 17 5 18 1 Solve the problem. 2) The federal government requires a car manufacturer to have a minimum miles per gallon (mpg) average over the models it makes. Suppose that the mpg's for the five models of a manufacturer are 19, 21, 22, 28, and 18, and the government requirement is 24 mpg. The sixth model is to be designed to meet the government requirement. What must the new mpg of this model be to meet the requirement? 3) The mathematics SAT scores of the seven students in a mathematics seminar are 524, 559, 580, 586, 615, 628, and 636. Suppose that the student with the score 524 drops the seminar and is replaced by a student with a score of 782. What will happen to the mean and the median scores of the class? 4) The mathematics SAT scores of the seven students in a mathematics seminar are 536, 551, 575, 596, 615, 625, and 633. Suppose the student with the score 536 drops the seminar and is replaced by a student with a score that is a low-end outlier. What will happen to the mean and the median scores of the class? 5) The host of a dinner party purchases wine based on the weighted average of clarity (9%), bouquet (3%), friendliness to the palate (8%), storageability of opened bottles (40%), and price (40%). Suppose that Bone Ranch Wave has scores in these categories of 4, 5, 3, 8, and 9, respectively. What is its rating? Provide an appropriate response. 6) The mean of a data set is always/sometimes/never (select one) one of the data points in a set of data. Explain your answer with brief examples. Solve the problem. 7) The following data set is the GPA's of the students in a statistics class. 1.93, 1.99, 2.00, 2.04, 2.12, 2.34, 2.55, 2.55, 2.75, 2.75, 2.80, 2.80, 2.85, 3.02, 3.12, 3.22, 3.31, 3.33, 3.45, 3.69 What value is the 25th percentile? 8) Suppose that your income is at the 69th percentile of wage earners in the United States. What percent of wage earners make more than you? 1 9) The weights (in pounds) of 30 newborn babies are listed below. a) Construct (by hand, and with the calculator) a boxplot for the data set. Show work for identifying outliers. b) What is the range? c) What is the range of the middle 50% of the distribution? 5.5 5.7 5.8 5.9 6.1 6.1 6.3 6.4 6.5 6.6 6.7 6.7 6.7 6.9 7.0 7.0 7.0 7.1 7.2 7.2 7.4 7.5 7.7 7.7 7.8 8.0 8.1 8.1 8.3 8.7 Identify potential outliers, if there are any, in the given data. 10) The test scores of 15 students are listed below. 36 54 53 65 66 69 70 72 75 77 78 82 87 90 99 Provide the appropriate response. 11) Describe what these boxplots tell you about the relationship between the state you live in and your salary, based on the same occupation. 12) Consider the boxplots from the previous problem. Classify each statement as True or False. a) The range of salaries in Illinois and Massachussets is almost the same. b) For the Nevada distribution of salaries, the number of salaries between Q2 and Q3 is larger than the number of salaries between the minimum and Q1. c) In Massachussets, about 25% of the salaries are lower than $35,000. d) The mean salary in Washington state is about $30,000. e) In Massachussets, the mean salary is higher than the median salary. 2 25) The amount of Jen's monthly phone bill is normally distributed with a mean of $55 and a standard deviation of $8. Fill in the blanks. 68% of her phone bills are between $___ and $___. Use the range rule of thumb to approximate the standard deviation. 26) 496, 598, 503, 528, 565, 601, 576, 543 Select the requested distribution. 27) a) Which of the distributions has the largest range? b) Which of the distributions has the greatest variation? b) Which one has the largest mean? A) B) a) They all have the same range. b) B has the largest standard deviation. c) They all have the same mean C) 5 Provide an appropriate response. 28) Consider the distribution of heights of all the NBA players. What would you expect the shape of the distribution to be? A) Skewed left B) Skewed right C) Symmetric 29) Consider the distribution of mathematics SAT scores of students in honors calculus at a liberal arts college. What would you expect the shape and variation of the distribution to be? A) Skewed right with considerable variation B) Symmetric with large variation C) Symmetric with little variation D) Skewed left with little variation 30) The distribution of prices of houses is (select one) a) bell shaped b) Uniform c) skewed to the left d) right skewed Which measure of the center is more appropriate to use? Explain why. Use the word resistant in your explanation. A) Right skewed 31) Two companies produce a certain type of light bulbs with a mean life of 500 hours. For company A, the standard deviation is 50 hours and for company B it's 70 hours. You must place an order of 1000 light bulbs of that type. Which company would you order from? Explain why. A) company A 6 32) Assume that the IQ scores of a group of students has a mean of µ = 100 and a standard deviation of s = 15. Show all your a) Use the Chebyshev's theorem to complete the following statements . At least 75% of the students in this group have an IQ score between ________ and ______ . At least ________% of the students in this group have an IQ score between 55 and 145. b) Use the Empirical rule to complete the following: About 99.7% of the students have IQ scores between ___________ and _____________ c) According to the Empirical rule about _______% of the IQ scores are between 800 and 1200. d) Since the distribution of IQ scores is normally distributed (bell shaped) we get a better approximation by using the Chebyshev's theorem or Empirical rule (circle one) e) Considering that scores that are MORE than two standard deviations away from the mean are considered unusual, complete the following: UNUSUALLY LOW IQ scores were below____________ . UNUSUALLY HIG IQ scores were above ____________ . 7