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AP Statistics Review 1 Name: Date Due: All work submitted should be representative of your knowledge and thus should be your own. No credit will be given for work that is plagiarized from another source. Homework submitted after the due date will not accepted. 1. Shoes How many pairs of shoes do students have? Do girls have more shoes than boys? Here are the data from a random sample of 20 female and 20 male students at a large high school. Female: Male: 50 13 14 10 26 50 7 11 26 13 6 4 31 34 5 5 57 23 12 22 19 30 38 7 24 49 8 5 22 13 7 10 23 15 10 35 38 51 10 7 mean = 30.35 stddev = 14.24 mean = 11.65 stddev = 9.42 a.) Find and interpret the percentile in the female distribution for the girl with 22 pairs of shoes. 5 out of 20 females reported having fewer than 22 pairs of shoes. The percentile of the girl with 22 pairs of shoes is 5/20 = 0.25, which means the girl is in the 25th percentile in the number of shoes distribution. b.) Find and interpret the percentile in the male distribution for the boy with 22 pairs of shoes. 17 out of 20 males reported having fewer than 22 pairs of shoes. The percentile of the boy with 22 pairs of shoes is 17/20 = 0.85, which means the boy is in the 85th percentile in the number of shoes distribution. c.) Who is more unusual: the girl with 22 pairs of shoe or the boy with 22 pairs of shoes? Explain. Female z-score = (22 – 30.35)/14.24 = -0.59; Male z-score = (22 – 11.65)/9.42 = 1.10 The male with 22 pairs of shoes is more unusual than the female with 22 pairs of shoes because the male is 1.10 standard deviations above the mean number of shoes for males, while the female is only 0.59 standard deviations below the mean number of shoes for females. 2. Teacher Raises A school system employs teachers at salaries between $28,000 and $60,000. The teachers’ union and the school board are negotiating the form of next year’s increase in the salary schedule. a.) If every teacher is given a flat $1,000 raise, what will this do to mean, median, extremes, quartiles and standard deviation of the salary distribution? Since a constant = 1,000 is being added to each observation in the distribution, the mean, median and extremes will all increase by 1,000, but the quartiles and the standard deviation will remain the same. b.) If each teacher receives a 5% raise instead of a flat $1000 raise, the amount of the raise will vary from $1,400 to $3,000, depending on the salary. What will this do to mean, median, extremes, quartiles and standard deviation of the salary distribution? Since each observation in the distribution is being multiplied by a constant = 0.05, the mean, median and extremes will increase 0.05 times. The quartiles and standard deviations will also increase 0.05 times. 3. The graph below displays the cumulative relative frequency of the length of phone calls made from the mathematics department office at Hinsdale South last month. a.) Estimate the interquartile range of this distribution. Illustrate your method on the graph. Q1 → 25th percentile → 13 minutes; Q3 → 75th percentile → 32 minutes The IQR of the call length distribution is approximately 32 – 13 = 19 minutes. b.) What is the percentile for the phone call that lasted 34 minutes? The call that lasted 34 minutes is approximately in the 82nd percentile. This means that 82% of the phone calls made lasted fewer than 34 minutes. 4. The figure below displays two density curves, each with three points marked. At which of these points on each curve do the mean and the median fall? a.) The density curve in part (a) is roughly symmetric. Therefore, the mean and median are equal and they are both represented by A in the diagram. b.) The density curve in part (b) is slightly skewed left. Therefore, the mean is less than the mean and is pulled in the direction of the tail. The median is represented by B and the mean is represented by A.