LONG ISLAND UNIVERSITY * DEPARTMENT OF MATHEMATICS MATHEMATICS 100 - EXTRA CREDIT ASSIGNMENT 1 Show all work 3.5 points total 1. {50, 64, 52, 55, 61, 70, 88, 90, 93, 66, 73, 75, 91, 70, 79} Based on the data, construct a five-class frequency distribution with a lower class limit of 50, an upper class limit of 99, and a class width of 10. Include the relative and cumulative frequencies for each class. Test Scores Frequency Relative frequency Cumulative frequency 2. Sketch a histogram for the frequency distribution you constructed in Question 1. Is the data normally distributed? 3. Given the dataset: {84, 68, 70, 74, 81, 64, 66, 73, 77, 72, 72, 72}, find the following: a. Mean b. Median c. Mode d. P30 4. Researchers at Pennsylvania State University conducted experiments with poplar trees. Listed below are weights (kg) of poplar trees given no treatment and poplar trees treated with fertilizer and irrigation. Find the range, SD, and variance of both datasets. Does there appear to be a difference between the two standard deviations? No treatment: 0.16, 0.03, 0.17, 0.38, 0.23 Fertilizer and irrigation: 2.04, 0.28, 0.93, 1.08, 2.39 5. Stanford-Binet IQ scores have a mean of 100 and a standard deviation of 15. Dmitri has an estimated IQ of 120. Given this information, answer the following: a. What is the difference (in raw units) between Dmitri's IQ score and the mean IQ score? b. How many standard deviations is that? c. Convert Dmitri's raw IQ score into a z-score. d. If we consider "usual" IQ scores to be those that convert to z-scores between -2 and 2, is Dmitri's IQ usual or unusual?