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Due 10/8 Name________________ Math 116 – Take Home related to the exam I grades – Fall 2009 In this problem, the population (individuals and variable) are the grades of ALL students taking statistics with me in the Fall semester of 2009 1) By just looking at the graphs, which class do you think did better? Explain. Which one is your class? Let’s label the graphs. 2) Here are the summary statistics for the three classes. Why are they statistics and not parameters? A B C D F mean Std-deviation Min Q1 Med Q3 max Sample size Complete this 8 am 11 am 2 pm 8 9 6 1 2 82.8 12.3 54 78 85.5 92 100 12 7 3 3 2 83.8 14.3 46 78 88 95 98 9 8 6 4 1 82.2 12.8 47 73 83.5 92.5 101 3) The shape of the distribution of grades of the 11 am class is: Symmetrical, bell left skewed right skewed 4) Consider the top graph. The lower whisker is longer than the upper whisker. What is the meaning of this? 1 5) Use the statistics of Exam 1 to complete the following: a) For the 8 am class, the middle 50% of the data are between _________ and _________ b) The top 75% of the 11 am class compares to the top 75% of which other class? c) For the 11 am class, 25% of the students scored at or below ________________ d) For the 2 pm class, 75% of the students scored at or above ________________ e) What is the 25th percentile of the class corresponding to the top graph? 5) If a student is selected at random from the population, what is the probability that the student selected got an A? Show how you find it. Round answer to 3 decimal places 6) a) Using the standard deviation as a unit - Use the mean and standard deviation of each class (see page 1) and label the tick marks of the following diagrams. Locate the mean at the X. 8 am class _|________|________|________|________X________|________|________|________|__ 11 am class _|________|________|________|________X________|________|________|________|__ 2 pm class _|________|________|________|________X________|________|________|________|__ b) Complete the following: 8 am class 11 am class 2 pm class Unusually low values are lower than Unusually high values are higher than 2 7) How many standard deviations from the mean is a given score? There is a number called a z-score that tells you the number of standard deviations that a certain number is above or below the mean. Here is the formula yourscore mean z z-score = (score – mean) / standard deviation s tan dard .deviation Use the formula to find the z-score corresponding to a score of 70. Round to two decimal places Show work 8) By the range rule of thumb any number which is more than ________ standard deviations away from the mean is considered an unusual value in the distribution. REWRITE this rule using z scores: 9) DO THIS AT HOME, ON ANOTHER PAPER – for your info only – I don’t want this back This will help you compare your grade to the grades of all students in your class. What is your grade? What is the z-score of your grade? Is your grade usual or unusual? If unusual, is it unusually low or high? 10) Frequency tables – relative frequency tables – probability distributions Let’s copy here the grouped data of YOUR CLASS Classes ?????? Frequency Relative frequency Probability 11) Use the calculator to find the statistics of the grouped data 12) Use the calculator to find the statistics of the probability distribution 3