20140210 Day4 Problem Set 1

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  BHSEC Queens Name: Date:Statistics Spring 2014 Period: PROBLEM SET 1: DUE MONDAY, FEBRUARY 24, 2014EXPECTATIONS: ã  You may use calculators or R for problem set computations; however, you are expected to set up/explaincomputations in writing. This is what constitutes “showing work” on such problems. ã  Problem sets are due to my mailbox in the main office by 4:30 pm on the due date. I will not accept alate homework assignment if you have not communicated with me about it (including absences). ã  If your work is too cramped/messy to allow for feedback/corrections, you won’t get feedback/corrections. ã  Problem sets are a small portion of your grade, but they are a very good predictor of how well you willdo on other components of this class.1. Classify the following variables from the class survey as either categorical or quantitative/continuous.Variable Question gender  Gender? age  What is your age, in years?  month.birth  What is your month of birth? random.num  Choose a number between 1 and 102. Consider the following data. 0 1 2 2.5 4 4 5 5 5 6 7.5 18 31 For the following problems, please round your answers to two decimal places.(a) What is the sample size  n ?(b) Find the median.(c) Compute the sample mean ¯ x .(d) Find the lower quartile.(e) Find the upper quartile.(f) Compute the interquartile range.(g) What is the high outlier cutoff? What is the low outlier cutoff? List all the outliers.(h) Find the variance and standard deviation. Include two decimal places.(i) In words, describe what the standard deviation represents.(j) Please carefully draw a boxplot of the data labeling the median, Q1, Q3, and outliers.3. A histogram is described as  positively/right skewed   if it looks like this:1  Notice how it appears that most of the data appears to be to the  left   of the mean and that the right tail   is longer. Use this definition to answer the following question.Suppose the median of a quantitative/continuous variable is closer to the lower quartile than the upperquartile. Is the distribution/histogram more likely to be positively/right skewed or negatively/leftskewed? Sketch a histogram to support your answer. (Hint: it may help you to construct a list of numbers where the condition above is satisfied.)4. The following is a  frequency table   of the age of students in statistics last year at BHSEC Queens; itlists the number of students of each age enrolled in Statistics during the spring of 2012.Age Frequency16 1217 4318 4Use the frequency table to find the following:(a) Mode age of students in statistics in the spring of 2012.(b) Median age of students in statistics in the spring of 2012.(c) Mean age of students in statistics in the spring of 2012. Round your answer to two decimal places.(d) Standard deviation of the age of students in statistics in the spring of 2012.5. Suppose you’ve turned in four (equally weighted) homework assignments and received grades of 70 , 75 , 80 , and 85. Suppose you miss the fifth assignment and thus get a grade of 0. How does this 0 change (1)the median of the data, (2) the mean of the data, (3) the range, (4) the IQR, and (5) the standarddeviation?  Support your claim for each with computations.  Write a short paragraph explaining whichof these statistics should be used to reflect your understanding of the material covered across all fivehomework assignments?2
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