STAT1401 University of Winnipeg Descriptive Statistics Problems Report

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Question Description

-Excel must be used where asked.

-Show details of your work. The solutions must be your own work no collaboration.

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Question # 1 data 100 105 105 110 115 115 120 120 120 130 140 150 155 160 180 195 230 235 255 360 Question # 6 data Franchise Hardee’s Arby’s Papa John’s Taco Bell Quiznos Dairy Queen Baskin-Robbins Domino’s Dunkin Donuts Pizza Hut KFC Corp McDonald’s Subway Locations 1397 2558 2615 4516 5110 5619 5889 8053 8082 10238 11553 24799 29612 Assignment 2 STAT-1401 Instructions • Be sure to include assignment cover sheet posted on Nexus as first page of your assignment. • Staple your assignment at the top left-hand corner. • Excel must be used where asked. • Show details of your work. The solutions must be your own work no collaborations. • No extensions in submission date and time will be granted. • No assignments via email will e accepted. • Due date is October 22 at 2:30pm (in class). 1) The cost of consumer purchases such as single-family housing, gasoline, Internet services, tax preparation, and hospitalization was provided in the Wall-Street Journal. Data posted on NEXUS are a sample of the cost of tax-return preparation by services such as H&R Block. Answer questions (a), (b), and (c) without using Excel: a) Compute the mean, median, and mode. Comment on the skewness of data. b) Compute the first and third quartiles. c) Compute and interpret the 79th percentile. d) Now use Excel and give the descriptive statistics of this data set. 2) Seven airline passengers in economy class on the same flight paid an average of $361 per ticket. Because the tickets were purchased at different times and from different sources, the prices varied. The first five passengers paid $420, $210, $333, $695, and $485. The sixth and seventh tickets were purchased by a couple who paid identical/equal fares. What price did each of them pay? 1 3) The following table gives the frequency distribution of the total miles driven during 2005 by 300 car owners. Miles driven in 2005 (in thousands) 0 to less than 5 5 to less than 10 10 to less than 15 15 to less than 20 20 to less than 25 25 to less than 30 30 to less than 35 35 to less than 40 Number of car owners 7 26 59 71 62 39 22 14 Find the mean, variance, standard deviation, median, first quartile and third quartile for the above data. 4) Twelve sheep were fed a special diet consisting of dried grass and barley for three months. At the end of the period the plasma insulin concentration (µU/ml) was determined for each sheep. The data are: 20.5 26.2 18.8 21.2 22.1 21.6 25.4 26.8 22.9 22.8 30.8 28.4 Without using Excel find: a) Variance of the data. b) The interquartile range (IQR). What does the IQR explain about the distribution of the plasma insulin concentration of the twelve sheep? c) Determine the proportion of plasma insulin concentration falling within 2 standard deviations of the mean. 5) The SAT scores of 100 students have a mean of 975 and a standard deviation of 105. The GPAs of the same 100 students have a mean of 3.16 and a standard deviation of 0.22. Is the coefficient of variation in SAT scores greater or less than that in GPAs? 6) Some of the best-known food franchises and the number of retail locations for each are given in data posted on NEXUS (The New York Times Almanac, 2010). a) Without using Excel, calculate a five-number summary (Min, Q1, Q2, Q3, Max). b) Now use Excel to draw the box plot using the data. Are there any outliers? 7) Use the sample data given below to find the coefficient of variation for each of the two samples. Compare and interpret the result in your own words? Heights (in.) of men: 71 66 72 69 68 69 Lengths (mm) of cuckoo eggs: 19.7 21.7 21.9 22.1 22.1 22.3 22.7 22.9 23.9 2 8) Assume total cholesterol value for a certain population is approximately bell shaped with a mean of 200mg/100ml and a standard deviation of 20mg/100ml. a) What is the proportion that an individual picked at random from this population will have a cholesterol level between 200 and 240 mg/100ml? b) What is the interval containing 95% of all cholesterol levels of this population? 9) The three quartiles for systolic blood pressure in a sample of n = 179 employees from a big business corporation were: Q1 = 108, Q2 = 116, Q3 = 120 and also P90 [the 90th percentile] = 127. a) How many employees have a systolic blood pressure between 116 and 127? b) A systolic blood pressure greater than 140 is considered high. Would a blood pressure of 140 be considered an outlier? Justify your answer. 3 ...
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