# VCU STAT 210 - Test 2 Practice Test #1(1) (4 pages)

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## Test 2 Practice Test #1(1)

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- Pages:
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- School:
- Virginia Commonwealth University
- Course:
- Stat 210 - Basic Practice of Statistics

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Test 2 Practice Test 1 1 To estimate the mean age of all students attending her university a statistician selected a simple random sample of 15 students Prior to going on vacation the statistician collected data for only 13 of the 15 students and determined that the median age of the 13 students was 21 years The statistician took the data with her on vacation so this median value of 21 is all you know about the ages of those 13 students You do however now know that the last two students were 19 and 31 years of age respectively Based on this information which of the following best describes the median age of all 15 students in the sample A 25 B 21 C 21 53 D 23 67 E Cannot be determined from the information provided A very popular leisure activity in the fall for many people is fantasy football In fantasy football you draft a team of real NFL players and compete head to head with other fantasy owners with scores based on the real performance of the players on your fantasy team The data below gives the number of rushing and receiving touchdowns scored in week 1 of fantasy football for a random sample of 10 teams Use this data to answer questions 2 through 6 Please write your final answer on the line before the question number You can use the calculator or you can choose to do the problems by hand in which case any work you show will be considered for partial credit 7 11 8 12 4 2 Calculate the mean of the data 3 Calculate the median of the data 4 Calculate the range of the data 5 Calculate the standard deviation of the data 6 Calculate the interquartile range of the data 7 6 2 15 7 8 Most fantasy leagues use a standard scoring system where players accumulate points for touchdowns yardage gained either rushing or passing kicking and defensive and special teams plays The data below give the number of fantasy points scored by a random sample of 24 fantasy teams that use the standard scoring system Construct an appropriate stem and leaf plot to graphically display this data 91 108 132 68 77 47 79 82 96 54 64 82 106 88 91 60 79 86 97 61 79 119 102 139 8 Consider the stem and leaf plot constructed in question 7 Use the stem and leaf plot to completely describe the distribution of the standard fantasy scores for this sample of 24 fantasy football teams 9 A few fantasy football leagues use exotic rules that often produce many more points than the points scored in a standard scoring league In one exotic scoring league a team scored 432 points and suppose this score were added to the sample of 24 fantasy points presented in question 7 Clearly this value of 432 would be considered an outlier For each of the following circle YES or NO to indicate whether the statement is a correct statement YES NO The mean is a measure of spread that is heavily influenced by the outlier YES NO The median is a measure of center that is heavily influenced by the outlier YES NO The interquartile range is a measure of spread that is resistant to the outlier YES NO The standard deviation is a measure of center that is resistant to the outlier Many fantasy football leagues are played for fun only while others have an entry fee that is then turned into prizes for the winners The boxplot below reveals the entry fees for a random sample of 100 fantasy football leagues Use this boxplot to answer questions 10 through 12 x x 0 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 Entry Fee 10 Which of the following best describes the spread of this distribution A The median of the data is 10 B The range of the data is 80 0 0 C The range of the data is 40 5 35 D The interquartile range of the data is 150 0 150 E The interquartile range of the data is 40 5 35 11 Which of the following best describes the shape of this distribution A The distribution has outliers at 100 and 150 B The distribution is symmetrical C The distribution is skewed to the left D The distribution is skewed to the right E The distribution is trimodal 12 Which of the following best describes the center of this distribution A The range of the data is 150 0 0 B The mean of the data is 10 C The median of the data is 10 D The median of the data is 22 5 E The distribution has outliers at 100 and 150 Questions 13 and 14 are multiple choice questions and question 15 is a true false question For questions 13 and 14 please write the letter of your answer on the line in front of the question number and for question 15 please write True or False on the line in front of the question number 13 Which of the following is a graphical procedure for displaying qualitative data A Stem and leaf plot B Histogram C Box plot D All of A B and C E None of A B and C 14 Which of the following is not a component of a 5 number summary A Median B Standard deviation C Upper quartile D Lower quartile E None of the above 15 For a given set of data a frequency histogram is constructed Using the same data and the same class intervals a relative frequency histogram is constructed TRUE or FALSE the frequency histogram and the relative frequency histogram will look the same except for the labeling of the vertical axis Test 2 Practice Test 1 Solutions 1 B With n 13 the median location n 1 2 13 1 2 7 so the 7 th ordered observation is the median 21 With the two values added n 15 so the median location 15 1 2 8 Since 19 is less than the median 21 is now the 8 th ordered observation and hence the median remains unchanged at 21 X 2 3 x 7 11 8 80 8 n 10 Median Location observations 10 n 1 10 1 11 5 5 2 2 2 Median average of the 5th and 6th ordered 7 8 7 5 2 4 Range Max Min 15 2 13 5 S 3 83 see page 77 for how to compute S 6 Median of the 5 smallest observations Q1 6 Median of the 5 largest observations Q3 11 IQR Q3 Q1 11 6 5 7 04 05 06 07 08 09 10 11 12 13 7 4 8 4 0 1 7 9 9 9 2 2 8 6 1 6 1 7 8 6 2 9 2 9 where 07 7 77 8 The distribution is fairly symmetric The data ranges from 47 to 139 and the center is around 80 Mean 86 96 Median 84 There are no outliers 9 YES YES …

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