VCU STAT 210  Test 2 Practice Test #2 (3 pages)
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Test 2 Practice Test #2
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 Virginia Commonwealth University
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 Stat 210  Basic Practice of Statistics
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Test 2 Practice Test 2 One of the most popular activities for tourists visiting Hawaii is snorkeling where it is possible to see an assortment of fish turtles eels octopi and other sea creatures A random sample of 24 tourists who visited Hawaii during 2014 and who snorkeled while there was selected and each tourist was asked the number of turtles that they saw while snorkeling The responses are given below Use this information to answer questions 1 through 9 For the problems requiring calculations 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 5 8 1 0 2 12 7 18 5 6 22 11 0 3 0 26 6 3 1 Based on the information above what is the population of interest 2 Consider the data above Construct an appropriate stem and leaf plot to graphically display this data 3 Calculate the mean of the data 4 Is the value for the mean calculated in question 3 denoted by or A B X 0 47 12 18 0 4 X The data for the number of turtles that the tourists saw while snorkeling for the sample of 24 tourists is repeated below 5 8 1 0 2 12 7 18 5 6 22 11 0 3 5 Calculate the median of the data 6 Calculate the range of the data 7 Calculate the standard deviation of the data 8 Calculate the interquartile range of the data 9 0 26 6 3 0 47 12 18 0 4 Consider the stem and leaf plot constructed in question 2 and the calculations made in questions 3 5 6 7 and 8 Use this information to completely describe the distribution of the number of turtles that the tourists saw while snorkeling for the sample of 24 tourists For questions 10 through 12 use the choices below and list the letters of all choices that meet the description it is possible for there to be more than one correct choice per statement A Median B Mean C Range D Interquartile Range E Standard deviation F Boxplot G Histogram H Pie chart I Bar graph J Stem and leaf plot 10 A graphical procedure that can be used to display qualitative data 11 A measure of spread that is resistant to outliers 12 A measure of center that is not resistant to outliers September 22 is the birth date of Kim Hyo Yeon a singer with the South Korean girl group Girls Generation Born in Incheon South Korea she began training in dance in elementary school supplementing her lessons with time at a local hip hop school Fans of Kim Hyo Yeon purchase t shirts folders and other items that display her image Of interest is the amount of money that her fans spend on items that display the image of Kim Hyo Yeon and the boxplot below displays the distribution of the amount of money spent on Kim Hyo Yeon items for a random sample of 127 fans The numbers above certain marks give the exact value of that mark Use this boxplot to answer questions 13 through 15 5 25 38 x 45 74 93 109 x 0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100 105 110 Amount of Money Spent 13 Which of the following best describes the spread of this distribution A The interquartile range of the data is 74 5 69 B The interquartile range of the data is 45 25 20 C The median of the data is 38 D The range of the data is 74 5 69 E The range of the data is 45 25 20 14 Which of the following best describes the shape of this distribution A The distribution is skewed to the right B The distribution is bimodal C The distribution has outliers at 93 and 109 D The distribution is symmetrical E The distribution is skewed to the left 15 Suppose two additional Kim Hyo Yeon fans are added to the sample one of these fans spent 30 and the other spent 50 on Kim Hyo Yeon items Based on the boxplot above and this additional information which of the following best describes the median amount spent by this sample of 129 fans A 40 B 38 C 45 D 52 11 E Cannot be determined from the information provided Test 2 Practice Test 2 Solutions 1 The population of interest is all tourists who visited Hawaii during 2014 and who snorkeled while there 2 0 0 1 1 2 2 3 3 4 4 3 1 0 2 0 3 0 3 0 0 4 5 8 7 5 6 6 2 1 2 8 8 2 6 7 X where 2 6 26 turtles x 5 8 4 216 9 n 24 24 4 B The mean that was calculated in question 3 was the sample mean 5 Median Location n 1 24 1 25 2 2 2 X 12 5 Median Average of the 12 th and 13th ordered observations 5 6 2 5 5 6 Range Max Min 47 0 47 7 S 10 95 see page 77 for how to compute S 8 Median of the 12 smallest observations Q1 1 2 2 1 5 Median of the 12 largest observations Q3 12 12 2 12 IQR Q3 Q1 12 1 5 10 5 9 The distribution is skewed to the right The data ranges from 0 to 47 range 47 S 10 95 IQR 10 5 and the center is between 5 and 10 Mean 9 Median 5 5 There is one outlier at 47 10 H and I A pie chart and bar graph can both be used for to display qualitative categorical data A boxplot histogram and stem and leaf plot are all used for quantitative data 11 D The interquartile range is a measure of spread that is resistant to outliers 12 B The mean is the measure of center that is not resistant to outliers 13 B The IQR is 45 25 20 the range would be 109 5 104 which was not a choice 14 15 A The outliers cause the distribution to be skewed to the right B The line in the box represents the median which is 38 When the two values are added one value is less than the median and one value is higher than the median so 38 is still the middle value Therefore the median remains unchanged at 38
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