Test 2 Practice Test #2One of the most popular activities for tourists visiting Hawaii is snorkeling, where it is possible to see an assortment offish, turtles, eels, octopi, and other sea creatures. A random sample of 24 tourists who visited Hawaii during 2014 andwho snorkeled while there was selected, and each tourist was asked the number of turtles that they saw whilesnorkeling. The responses are given below. Use this information to answer questions 1 through 9. For the problemsrequiring calculations, you can use the calculator, or you can choose to do the problems by hand, in which case anywork 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 0 47 12 18 0 41. 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 ´X?(A) (B) ´XThe 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 0 26 6 3 0 47 12 18 0 4__________ 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. 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 whilesnorkeling 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 ispossible 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 inIncheon, South Korea, she began training in dance in elementary school, supplementing her lessons with time at a localhip hop school. Fans of Kim Hyo-Yeon purchase t-shirts, folders, and other items that display her image. Of interest isthe amount of money that her fans spend on items that display the image of Kim Hyo-Yeon, and the boxplot belowdisplays the distribution of the amount of money spent on Kim Hyo-Yeon items for a random sample of 127 fans. Thenumbers above certain marks give the exact value of that mark. Use this boxplot to answer questions 13 through 15. 5 25 38 45 74 93 109 x---------------------- ----------------------------------x • •------------------------------------------------------------------------------------------------------------------------------------------0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100 105 110Amount 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 theother 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 providedTest 2 Practice Test #2 Solutions1. The population of interest is all tourists who visited Hawaii during 2014 and who snorkeled whilethere.2. 0 1, 0, 2, 0, 3, 0, 3, 0, 0, 4 0 5, 8, 7, 5, 6, 61 2, 1, 2 1 8, 82 22 63344 7 where 2 | 6 = 26 turtles3. ´X =∑xn=5+8+…+ 424=21624=9 4. B – The mean that was calculated in question 3 was the sample mean, ´X5. Median Location = n+12=24 +12=252 = 12.5; Median = Average of the 12th and 13th orderedobservations = (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 = 1.5Median of the 12 largest observations = Q3 = (12 + 12)/2 = 12IQR = 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. Aboxplot, 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. A – The outliers cause the distribution to be skewed to the right.15. B – The line in the box represents the median, which is 38. When the two values are added, onevalue is less than the median and one value is higher than the median, so 38 is still the middle value.Therefore the median remains
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