20 1) To the right is a histogram showing the total number of adoptions in each of the 50 states and the District of 15 Columbia. Use it to answer the following questions: a) What is the best measure for the center of this data: Number of States 10 the Mean or Median? (1 point) 5 b) What is the best measure for the spread of this data: Standard Deviation or IOR? (1 point) 1000 2000 3000 4000 5000 6000 Number of Adoptions c) Why did you choose your answers for parts (a) and (b)? (1 point) d) Would you expect the mean number of adoptions or the median number of adoptions to be higher? Explain your reasoning. (2 points) e) Explain why use of the Empirical Rule would NOT be appropriate for this histogram. (2 points) 2) After entering test scores from her statistics class, the instructor then calculates the mean and the median of all the scores and finds that the mean is significantly smaller than the median. What might this imply (a description) about the shape of the distribution of student scores? (2 points)4) A study of the effects of caffeine asked volunteers to take a memory test 2 hours after drinking soda. Some drank caffeine-free cola, some drank regular cola (with caffeine), and others drank a mixture of the two (getting half the dose of caffeine). The boxplots to the right are for each group's scores. All are drawn using the same scale. Variable a) What are the best measures of center and High Caffeine- spread for the distribution of scores for those who consumed a high amount of caffeine? Why? (3 points) Low Caffeine b) What are the best measures of center and No Caffeine spread for the distribution of scores for those who consumed no caffeine? Why? (3 points) 15 20 25 30 c) Which distribution has a mean value that is most equal to the median value? Why? (1 point) d) Which group has the largest median value? (1 point) e) Which group has the largest range of scores? (Hint: Outliers are still part of the data!) (1 point) f) Which group has the largest Interquartile Range (IQR) of scores? (1 point) 5) Light bulbs are measured in lumens (light output), watts (energy used), and hours (life). A standard white light bulb has a mean life of 675 hours and a standard deviation of 50 hours. A soft white light bulb has a mean life of 700 hours and a standard deviation of 35 hours. In a test at a local science competition, both light bulbs lasted 750 hours. Use z-scores to determine which light bulb's life span was more notable. (Round your answers to two decimal places). (3 points)3) Below is the annual # of deaths from earthquakes in the United States from 1993-2011 (19 years). 23 40 40 245 54 35 38 67 81 125 21 65 78 82 95 54 190 69 a) Using your graphing calculator, first enter the data into L1. Then go to STAT-CALC-1-Var Stats and report here the 5-number summary (all 5 numbers). (3 points) b) Calculate the fences for a modified boxplot. Be sure to write the formulas and show your work. (3 points) c) Examine your fences against the data. Are there any outliers? If so, what are they? (1 point) d) Sketch/construct a modified boxplot and be sure to label each value from the 5-number summary, the fences, and any outliers from part cabove. Please include the x-axis and its scale. Don't forget the difference between a fence (dotted line) and a whisker (solid line) when sketching. Try to be as neat as possible. (5 points) e) After examining your boxplot, what are the best measures for the center and spread of this distribution? Explain why for full credit! (3 points)