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Name: _________________________________________________ Per. ____ Date: _______________Chapter 1 Problem Set A.P.StatisticsDevicePercent who OwnCell Phone85%MP3 Player83%Handheld Video Game Player41%Laptop38%Portable CD/Tape Player20%Here are the percent of 15-18 year olds that own the following personal media devices, according to the Kaiser Family Foundation: a) Make a well-labeled bar graph to display the data. Describe what you see. b) Would it be appropriate to make a pie chart for these data? Why or why not?A research study asked children which of four different emotions they associated with thecolor red. The response and gender of each child are given in the following table.JoyHappinessLoveAngerMale28204018Female61258060 a) Use the data in the two-way table to calculate the marginal distribution (in percents) of emotions.Make a graph to display the marginal distribution in (a) and describe what you see.Use the data in the table to calculate the marginal distribution (in percent) of gender.Use the data in the table to calculate the conditional distribution of gender for each emotion. Construct a segmented bar graph to display this distribution.Hallux abducto valgus (call it HAV) is a deformation of the big toe that is not common among young people and often requires surgery. Doctors used X-rays to measure the angle (in degrees) of deformity in 38 consecutive patients under the age of 21 who came to a medical center for surgery to correct HAV. The higher the angle measure the more severe the deformity. Here are the data. 13 14 16 16 17 18 18 20 20 20 21 21 21 21 22 23 25 25 25 6 26 26 26 28 28 28 30 30 30 31 32 32 32 34 38 38 50Make a histogram of these data. Choose an appropriate bin width and scale, and label each axis.Write a brief discussion of the distribution of the angle of deformity among young patients needing surgery for this condition.The dotplots below show the total family income of randomly-chosen individuals from Indiana (38 individuals) and New Jersey (44 individuals). Write a few sentences comparing the distribution of total family incomes in these two samples.What measures would you use to describe the center and spread of the distribution of total family incomes in Indiana? Justify your answer. A student studying the sleeping habits of seniors at his school asked 34 randomly-selected seniors how many hours of sleep they got the previous night. The data, rounded to the nearest half-hour, is given in the table below. ?8 7.5 9 7.5 9 6 5 9 7.5 7 8 7 8.5 8 6.5 8.5 6 7 7.5 7 6 8.5 7 8 7 7.5 7 6 7 8 7.5 6 7 a) Use your calculator to find the mean and standard deviation of these data.b) Find the five number summary for these data and make a box plot.c) Determine if there are any outliers in these data. Show your work.d) Suppose 4 more values were added to the data, each exactly equal to the mean. Would this have any impact on the standard deviation? Explain, without using any calculations.6) Below are dotplots of three different distributions, A, B, and C. Which one has the largest standard deviation? Justify your answer. Below are the lengths, in minutes, of the 25 most popular movies, as voted on by visitors to a web site devoted to movies. 142 195 201 139 106 175 96 121 130 109 200 133 102 178 165 161 124 146 115 118 154 152 207 112 136 a) Make a stemplot of these data. b) The mean of this distribution is 144.7 and the median is 139. Explain why you could have predicted that the mean would be higher than the median by looking at the stemplot.8) The two-way table below shows the relationship between means of transportation to workand gender for a simple random sample of 250 working adults in the United States.Discuss the relationship between gender and means of transportation to work for the workingadults in this sample. Provide appropriate marginal and conditional distributions to support youranswer. You may choose whatever methods you want to present those distributions.Drive AloneCar PoolPublic TransportationMale113166Female852379) As a part of the United States Department of Agriculture’s Super Dump cleanup efforts in the early 1990s,various sites in the country were targeted for cleanup. Three of the targeted sites—River X, River Y, andRiver Z—had become contaminated with pesticides because they were located near abandoned pesticide dump sites. Measurements of the concentration of aldrin (a commonly used pesticide) were taken at twenty randomly selected locations in each river near the dump sites.The boxplots shown below display the five-number summaries for the concentrations, in parts per million (ppm) of aldrin, for the twenty locations that were sampled in each of the three rivers.-190563500a) Compare the distributions of the concentration of aldrin among the three rivers.b) The twenty concentrations of aldrin for River X are given below.3.4 4.0 5.6 3.7 8.0 5.5 5.3 4.2 4.3 7.38.6 5.1 8.7 4.6 7.5 5.3 8.2 4.7 4.8 4.6Construct a stemplot that displays the concentrations of aldrin for River X.c) Describe a characteristic of the distribution of aldrin concentrations in River X that can be seen in thestemplot but cannot be seen in the boxplot.10) When asked for summary statistics, MINITAB produced the following output: Variable N Mean SE Mean StDev Minimum Q1 Median Q3 Maximum Damage 50 22.39 3.60 25.45 0.00 2.23 12.66 41.63 88.60 Give the five-number summary, and explain why you can see from these five numbers that the distribution is strongly skewed to the right. ................
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