Concept explainers
Hazardous waste: Following is a list of the number of hazardous waste sites in each of the 50 states of the United States in a recent year. The list has been sorted into numerical order.
- Find the first and third
quartiles of these data. - Find the
median of these data. - Find the upper and lower outlier boundaries.
- Are there any outliers? If so, list them.
- Construct a boxplot for these data.
- Describe the shape of this distribution.
- What is the 30th percentile?
- What is the 85th percentile?
- The state of Georgia has 16 hazardous waste sites. What percentile is this?
a)
To find the first and third quartiles of the given data.
Answer to Problem 31E
First quartile = 10.5 and third quartile = 32
Explanation of Solution
Formula:
First quartile
Third quartile
Calculation:
Given data sorted in ascending order:
0 | 9 | 14 | 20 | 40 |
1 | 9 | 14 | 21 | 48 |
2 | 11 | 14 | 25 | 49 |
2 | 12 | 14 | 26 | 49 |
3 | 12 | 15 | 29 | 52 |
5 | 12 | 15 | 30 | 67 |
6 | 12 | 15 | 32 | 86 |
9 | 12 | 16 | 32 | 97 |
9 | 13 | 19 | 32 | 97 |
9 | 13 | 19 | 38 | 116 |
Here, n = 50
First need to find First quartile and third quartile
First Quartile:
First quartile is 10.5
Third quartile:
Third quartile is 32
b)
To find median of the data.
Answer to Problem 31E
Median is 15
Explanation of Solution
Formula:
Calculation:
c)
To find upper and lower outlier boundaries.
Answer to Problem 31E
Lower outlier boundary is -21.5
Upper outlier boundary is 64.25
Explanation of Solution
Formula:
IQR:
Calculation:
Therefore,
d)
To find the list of outliers.
Answer to Problem 31E
The outlier points are 67,86,97,97,116
Explanation of Solution
Outliers are those values which are less than
Here,
Lower outlier boundary is -21.5
Upper outlier boundary is 64.5
There is no any value less than -21.5. But there are five values larger than 64.5 which are:
67,86,97,97,116
Hence outlier points are 67,86,97,97,116
e)
To construct a boxplot from given data
Explanation of Solution
Boxplot from given data:
f)
To find shape of the distribution
Answer to Problem 31E
The shape of the distribution is positively-skewed.
Explanation of Solution
Here, median is close to first quarter. Hence the shape of the distribution is positively-skewed.
g)
To find 30th percentile
Answer to Problem 31E
30th percentile is 12
Explanation of Solution
Therefore,
h)
To find 85th percentile
Answer to Problem 31E
85th percentile is 49
Explanation of Solution
Therefore,
h)
To find percentile rank of Georgia.
Answer to Problem 31E
Percentile rank of Georgia at 16 is 54%
Explanation of Solution
Formula:
Calculation:
Want to see more full solutions like this?
Chapter 3 Solutions
Loose Leaf Version For Elementary Statistics
- Please show as much work as possible to clearly show the steps you used to find each solution. If you plan to use a calculator, please be sure to clearly indicate your strategy. Consider the following game. It costs $3 each time you roll a six-sided number cube. If you roll a 6 you win $15. If you roll any other number, you receive nothing. a) Find the expected value of the game. b) If you play this game many times, will you expect to gain or lose money?arrow_forward= 12:02 WeBWorK / 2024 Fall Rafeek MTH23 D02 / 9.2 Testing the Mean mu / 3 38 WEBWORK Previous Problem Problem List Next Problem 9.2 Testing the Mean mu: Problem 3 (1 point) Test the claim that the population of sophomore college students has a mean grade point average greater than 2.2. Sample statistics include n = 71, x = 2.44, and s = 0.9. Use a significance level of a = 0.01. The test statistic is The P-Value is between : The final conclusion is < P-value < A. There is sufficient evidence to support the claim that the mean grade point average is greater than 2.2. ○ B. There is not sufficient evidence to support the claim that the mean grade point average is greater than 2.2. Note: You can earn partial credit on this problem. Note: You are in the Reduced Scoring Period. All work counts for 50% of the original. Preview My Answers Submit Answers You have attempted this problem 0 times. You have unlimited attempts remaining. . Oli wwm01.bcc.cuny.eduarrow_forwardThere are four white, fourteen blue and five green marbles in a bag. A marble is selected from the bag without looking. Find the odds of the following: The odds against selecting a green marble. The odds in favour of not selecting a green marble The odds in favor of the marble selected being either a white or a blue marble. What is true about the above odds? Explainarrow_forward
- Please show as much work as possible to clearly show the steps you used to find each solution. If you plan to use a calculator, please be sure to clearly indicate your strategy. 1. The probability of a soccer game in a particular league going into overtime is 0.125. Find the following: a. The odds in favour of a game going into overtime. b. The odds in favour of a game not going into overtime. c. If the teams in the league play 100 games in a season, about how many games would you expect to go into overtime?arrow_forwardexplain the importance of the Hypothesis test in a business setting, and give an example of a situation where it is helpful in business decision making.arrow_forwardA college wants to estimate what students typically spend on textbooks. A report fromthe college bookstore observes that textbooks range in price from $22 to $186. Toobtain a 95% confidence level for a confidence interval estimate to plus or minus $10,how many students should the college survey? (We may estimate the populationstandard deviation as (range) ÷ 4.)arrow_forward
- In a study of how students give directions, forty volunteers were given the task ofexplaining to another person how to reach a destination. Researchers measured thefollowing five aspects of the subjects’ direction-giving behavior:• whether a map was available or if directions were given from memory without a map,• the gender of the direction-giver,• the distances given as part of the directions,• the number of times directions such as “north” or “left” were used,• the frequency of errors in directions. Identify each of the variables in this study, and whether each is quantitative orqualitative. For each quantitative variable, state whether it is discrete or continuous. Was this an observational study or an experimental study? Explain your answer.arrow_forwardexplain the difference between the confident interval and the confident level. provide an example to show how to correctly interpret a confidence interval.arrow_forwardSketch to scale the orbit of Earth about the sun. Graph Icarus’ orbit on the same set of axesWhile the sun is the center of Earth’s orbit, it is a focus of Icarus’ orbit. There aretwo points of intersection on the graph. Based on the graph, what is the approximate distance between the two points of intersection (in AU)?arrow_forward
- The diameters of ball bearings are distributed normally. The mean diameter is 67 millimeters and the standard deviation is 3 millimeters. Find the probability that the diameter of a selected bearing is greater than 63 millimeters. Round to four decimal places.arrow_forwardSuppose you like to keep a jar of change on your desk. Currently, the jar contains the following: 22 Pennies 27 Dimes 9 Nickels 30 Quarters What is the probability that you reach into the jar and randomly grab a penny and then, without replacement, a dime? Express as a fraction or a decimal number rounded to four decimal places.arrow_forwardA box contains 14 large marbles and 10 small marbles. Each marble is either green or white. 9 of the large marbles are green, and 4 of the small marbles are white. If a marble is randomly selected from the box, what is the probability that it is small or white? Express as a fraction or a decimal number rounded to four decimal places.arrow_forward
- Big Ideas Math A Bridge To Success Algebra 1: Stu...AlgebraISBN:9781680331141Author:HOUGHTON MIFFLIN HARCOURTPublisher:Houghton Mifflin HarcourtGlencoe Algebra 1, Student Edition, 9780079039897...AlgebraISBN:9780079039897Author:CarterPublisher:McGraw HillHolt Mcdougal Larson Pre-algebra: Student Edition...AlgebraISBN:9780547587776Author:HOLT MCDOUGALPublisher:HOLT MCDOUGAL