
Concept explainers
(a)
To find: Inter
(a)

Answer to Problem 66E
Solution: The Inter
Explanation of Solution
Calculation: The Inter Quartile Range
Follow the steps given below:
Step 1: Enter the data in a Minitab worksheet.
Step 2: Go to Stat and select basic statistics.
Step 3: Then select Display
Step 4: Then click on Statistics tab and tick mark the option against Interquartile Range and click on OK twice.
From the Minitab output the Inter Quartile Range
Interpretation: The Inter Quartile Range
(b)
To find: The outliers using
(b)

Answer to Problem 66E
Solution: There are no outliers in the provided data. Any value above 77.48 or below 23.32 would be considered outliers as they are upper whisker and lower whisker, respectively. There is no value above or below those numbers respectively.
Explanation of Solution
Calculation: To obtain the value of first and third quartile, follow the steps given below in Minitab,
Step 1: Enter the data in a Minitab worksheet.
Step 2: Go to Stat and select basic statistics.
Step 3: Then select Display Descriptive Statistics. Enter the name of the column containing the Reflectance data in the variables textbox.
Step 4: Then click on Statistics tab and tick mark the option against first quartile and third quartile and click on OK twice.
The value of
The formula for upper whisker is,
Where
The formula for lower whisker is,
where
Upper whisker of boxplot is found to be 77.48, so any values above 77.48 would be considered outliers. There is no value that is either above upper whisker or below lower whisker, so there is no outlier.
Interpretation: Outliers refers to those data points that lie either above upper whisker or below lower whisker in boxplot. From the calculations done above, it is clear that the data does not contain any outlier.
(c)
To graph: A boxplot of the provided data and describe the distribution using it.
(c)

Explanation of Solution
Graph: Follow the steps given below to obtain the boxplot:
Step 1: Enter the data into a Minitab worksheet.
Step 2: Go to ‘Graph’ and click on ‘Boxplot’.
Step 3: In the dialogue box that appears select ‘Simple’ and click OK.
Step 4: Next enter the name of the column containing the data of reflectance of smolts in the filed marked as ‘Graph variables’ and click on OK.
The boxplot is obtained as shown below,
Interpretation: The boxplot is generally preferred to describe data set having unsymmetrical distribution. The boxplot shows First quartile, Median, and Third quartile. The boxplot of the data represents there are no outliers in the data.
(d)
To graph: A modified boxplot and describes the distribution using it.
(d)

Explanation of Solution
Graph: Follow the steps given below to obtain the modified boxplot:
Step 1: Enter the data into a Minitab worksheet.
Step 2: Go to ‘Graph’ and click on ‘Boxplot’.
Step 3: In the dialogue box that appears select ‘Simple’ and click OK.
Step 4: Next enter the name of the column containing the data of reflectance of smolts in the filed marked as ‘Graph variables’ and click on OK.
The boxplot is obtained as shown below,
Interpretation: The modified boxplot is generally used to display data graphically when the distribution of data is unsymmetrical and skewed as it can clearly show outliers. In the above modified boxplot, there is no outlier, which indicates that the data distribution is symmetrical.
(e)
To graph: A stem plot of the provided data.
(e)

Answer to Problem 66E
Solution: The stemplot of the data is shown below:
Explanation of Solution
Graph:
Follow the steps given below to obtain the stemplot:
Step 1: Enter the provided data in a Minitab worksheet.
Step 2: Go to Graph and select stem and leaves.
Step 3: Enter the name of the column containing the provided data in the Graph variables textbox and click on OK.
The obtained stem plot is displayed below,
Interpretation: The stemplot of data is generally drawn when size of data is somewhat small and all the data values are positive. The graph shows all the data values on stemplot. In the stemplot shown above there is no outliers and therefore, it indicates that the distribution of the data is symmetrical.
(f)
To find: The Boxplot, Modified boxplot, and stemplot and their advantages and disadvantages.
(f)

Answer to Problem 66E
Solution: In boxplot, data is displayed based on five-number summary, which includes Minimum, Maximum, First quartile, Third Quartile, and Median. In Modified boxplot, also data is displayed based on five-number summary, but it also shows outliers. In stemplot, data values are arranged in stem consisting of all digits except right most and leaves contain final digit. Advantages of boxplots is that it is suitable for large unsymmetrical data while advantages of stemplot is that it shows all numerical value of data on graph itself. Disadvantage of Boxplot is that it is not suitable for unsymmetrical data and it does not retain exact numerical values while disadvantage of stemplot is that it is used only for positive numbers only and if data size is small.
Explanation of Solution
The comparison of Boxplot, Modified boxplot, and stemplot is shown below:
Boxplot |
Modified Boxplot |
Stemplot |
|
Description |
It displays data based on |
It displays data based on five number summary including Minimum, Maximum, First quartile, Third Quartile and Median. |
In stemplot data values are arranged in stem consisting of all digits except right most digit and leaves contain final digit |
Advantages |
1. It displays five number summary graphically. 2. It is suitable for unsymmetrical data. 3. It can handle large data set. |
1. It displays five number summary. 2. It is suitable for unsymmetrical data which is skewed. 3. It shows outliers clearly. |
1. It can display both symmetrical and unsymmetrical data graphically. 2. It can indicate outliers also. 3. It displays all numerical values of data on stemplot. |
Disadvantages |
1. It is not suitable for data set having symmetrical distribution. 2. It does not display outliers on graph. |
1. It is not suitable for data set having symmetrical distribution. |
1. It is not suitable if data size is very large. 2. It is not used for negative numbers. |
Interpretation: There are various ways to display data graphically, Boxplot is suitable for unsymmetrical data which are skewed, it can handle large data set as well, it shows five-number summary and displays Maximum, Minimum, first quartile, third quartile, and median, and also shows outliers. Stemplot plot is used if data size is small and greater than 0.
Want to see more full solutions like this?
Chapter 1 Solutions
Introduction to the Practice of Statistics: w/CrunchIt/EESEE Access Card
- « CENGAGE MINDTAP Quiz: Chapter 38 Assignment: Quiz: Chapter 38 ips Questions ra1kw08h_ch38.15m 13. 14. 15. O Which sentence has modifiers in the correct place? O a. When called, she for a medical emergency responds quickly. b. Without giving away too much of the plot, Helena described the heroine's actions in the film. O c. Nearly the snakebite victim died before the proper antitoxin was injected. . O O 16 16. O 17. 18. O 19. O 20 20. 21 21. 22. 22 DS 23. 23 24. 25. O O Oarrow_forwardQuestions ra1kw08h_ch36.14m 12. 13. 14. 15. 16. Ӧ 17. 18. 19. OS 20. Two separate sentences need Oa. two separate subjects. Ob. two dependent clauses. c. one shared subject.arrow_forwardCustomers experiencing technical difficulty with their Internet cable service may call an 800 number for technical support. It takes the technician between 30 seconds and 11 minutes to resolve the problem. The distribution of this support time follows the uniform distribution. Required: a. What are the values for a and b in minutes? Note: Do not round your intermediate calculations. Round your answers to 1 decimal place. b-1. What is the mean time to resolve the problem? b-2. What is the standard deviation of the time? c. What percent of the problems take more than 5 minutes to resolve? d. Suppose we wish to find the middle 50% of the problem-solving times. What are the end points of these two times?arrow_forward
- Exercise 6-6 (Algo) (LO6-3) The director of admissions at Kinzua University in Nova Scotia estimated the distribution of student admissions for the fall semester on the basis of past experience. Admissions Probability 1,100 0.5 1,400 0.4 1,300 0.1 Click here for the Excel Data File Required: What is the expected number of admissions for the fall semester? Compute the variance and the standard deviation of the number of admissions. Note: Round your standard deviation to 2 decimal places.arrow_forward1. Find the mean of the x-values (x-bar) and the mean of the y-values (y-bar) and write/label each here: 2. Label the second row in the table using proper notation; then, complete the table. In the fifth and sixth columns, show the 'products' of what you're multiplying, as well as the answers. X y x minus x-bar y minus y-bar (x minus x-bar)(y minus y-bar) (x minus x-bar)^2 xy 16 20 34 4-2 5 2 3. Write the sums that represents Sxx and Sxy in the table, at the bottom of their respective columns. 4. Find the slope of the Regression line: bi = (simplify your answer) 5. Find the y-intercept of the Regression line, and then write the equation of the Regression line. Show your work. Then, BOX your final answer. Express your line as "y-hat equals...arrow_forwardApply STATA commands & submit the output for each question only when indicated below i. Generate the log of birthweight and family income of children. Name these new variables Ibwght & Ifaminc. Include the output of this code. ii. Apply the command sum with the detail option to the variable faminc. Note: you should find the 25th percentile value, the 50th percentile and the 75th percentile value of faminc from the output - you will need it to answer the next question Include the output of this code. iii. iv. Use the output from part ii of this question to Generate a variable called "high_faminc" that takes a value 1 if faminc is less than or equal to the 25th percentile, it takes the value 2 if faminc is greater than 25th percentile but less than or equal to the 50th percentile, it takes the value 3 if faminc is greater than 50th percentile but less than or equal to the 75th percentile, it takes the value 4 if faminc is greater than the 75th percentile. Include the outcome of this code…arrow_forward
- solve this on paperarrow_forwardApply STATA commands & submit the output for each question only when indicated below i. Apply the command egen to create a variable called "wyd" which is the rowtotal function on variables bwght & faminc. ii. Apply the list command for the first 10 observations to show that the code in part i worked. Include the outcome of this code iii. Apply the egen command to create a new variable called "bwghtsum" using the sum function on variable bwght by the variable high_faminc (Note: need to apply the bysort' statement) iv. Apply the "by high_faminc" statement to find the V. descriptive statistics of bwght and bwghtsum Include the output of this code. Why is there a difference between the standard deviations of bwght and bwghtsum from part iv of this question?arrow_forwardAccording to a health information website, the distribution of adults’ diastolic blood pressure (in millimeters of mercury, mmHg) can be modeled by a normal distribution with mean 70 mmHg and standard deviation 20 mmHg. b. Above what diastolic pressure would classify someone in the highest 1% of blood pressures? Show all calculations used.arrow_forward
- Write STATA codes which will generate the outcomes in the questions & submit the output for each question only when indicated below i. ii. iii. iv. V. Write a code which will allow STATA to go to your favorite folder to access your files. Load the birthweight1.dta dataset from your favorite folder and save it under a different filename to protect data integrity. Call the new dataset babywt.dta (make sure to use the replace option). Verify that it contains 2,998 observations and 8 variables. Include the output of this code. Are there missing observations for variable(s) for the variables called bwght, faminc, cigs? How would you know? (You may use more than one code to show your answer(s)) Include the output of your code (s). Write the definitions of these variables: bwght, faminc, male, white, motheduc,cigs; which of these variables are categorical? [Hint: use the labels of the variables & the browse command] Who is this dataset about? Who can use this dataset to answer what kind of…arrow_forwardApply STATA commands & submit the output for each question only when indicated below İ. ii. iii. iv. V. Apply the command summarize on variables bwght and faminc. What is the average birthweight of babies and family income of the respondents? Include the output of this code. Apply the tab command on the variable called male. How many of the babies and what share of babies are male? Include the output of this code. Find the summary statistics (i.e. use the sum command) of the variables bwght and faminc if the babies are white. Include the output of this code. Find the summary statistics (i.e. use the sum command) of the variables bwght and faminc if the babies are male but not white. Include the output of this code. Using your answers to previous subparts of this question: What is the difference between the average birthweight of a baby who is male and a baby who is male but not white? What can you say anything about the difference in family income of the babies that are male and male…arrow_forwardA public health researcher is studying the impacts of nudge marketing techniques on shoppers vegetablesarrow_forward
- MATLAB: An Introduction with ApplicationsStatisticsISBN:9781119256830Author:Amos GilatPublisher:John Wiley & Sons IncProbability and Statistics for Engineering and th...StatisticsISBN:9781305251809Author:Jay L. DevorePublisher:Cengage LearningStatistics for The Behavioral Sciences (MindTap C...StatisticsISBN:9781305504912Author:Frederick J Gravetter, Larry B. WallnauPublisher:Cengage Learning
- Elementary Statistics: Picturing the World (7th E...StatisticsISBN:9780134683416Author:Ron Larson, Betsy FarberPublisher:PEARSONThe Basic Practice of StatisticsStatisticsISBN:9781319042578Author:David S. Moore, William I. Notz, Michael A. FlignerPublisher:W. H. FreemanIntroduction to the Practice of StatisticsStatisticsISBN:9781319013387Author:David S. Moore, George P. McCabe, Bruce A. CraigPublisher:W. H. Freeman





