
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,
(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
- Examine the Variables: Carefully review and note the names of all variables in the dataset. Examples of these variables include: Mileage (mpg) Number of Cylinders (cyl) Displacement (disp) Horsepower (hp) Research: Google to understand these variables. Statistical Analysis: Select mpg variable, and perform the following statistical tests. Once you are done with these tests using mpg variable, repeat the same with hp Mean Median First Quartile (Q1) Second Quartile (Q2) Third Quartile (Q3) Fourth Quartile (Q4) 10th Percentile 70th Percentile Skewness Kurtosis Document Your Results: In RStudio: Before running each statistical test, provide a heading in the format shown at the bottom. “# Mean of mileage – Your name’s command” In Microsoft Word: Once you've completed all tests, take a screenshot of your results in RStudio and paste it into a Microsoft Word document. Make sure that snapshots are very clear. You will need multiple snapshots. Also transfer these results to the…arrow_forward2 (VaR and ES) Suppose X1 are independent. Prove that ~ Unif[-0.5, 0.5] and X2 VaRa (X1X2) < VaRa(X1) + VaRa (X2). ~ Unif[-0.5, 0.5]arrow_forward8 (Correlation and Diversification) Assume we have two stocks, A and B, show that a particular combination of the two stocks produce a risk-free portfolio when the correlation between the return of A and B is -1.arrow_forward
- 9 (Portfolio allocation) Suppose R₁ and R2 are returns of 2 assets and with expected return and variance respectively r₁ and 72 and variance-covariance σ2, 0%½ and σ12. Find −∞ ≤ w ≤ ∞ such that the portfolio wR₁ + (1 - w) R₂ has the smallest risk.arrow_forward7 (Multivariate random variable) Suppose X, €1, €2, €3 are IID N(0, 1) and Y2 Y₁ = 0.2 0.8X + €1, Y₂ = 0.3 +0.7X+ €2, Y3 = 0.2 + 0.9X + €3. = (In models like this, X is called the common factors of Y₁, Y₂, Y3.) Y = (Y1, Y2, Y3). (a) Find E(Y) and cov(Y). (b) What can you observe from cov(Y). Writearrow_forward1 (VaR and ES) Suppose X ~ f(x) with 1+x, if 0> x > −1 f(x) = 1−x if 1 x > 0 Find VaRo.05 (X) and ES0.05 (X).arrow_forward
- Joy is making Christmas gifts. She has 6 1/12 feet of yarn and will need 4 1/4 to complete our project. How much yarn will she have left over compute this solution in two different ways arrow_forwardSolve for X. Explain each step. 2^2x • 2^-4=8arrow_forwardOne hundred people were surveyed, and one question pertained to their educational background. The results of this question and their genders are given in the following table. Female (F) Male (F′) Total College degree (D) 30 20 50 No college degree (D′) 30 20 50 Total 60 40 100 If a person is selected at random from those surveyed, find the probability of each of the following events.1. The person is female or has a college degree. Answer: equation editor Equation Editor 2. The person is male or does not have a college degree. Answer: equation editor Equation Editor 3. The person is female or does not have a college degree.arrow_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





