*Give all numerical answers to two decimal places.
The speeds of vehicles (in km/h) for a sample of 22 cars driving down a particular road are as follows:
|
52.2
|
64
|
68.4
|
50.1
|
80.3
|
61
|
79.3
|
55.4
|
86.2
|
54.9
|
68.1
|
|
57.9
|
25.9
|
63.6
|
54.2
|
70.3
|
50.9
|
85.7
|
61.7
|
31.5
|
67.1
|
59.8
|
Left- tail pre 28.3, right tail pre 17.8
Left tail post 4.1, Right tail post: 17.8
a) Find the five-number summary for this data set. (Find the answers by hand, not using JMP, which calculates the quartiles slightly differently.)
b) Create a basic (quantile) boxplot for this data set. You do not need to attach it to this assignment. What appears to be the shape of the data distribution of speeds on this road?
• Approximately symmetric
• Skewed to the right
• Skewed to the left
c) If you constructed a modified (outlier) boxplot for this data set, a data value would be labelled as suspected outlier if it was less than Correct answer: or greater than Correct answer: .
d) How many outliers are contained in this data set?
(e) Create a modified (outlier) boxplot for this data set. You do not need to attach it to this assignment. What is the actual shape of the data distribution of speeds on this road (excluding outliers)?
• Skewed to the left
• Approximately symmetric
• Skewed to the right
Question 1
A stock analyst randomly selected stocks in each of two industries (Consumer Goods and Technology) and compiled the one-year percentage return for each stock. The data are shown in the table below. Note that a negative return represents a stock that lost money over the course of the year.
Consumer Stocks
3.7 9.2 5.8 13.6 -1.1 3.8 14.9 6.2 11.1 -2.6 8.7 0.4 10.0
Technology Stocks
4.8 20.9 -10.6 7.7 13.8 -18.6 10.4 18.4 22.6 12.3 -27.5 5.9 16.3 29.5 -5.4 2.6 12.3
(a) Using JMP, create side-by-side boxplots comparing the distributions of returns for the two sectors. To do this, create a new data table with two columns called Return and Sector. In the first column, enter all 30 returns (first the 13 Consumer Goods returns and then the 17 Technology returns). In the second column, type "Consumer" in the first 13 cells and "Technology" in the next 17 cells. Go to Analyze > Fit Y by X. Choose Return as Y and Sector as X. Click OK. Now, under the red arrow, select Quantiles. Also under the red arrow in Display Options, remove the points and the line for the grand mean. Attach your graph to your assignment.
***NOTE: You MUST follow the proper instructions for attaching an image to your assignment. Copying and pasting the image or dragging and dropping it WILL NOT WORK. (It will show up in your window, but when you submit your assignment, the marker will NOT be able to see it.)
(b) Compare the two distributions with respect to center, shape and spread.
(c) Based on these data, give one reason an invester might prefer to invest in Technology stocks rather than Consumer Goods stocks.
(d) Based on these data, give one reason an investor might prefer to invest in Consumer Goods stocks rather than Technology stocks.
Question 2
The total energy consumption (in kWh) for the month of April 2013 is shown below for a sample of 28 houses in Winnipeg:
|
573
|
466
|
622
|
539
|
480
|
653
|
512
|
784
|
438
|
541
|
592
|
482
|
605
|
553
|
|
492
|
733
|
536
|
428
|
545
|
477
|
624
|
510
|
672
|
434
|
581
|
506
|
570
|
487
|
(a) Construct a stemplot (with split stems) for this data set. (Type the stemplot yourself - don't use JMP.) To get a "nice" looking stemplot, before you split the stems, you should first trim the leaves. For example, the data value 539 will be trimmed to 53 and should be represented in the stemplot as 5|3.
(b) What is the shape of the data distribution?
(c) Use JMP to construct a histogram (in horizontal layout) for this dataset. To do this, enter the data in a column titled "Energy". Go to Analyze > Distribution. Click Energy, then Y, Columns and OK. Under the red arrow, you can remove the boxplot and numerical summaries leaving only the histogram, but this isn't necessary. Now attach the histogram to your assignment.
(d) Would it be more appropriate to summarize this data distribution with the five-number summary or with the mean and standard deviation? Explain.
(e) The average daily energy consumption for one home in Winnipeg is shown below for each month in 2011 and 2012:
|
Jan
2011
|
Feb
2011
|
Mar
2011
|
Apr
2011
|
May
2011
|
Jun
2011
|
Jul
2011
|
Aug
2011
|
Sep
2011
|
Oct
2011
|
Nov
2011
|
Dec
2011
|
|
40.2
|
37.1
|
28.8
|
17.9
|
9.3
|
7.8
|
5.7
|
5.2
|
8.7
|
18.1
|
26.9
|
35.8
|
|
Jan
2012
|
Feb
2012
|
Mar
2012
|
Apr
2012
|
May
2012
|
Jun
2012
|
Jul
2012
|
Aug
2012
|
Sep
2012
|
Oct
2012
|
Nov
2012
|
Dec
2012
|
|
39.6
|
38.2
|
29.3
|
19.4
|
10.6
|
8.8
|
6.2
|
5.0
|
9.9
|
15.4
|
28.2
|
38.7
|
Use JMP to construct a timeplot of the data. Enter the data in a new column called Monthly Energy. Under the Analyze menu, select Modeling > Time Series. Click Monthly Energy, then Y, Time Series and OK. Click the red arrow, uncheck the Autocorrelation and Partial Autocorrelation options. Click the red arrow again and go to Graph and uncheck mean line. Now attach the graph to your assignment. arrow, uncheck the Autocorrelation and Partial Autocorrelation options. Click the red arrow again and go to Graph and uncheck mean line. Now attach the graph to your assignment.
(f) Describe the overall trend you see on the timeplot.