CS 112 Assignment 2

Due: Thursday, February 16, at the beginning of class

You can turn in your assignment up until 5:00pm on 2/16/11 without penalty, but it is best to hand in the assignment at the beginning of class. Your hardcopy submission should include a cover sheet and printouts of five code files: lab3.m, redsox.m, colonTest.m, smartPhones.m and analyzeData.m. Your electronic submission is described in the section Uploading your saved work. (If you'd like to save paper, you can cut and paste all of your code files into one script, but your electronic submission should contain the five separate files.)

Reading

Getting Started: Download assign2_programs from cs112d

Uploading your saved work

• Browse through your directory and find the drop/assign02 folder
• Upload your assign2_programs folder (that you renamed) into your drop/assign02 folder
• When done uploading, be sure to delete your renamed assign2_programs folder from the Desktop by dragging it to the trash can, and then empty the trash (Finder--> Empty Trash).
• Be sure to Exit out of MATLAB when you are done

When you are done with this assignment, you should have five code files stored in your assign2_programs folder: lab3.m, redsox.m, colonTest.m, smartPhones.m, analyzeData.m.

Exercise 1: Practice with conditional expressions

Create a new file in MATLAB called lab3.m (that you will turn in). Make sure your current directory is set appropriately.

In lab3.m, first use MATLAB's input function to prompt the user for three pieces of information: 1) a numerical month (between 1 and 12), 2) a day (between 1 and 31) and 3) the user's name. Store each of these values in a variable (e.g. month is 7 (for July), day is 28 and name is 'Rosa'). To prompt the user for a string, provide a second input 's' when calling the input function:

name = input('Enter your name: ', 's');   % name is a string

Then write MATLAB expressions that correspond to the following:

1. Create a variable valentine that is true on February 14 and false otherwise.
   
2. Create a variable cs112midterm that is true on February 23 and April 5 and false otherwise.
   
3. Create a variable springBreak that is true between March 17 and March 25 (inclusive).
   
4. Create a variable luckyDay that is true if the month and day are both odd or both even, and false otherwise.
5. If month and day are your birthday, then print out a personalized birthday greeting such as "Happy Birthday to Sohie!", otherwise print "Not Sohie's birthday". The disp function can be used to print text that combines literal strings with variables whose value is a string:

   >> place = 'SCI 160a';
   >> disp(['class will be held in ' place ' today']);
   class will be held in SCI 160a today

6. If month is December, January or February, then print the lyrics of the first stanza of the song, "Frosty the Snowman" (on four separate lines), otherwise print a message of your choosing (this can be a single line).

   Frosty the Snowman was a jolly happy soul,    With a corncob pipe and a button nose and two eyes made out of coal.    Frosty the Snowman is a fairy tale they say,    He was made of snow but the children know how he came to life one day.

Exercise 2: The Red Sox roster

In this exercise, you'll work with the following subset of data from the Boston Red Sox baseball team roster from the 2007 (World Series winning!) season:

Player Name	Player Number	Weight	At Bats	Home Runs	Batting Average	2007 Salary	Runs Batted In	Runs	Stolen Bases
Jason Varitek	33	230	435	17	.255	11,000,000	68	57	1
David Ortiz	34	230	549	35	.332	13,250,000	117	116	3
Manny Ramirez	24	200	483	20	.296	17,016,381	88	84	0
J.D. Drew	7	200	466	11	.270	14,400,000	64	84	4
Mike Lowell	25	210	589	21	.324	9,000,000	120	79	3
Julio Lugo	23	175	570	8	.237	8,250,000	73	71	33
Kevin Youkilis	20	220	528	16	.288	424,500	83	85	4
Coco Crisp	10	180	526	6	.268	3,833,333	60	85	28
Dustin Pedroia	15	180	520	8	.317	380,000	50	86	7

Generating some Red Sox statistics:

>> powerHitter = names(homeRuns > 20)
powerHitter =
     'Ortiz'   'Lowell'

Note that you can place a semi-colon at the end of the initial assignment statements in redsox.m to suppress the printout of the statistics.

In the exercise below, you may use MATLAB's   mean, sum, length, and any.

Write MATLAB code to do the following:

1. Create a variable totalStolen with the total number of stolen bases in 2007.
2. Create a variable avgWt with the average weight of a Red Sox player.
3. Create a variable bestBatters with the name(s) of player(s) whose batting average is greater than or equal to 0.300.
4. Create a variable expensiveHomer that is true if any player costs more than $500,000 per homerun.
5. Create a variable bigHitter that is true if any players hit more than 10 homeruns with batting averages less than .290.
6. Create a vector highRBI with the name(s) of player(s) whose Runs Batted In is greater than or equal to Runs.
7. Create a variable bigBatter that contains the number(s) of the player(s) with more than 550 at bats or more than 20 stolen bases.
8. Create a variable weightInGold that contains the number of players who are paid more than $25,000 per pound of body weight in the 2007 season.

Add comments to your code so that it is clear and easy to read. Always include your name and date at the top of each file. Save your final version of redsox.m in your assign2_programs folder to upload to the cs server.

Exercise 3: Indexing with colon notation

In lecture you learned how to use colon notation to specify a sequence of regularly spaced numbers. You also learned how to use indexing to read and store values in specific locations of a vector. This exercise combines these two concepts. Colon notation can be used to specify an evenly spaced sequence of vector indices or contents, as shown in the following examples:

>> nums = 1:8
nums = 
  1   2   3   4   5   6   7    8
>> nums(1:2:5) = 10
nums = 
  10   2   10    4   10   6   7   8
>> nums(2:3:8) = [13 9 16]
nums =
  10   13   10   4   9    6   7   16
>> nums2 = nums([1:3 6:8])
nums2 =
  10   13   10   6   7   16
>> nums([1:3 6:8]) = 12:-2:2
nums =
12   10   8   4   9   6   4   2

The following program, colonTest.m is contained in your assign2_programs folder. Follow the instructions in the comments to rewrite the existing code statements and add five additional statements that use colon notation:

% colonTest.m
% program that provides practice with colon notation and indexing

% rewrite each of the next 4 statements using colon notation
nums1 = [10 9 8 7 6 5 4 3 2 1]
nums2 = nums1([2 4 6 8 10 7 4 1])
nums1([3 4 5 6]) = [9 6 3 0]
nums3 = [1 2 3 1 2 3 1 2 3]

% replace the next 3 statements with a single assignment statement
% that uses colon notation
nums2(6) = 10
nums2(7) = 20
nums2(8) = 30

% for each of the following examples, use "end" in the colon
% notation, for example: nums8 = nums1(3:end)

% write a statement that assigns nums4 to a vector that contains
% the odd-indexed elements of nums1

% write a statement that assigns nums5 to a vector of the
% elements contained in the top half (higher indices) of nums2

% write a statement that assigns nums6 to a vector that contains
% every 3rd element of nums1, starting with index 2

% write a statement that places the value 0 in all of the 
% evenly indexed locations of nums2

% write a statement that places the numbers 8 12 16 20 in the 
% successive odd-indexed elements of nums2

If you write each code statement with no semi-colon at the end, so that the value generated is printed out during execution of the code, then your program should generate the following printout:

>> colonTest
nums1 =
  10  9  8  7  6  5  4  3  2  1
nums2 =
   9  7  5  3  1  4  7  10
nums1 =
  10  9  9  6  3  0  4  3  2  1
nums3 =
   1  2  3  1  2  3  1  2  3
nums2 =
   9  7  5  3  1  10  20  30
nums4 =
  10  9  3  4  2
nums5 =
   1  10  20  30
nums6 =
   9  3  3
nums2 =
   9  0  5  0  1  0  20  0
nums2 =
   8  0  12  0  16  0  20  0

Place comments at the top of your file with your name and date. Your final submission should include a copy of your final colonTest.m code file.

Problem 1: Smartphones

With her curiosity piqued by a couple recent surveys on trends in the smartphone market and use of smartphones by healthcare professionals, Wendy Wellesley decided to collect some data on smartphone preferences and uses among Wellesley students. Wendy conducted a survey of smartphone owners with the following questions:

• Which brand of smartphone do you own? (1) Apple iPhone, (2) Google Android, (3) T-Mobile Blackberry, (4) Other
• If you were to buy a new smartphone in the next 6 months, which brand would you buy? (1) Apple iPhone, (2) Google Android, (3) T-Mobile Blackberry, (4) Other
• How many minutes per day do you spend doing the following activities on your smartphone: talking? texting? doing e-mail? using the internet? listening to music? playing games?

The file smartPhones.m in your assign2_programs contains Wendy's survey data. The file creates two vectors, currentPhones and newPhones that contain the integers 1-4 indicating the smartphone brand owned and desired by each of the 150 students who completed the survey. The file also creates six vectors that each contain the number of minutes per day spent on each smartphone activity, for each survey participant.

Add code to the smartPhones.m code file to perform the following tasks:

• Display two bar graphs showing the percentage of each brand currently owned (iPhone, Android, Blackberry, other) and percentage of each brand that students would buy in the future
• Display a third bar graph showing the average number of minutes per day spent on each of the six smartphone activities
• Print three messages to the user indicating whether the percentage of iPhones, Androids and Blackberries would increase or decrease

To complete these tasks, consider the following background, tips and guidelines:

• The bar function can be used to create a bar graph, as shown in the example below that displays the party affiliations of Massachusetts voters. This example prints strings on the X axis using the XTickLabel property. The three strings are stored in a cell array, designated by the surrounding curly braces {}, similar to the names of the Redsox players in Exercise 2. The final statement sets the Position property for the current figure window, which allows the user to specify the location and dimensions of the figure window. The four numbers in the vector [100 100 500 250] specify, in order, the distance from the left side of the figure window to the left side of the computer screen, the distance from the bottom of the figure window to the bottom of the screen, the width and the height of the window.

  >> voterParty = [37.1 11.4 51.2];
  >> bar(voterParty)
  >> set(gca, 'XTickLabel', {'Democrats' 'Republicans' 'Independents'})
  >> ylabel('% of registered voters')
  >> title('Party Affiliation of Massachusetts Voters')
  >> set(gcf, 'Position', [100 100 500 250])

  

  In your code, the zeros function can be used to create a vector to store the percentages of iPhones, Androids, Blackberries and other smartphones, and the percentages of each brand can then be calculated and stored in each location of the vector.

• Use subplot, described here, to display the three bar graphs in one figure window in 3 x 1 configuration.
• Create two vectors to store (1) the percentage of each phone brand currently in use and (2) the percentage of each phone brand that students will buy in the future. Your program should calculate these percentages and use them to determine whether the percentage of each phone type will increase or decrease.

• For each of the three main phone brands, print a message something like this:

  iPhones would decrease from 46% to 34%

  Remember that numbers need to be converted to strings when using disp:

  >> slugs = 32.15;
  >> disp(['there are ' num2str(slugs) ' slugs in a pound']);
  there are 32.15 slugs in a pound

Your final submission should include a copy of your final smartPhones.m code file.

Problem 2: Cleaning up the data

Unreliable measurement instruments or unpredictable environments can sometimes yield data that is clearly erroneous. To obtain a reliable assessment of simple properties like the mean value of the data, it may be desirable to remove data samples that are clearly outside the expected range. Such samples are sometimes referred to as outliers. An advantage to analyzing data in MATLAB, with its general programming language, is that we can easily write a program to preprocess the data in a customized way. In this problem, you will complete a program that removes outlying data samples, using the mean and standard deviation of the data.

Imagine that you collected sonar data on the depth of the ocean floor over a large region that is essentially flat. Due to instrument problems and the occasional large marine animal, some measurements are clearly invalid. For simplicity, assume that all of the erroneous measurements are underestimates of the true depth of the ocean floor. The file analyzeData.m in your assign2_programs folder uses the load command to load 1000 depth measurements from a file named depthData.mat into a vector named depthData, and creates a plot of this initial data:

Most of the data is at a depth of around 10,000 feet. The erroneous data samples appear as downward spikes in the data, at depths that are significantly less than 10,000 feet. One principled way to go about removing outlying data is to remove samples whose value is far from the mean value, using the standard deviation to determine the range of values to remove. The standard deviation captures how spread out the data values are, and is given by the following formula:

N is the number of samples in the data, v_i is the i^th data sample, and v is the mean value of the data. If the distribution of the data follows a bell-shaped curve (which is not really the case here), almost all of the data should lie within three standard deviations of the mean value (see here for more information).

For the ocean floor depth data, we could just remove all samples that are more than three standard deviations away from the mean depth value. A problem with this strategy is that an initial calculation of the mean and standard deviation of all of the data will be biased by the presence of the outlying data samples. Thus, we will instead use a more conservative approach that removes data in two stages, as described in the following steps, which also print, display and save the data:

1. calculate and print the mean and standard deviation of the original data
2. modify the data so that samples whose value is more than 4 standard deviations away from the mean value are removed
3. calculate and print the mean and standard deviation of the modified data, and plot the modified data
4. ask the user if she would like to remove more outliers from the data. If so,
   • 4a. modify the data again so that samples whose value is more than 3 standard deviations away from the mean are removed, using the newly calculated mean and standard deviation from step 3
   • 4b. calculate and print the mean and standard deviation of the newly modified data, and plot this new data
5. save the final modified data and its mean and standard deviation in a file named newData.mat

Expand the analyzeData.m code file to perform the above steps. When completing this program, keep in mind the following background, tips and guidelines:

• The built-in mean function can be used to calculate the mean value of the data, but you must compute the standard deviation using the above formula. It is OK to use the built-in std function to check your calculation - you should obtain similar results. Keep in mind that the number of samples in the data changes after each modification.
• Logical vectors can be used to represent the locations of values in a vector that satisfy a certain logical condition. Steps 2 and 4a describe which data values to remove - how can you rephrase these steps to describe which data values to preserve? This will facilitate your thinking about how to construct a logical vector that has a 1 in locations of data to preserve.
• Create two variables to store the mean and standard deviation of the original data stored in the depthData vector, and re-use these two variable names to store the new mean and standard deviation in steps 3 and 4b. When modifying the data in steps 2 and 4a, re-use the same variable name, depthData.
• Calculating the standard deviation and the modified data each involve multiple conceptual steps. Try to incorporate all of these steps into a single assignment statement for each of these two variables. Be careful about the placement of parentheses in these statements!
• The values of variables can be printed by omitting the semi-colon at the end of assignment statements or by using disp.
• When asking the user whether more outliers should be removed, assume that the user replies with a string, such as yes or no. Two strings can be compared with the strcmp function that returns true (logical value 1) if the two strings are equal:

  name = input('Enter your name: ', 's');
  if strcmp(name, 'Sohie')
      disp('I know you! You''re our Lab Instructor!')
  else
      disp('I don''t know you')
  end

• Click here for information about using .mat files to store and retrieve variables using save and load.
• Multiple plots can be displayed within a single figure window using the subplot function, described here. The analyzeData.m code file contains a call to subplot that specifies that the figure window should have one row of three plotting areas, and that the first plot should appear in the leftmost area. Use subplot to place the plot of the intermediate data in the center plotting area and the final data (if further analysis is requested by the user) in the rightmost area. You can expand the window in the horizontal direction by dragging the borders of the window horizontally. Note that the range of values plotted on the axes will differ for the three plots.
• Place comments at the beginning of the code file with your name and date, and place a few comments throughout your program briefly describing what is accomplished by small groups of code statements.
• At the end of your program, add comments that record the values of the mean and standard deviation after steps 1, 3, and 4b, and answer the following question: How did the mean and standard deviation change between the initial, intermediate and final data, and why did these quantities change in this way?

Your final submission should include a copy of your final analyzeData.m code file.