DATA 8 Midterm-Exam-Reg Spring 2021 Midterm-Exam
INSTRUCTIONS
This is your exam. Complete it either at exam.cs61a.org or, if that doesn’t work, by emailing course staff with your
solutions before the exam deadline.
This exam is intended for the student with email address zlyu@berkeley.edu. If this is not your email address,
notify course staff immediately, as each exam is different. Do not distribute this exam PDF even after the exam ends,
as some students may be taking the exam in a different time zone.
For questions with circular bubbles, you should select exactly one choice.

You must choose either this option

Or this one, but not both!

For questions with square checkboxes, you may select multiple choices.
2 You could select this choice.
2 You could select this one too!
You may start your exam now. Your exam is due at 09:00PM Pacific Time. Go to the next page to begin.
Exam generated for zlyu@berkeley.edu 2
For fill-in-the-blank coding questions, there will be a template for you to follow. You should
copy and paste the provided template, then fill in the __ to answer the question.
You can put anything inside the blanks, including commas, parentheses, and periods. Note that
the length of the blank does not necessarily correspond to the length of the code you should
write.
The exam is worth 100 points.
If you encounter any logistical problems during the exam, please contact us at data8berkeley@gmail.com. We
will not be answering any questions related to the contents of the exam.
(a)
Your name:
(b) Your @berkeley.edu email address:
Exam generated for zlyu@berkeley.edu 3
(c) Honor Code: All work on this exam is my own.
By writing your full name below, you are agreeing to this code:
(d) Important: You must type the following statement exactly into the box below. Failure to do so, or simply
copy+pasting it, may result in points deducted on the exam.
“l certify that all work on this exam is my own. l acknowledge that collaboration of any kind is forbidden,
and that l will face severe penalties if l am caught, including at minimum, harsh penalties to my grade and
a letter sent to the Center for Student Conduct.”
Exam generated for zlyu@berkeley.edu 4

1. (20.0 points) Dreams and Nightmares
   Dream is the username of a famous Minecraft speedrunner. Minecraft speedrunners try to win the game as
   quickly as possible. Dream has been accused of modifying his version of the game to increase the probability
   that characters called “piglins” return items called “ender pearls” when the player initiates a trade, a “piglin
   barter”, with the piglins.
   One of the TAs, King, recorded data from six consecutive live streams of Dream playing Minecraft and found
   that 42 of the 252 piglin barters dropped ender pearls.
   King is a Minecraft expert, so he knows that the true probability a piglin returns an ender pearl in the official
   version of Minecraft is 5%.
   Provide a null and alternate hypothesis King can use to test if Dream’s version of Minecraft was modified as
   described.
   (a) (1.0 pt) Null hypothesis:
   (b) (1.0 pt) Alternative hypothesis:
   (c) (4.0 pt) Which of the following are valid test statistics? Variable names are descriptive. Select all that
   apply.
   2 TVD(sample, observed)
   2 num_ender_pearls_in_sample – 42
   2 42/252 – 0.05
   2 abs(proportion_ender_pearls – 0.05)
   2 42 – 0.05*252
   2 proportion_ender_pearls_in_sample – 0.05
   2 num_ender_pearls_in_sample
   2 abs(num_ender_pearls_sample – 42)
   2 proportion_ender_pearls_in_sample
   Exam generated for zlyu@berkeley.edu 5
   (d) (6.0 pt) Copy and paste the following code, then fill it in to perform the hypothesis test correctly. As a
   test statistic, use the number of non-ender pearls in a sample.
   model_proportions = make_array(_,_)
   test_stats = _
   for i in np.arange(10000):
   prop_non_ender_pearls = _
   num_non_ender_pearls = _
   test_stats = _
   observed_stat = _
   (e) (2.0 pt) Write a line of code to calculate the p-value of the test assuming test_stats has been defined.
   p_value = _
   Exam generated for zlyu@berkeley.edu 6
   (f) (4.0 pt) King calculated a p-value of 0%. Which of the following conclusions can he draw? Select all that
   apply.
   2 With a p-value cutoff of 1%, King accepts his alternative hypothesis (from part 2)
   2 Dream cheated by modifying his version of Minecraft to increase the likelihood of piglin trades returning
   ender pearls.
   2 With a p-value cutoff of 1%, King rejects his alternative hypothesis (from part 2)
   2 With a p-value cutoff of 1%, King fails to reject his null hypothesis (from part 1)
   2 With a p-value cutoff of 1%, King can reject his null hypothesis (from part 1)
   2 Because the study was observational, King cannot make any conclusions
   2 It’s statistically unlikely that the version of Minecraft Dream was playing had a 5% likelihood of piglin
   trades returning ender pearls
   2 Dream did not cheat or modify his version of Minecraft
   (g) (2.0 pt) King ran another, separate hypothesis test on another aspect of Dream’s speedrun data and
   generated the following distribution of test statistics (note: this is a completely separate hypothesis test,
   meaning the test statistic could be different than the ones before).
   Which of the following are potential p values he would calculate for that test?
   The observed value is plotted as the red dot on the x-axis and has a value of 255.
   The bins are np.arange(235, 260).
   2 97.5%
   2 99%
   2 4.75%
   2 2%
   2 65%
   2 0%
   Exam generated for zlyu@berkeley.edu 7
2. (8.0 points) Visualizations
   During shelter-in-place, many Data 8 students explored new hobbies. Angela takes a poll about their hobbies
   and puts her findings in the hobbies table. Angela wonders how to visualize the collected data for presentation
   at her next discussion.
   The first few rows of the hobbies table are shown below:
   favorite color favorite hobby hours of sleep wake up time favorite food
   blue baking 7 early crepe
   green running 10 late boba
   purple tv shows 8 late pizza
   blue basketball 7 early mango
   blue hiking 6 both pizza
   . . . (913 rows omitted)
   (a) (1.0 pt) The best visualization to understand the distribution of the top 5 most popular foods in this
   discussion is (Choose only one):

Histogram

Bar Chart

Line Plot

Scatter Plot

(b) (1.0 pt) Given the hobbies table, which methods would you use to help you plot the visualization you
chose in part a? (Select all that apply):
2 .apply
2 .join
2 .pivot
2 .group
2 .sort
2 None of the above
(c) (1.0 pt) The best visualization to understand the association between favorite hobby and wake up time in
this discussion is (Choose only one.):

Overlaid Bar Chart

Scatter Plot

Overlaid Histogram

Bar Chart

Line Plot

Exam generated for zlyu@berkeley.edu 8
(d) (1.0 pt) Which visualization would best display the association between hours of sleep and early or late
wake up time? (Choose only one.)

Overlaid Bar Chart

Overlaid Histogram

Bar Chart

Line Plot

Scatter Plot

(e) (1.0 pt) What visualization is impossible to make without modifying the hobbies table? (Select all that
apply):
2 Line Plot
2 Overlaid Histogram
2 Overlaid Bar Chart
2 Scatter Plot
2 Bar Chart
(f) (1.0 pt) Which of the following variables are categorical? (Select all that apply):
2 Wake up time
2 Favorite hobby
2 Favorite food
2 Hours of sleep
2 Favorite color
(g) (1.0 pt) Select all that are correct:
2 Whether a student attended discussion on a given day is a categorical variable.
2 The size of attendance at a particular discussion section on a given day is a numerical variable.
2 Whether a student attended discussion on a given day is a numerical variable.
2 The size of attendance at a particular discussion section on a given day is a categorical variable.
(h) (1.0 pt) Angela wants to choose a finger food to send to the students in her discussion section. She uses
the level of support (i.e., number of rows in the table) for each favorite food (Bagels, Chicken Nuggets,
Samosas, Trinidad Cod Fritters, and Wontons) as the basis for her selection. Ultimately, she selects the
food option with the most support (favorite).(Select all that apply):
2 Level of support for a food option is a numerical variable.
2 Level of support for a food option is a categorical variable.
2 Favorite food option is a categorical variable.
2 Favorite food option is a numerical variable.
Exam generated for zlyu@berkeley.edu 9

3. (28.0 points) The Ultimate Ubiquitous Uniqlo
   The uniqlo table has 3 columns:

• Store Number: The store number of a Uniqlo store
• Item Number: The item number of a given clothing piece sold at that store
• Quantity: The number of a particular clothing piece at the particular store.
  Store Number Item Number Quantity
  446 25 51
  391 2 17
  446 32 36
  172 25 83
  172 1 52
  . . . (13037 rows omitted)
  The names of the actual Uniqlo stores are contained in the stores table, which has one row per unique store
  and columns for the store number and corresponding store name.
  Store Number Store Name
  1 Marronnier Gate Ginza
  2 New York City 5th Ave.
  . . . (8750 rows omitted)
  The items table similarly contains information about each unique item number. It has columns for the item’s
  corresponding clothing name, the type of clothing (either a top or a bottom) and the clothing style (either
  women’s or men’s). Assume every unique clothing name is available in both women’s and men’s styles.
  Item Number Clothing Name Type Style
  1 Ultra Light Down Jacket top women
  2 Ultra Light Down jacket top men
  3 Crew Neck T-Shirt top men
  4 Classic Straight Leg Jeans bottom men
  . . . (9826 rows omitted)
  (a) (1.0 pt) Write a line of code that outputs the number of unique (store, item) pairs that are possible.
  Exam generated for zlyu@berkeley.edu 10
  (b) (3.0 pt) Katherine wants to combine the data from the three tables into one table that has five columns
  in the following order: Store Name, Clothing Name, Type, Quantity, and Style. Write a line of code to
  create this table and assign it to the name result.
  result = _
  (c) (3.0 pt) Katherine wants to know how much space she is saving by using store numbers in the original
  uniqlo table instead of using the full store names. She writes the following partially completed code to
  calculate the total number of characters across all store names in all rows of result. (e.g. the string “Mc
  Donald’s” has 11 characters)
  num_characters_store_names = _____
  Copy/paste the code above and fill in the blanks.
  Exam generated for zlyu@berkeley.edu 11
  (d) (4.0 pt) Katherine wants to create a ratio function that takes in a store name to return the ratio of the
  number of tops to the number of bottoms at that store. She writes the following partially completed code:
  def ratio(store_name):
  num_tops = __
  num_bots = __
  return __
  Copy/paste the code above and fill in the blanks. You may use the result table in your solution.
  (e) (3.0 pt) Katherine wants to use result to create a tops_bots table that has a column for store names, a
  column for tops, and a column for bottoms. She wants each row to contain the median quantity of tops
  and bottoms for each unique store. Fill out the following code to create and assign this table.
  tops_bots = _
  Exam generated for zlyu@berkeley.edu 12
  (f) (3.0 pt) Katherine wants to create a new_ratio function that takes in a store name to calculate the ratio
  between the number of median tops and median bottoms at the store. She writes the following partially
  completed code:
  def new_ratio(store_name):
  tops_bots_store = ___________
  return _____________________
  Copy/paste the code above and fill in the blanks. You may use the top_bots table in your solution.
  (g) (3.0 pt) Using the function you just wrote, create a new two-column table called store_ratios that has
  one row for each store name and a column called “Tops to Bottoms” with the median top to bottom ratio.
  store_ratios = __________
  (h) (1.0 pt) Write a line of code to visualize the distribution of median top to bottom ratios.
  Exam generated for zlyu@berkeley.edu 13
  (i) (3.0 pt) Write a line of code to return the unique clothing name of a specific style that has the highest
  total quantity across all Uniqlo stores.
  (j) (4.0 pt) Katherine wants to create an array containing the differences between the average quantity of
  women’s and men’s styles for each unique clothing piece in the result table. She writes the following
  partially completed code:
  all_averages = __

Copy/paste the code above and fill in the blanks.
Exam generated for zlyu@berkeley.edu 14

4. (11.0 points) WandaVision vs Queen’s Gambit
   Alvin surveyed Data 8 staff members about how much time they spend on various streaming platforms each
   month. The table, streaming, has two columns, “service” and “time”, and a few rows are shown below. Each
   TA was asked for their watch time (in hours) for Disney+ and Netflix, and then the table was reordered to
   preserve anonymity. There are 35 staff members recorded in the sample, and 2 streaming services, so there are
   a total of 70 rows.
   service time
   Netflix 15
   Netflix 12
   Disney+ 8
   Netflix 14
   Disney+ 2
   Disney+ 8
   Disney+ 2
   Netflix 3
   . . . (62 rows omitted)
   Alvin wants to know if staff members watch Netflix more than they watch Disney+. Alvin asks Sophia to help
   him to test this claim.
   Define a null and alternative hypothesis for this test.
   (a) (2.0 pt) Null Hypothesis:
   (b) (2.0 pt) Alternative Hypothesis:
   Exam generated for zlyu@berkeley.edu 15
   (c) (3.0 pt) Which of the following could be valid simulated test statistics to test these hypotheses? Select all
   that apply.
   2 The number of TAs in a copy of streaming with shuffled labels who watched Netflix more than they
   watched Disney+, minus 10
   2 The median value of Netflix stream time – the median value of Disney+ stream time in a copy of
   streaming with shuffled labels
   2 The number of TAs in the streaming table who watched Netflix more than they watched Disney+
   2 The number of TAs in a copy of streaming with shuffled labels who watched Netflix more than they
   watched Disney+
   2 The median value of Netflix stream time – the median value of Disney+ stream time in the streaming
   table
   2 The number of TAs in the streaming table who watched Netflix more than they watched Disney+,
   minus 10
   (d) (3.0 pt) Which of the following are valid ways of shuffling labels for this hypothesis test? Note:
   np.random.choice(arr, n, replace=False) returns n samples from arr without replacement. Select all
   that apply.
   2 shuffled_table = streaming.sample()
   2 shuffled_table = streaming.sample(with_replacement=False)
   2 shuffled_labels = streaming.sample().column(“time”)
   shuffled_table = streaming.with_column(“time”, streaming.column(“time”))
   2 shuffled_labels = streaming.sample(with_replacement=False).column(“time”)
   shuffled_table = streaming.with_column(“time”, streaming.column(“time”))
   2 shuffled_labels = streaming.sample(with_replacement=False).column(“service”)
   shuffled_table = streaming.with_column(“service”, shuffled_labels)
   2 shuffled_column = streaming.take(np.random.choice(np.arange(streaming.num_rows), 35, replace=False).column(“time”)
   shuffled_table = streaming.with_column(“time”, shuffled_column)
   2 shuffled_table = streaming.sample(with_replacement=False)
   disney_plus_rows = shuffled_table.take(np.arange(34)).select(“time”)
   netflix_rows = shuffled_table.take(np.arange(35, 70)).select(“time”)
   (e) (1.0 pt) Can Alvin use his hypothesis test to make claims about Data 8 students?

No, because Data 8 staff are a convenience sample and might not represent Data 8 students.

Yes, because the experiment is not making any claims about cause and effect, so it doesn’t need to be

a randomized control trial.

No, because the experiment is not a randomized control trial.

Yes, because Data 8 staff are a random sample.

Exam generated for zlyu@berkeley.edu 16

5. (10.0 points) TikTok Data 8 O’Clock
   The Data 8 team has just launched a TikTok account.
   You may tackle each of Parts I and II in either order.
   (a) Part I
   i. Four members of the staff — Carlos, Natalie, Parham, and Stephanie — have auditioned to perform
   an activity in a promotional TikTok video for Data 8. Prof. Sahai will select exactly one of the four
   auditioners at random (with equal probability). The selected auditioner then selects exactly one
   activity at random (with equal probability) — from among acting, dancing, and singing — to perform
   in the video.
   For each of the following problems, express your answer as a Python expression (e.g., 1/8 + 1/9).
   If there’s not enough information to answer the question, write “N/A”
   A. (1.0 pt) Determine the probability that Stephanie is selected to perform, and they choose to sing
   in the video.
   B. (1.0 pt) Determine the probability that Stephanie is selected to perform, but they choose not to
   sing in the video.
   C. (1.0 pt) Prof. Sahai did not select Parham to perform in the video. Determine the probability
   that Stephanie was selected.
   Exam generated for zlyu@berkeley.edu 17
   (b) Part II
   The course staff decide to release a TikTok video at the beginning of every week of the semester, for a
   total of fourteen (14) weeks. Each video has an 19% chance of going viral in each of the first 24 hours
   after its release. Thereafter, it has no chance of going viral.
   i. (2.0 pt) Determine the probability that none of the fourteen videos goes viral within 24 hours of
   release.
   ii. (2.0 pt) After seeing the Data 8 team transition to a position of social-media influence, the CS 61a
   course staff turn jealous and decide to pirate Data 8 TikTok videos.
   There is a 11% chance that the CS 61a staff copy three (3) or more Data 8 TikTok videos, a 17%
   chance that they copy exactly two (2) Data 8 TikTok videos, and a 58% chance that they do not
   pirate (copy) any TikTok video from Data 8.
   Determine the probability that the CS61a staff copy exactly one Data 8 TikTok video. Express your
   answer as a percent.
   iii. (3.0 pt) To attract future students to Data 8, Babak commits to performing an entire lecture as
   Gollum, if each of the fourteen (14) Data 8 TikTok videos reaches the “For You” page, or if at least
   one of the Data 8 TikTok videos gets over ten million views.
   Each video has a 40% chance of reaching the “For You” page. Moreover, and independently, each video
   has a 7% chance of getting over ten million views.
   Determine the probability that Babak must deliver on his promise to conduct an entire lecture as
   Gollum.
   Exam generated for zlyu@berkeley.edu 18
6. (12.0 points) Programming in Python
   For each question below, write Python code to answer the question using what we have taught you in this
   class. If we run your Python code, it should evaluate to the answer to the question.
   (a) (2.0 pt) Fill in the following code to create a 5 element array such that np.count_nonzero and sum called
   on the array will return the same value.
   make_array(_)
   (b) (2.0 pt) Fill in the following code to create a 5 element array such that np.count_nonzero and sum called
   on the array will return different values.
   make_array(_)
   (c) (2.0 pt) Using only one line of Python code, construct an array called squaredincrsthatcontainsthesuccessiveincrements(increases)inthesequenceofsquaresof thef irsttenpositiveintegers :
   1
   2
   , 2
   2
   , 3
   2
   , …, 102 For example, the increment from 1
   2 to 2
   2 is 3.
   (d) (2.0 pt) Consider an array, called banking, that contains the values of daily deposits to
   a bank account. Write a single line of Python code that constructs an array that contains
   the successive daily balances of the bank account after each deposit. The bank account’s
   starting balance is $25,300.
   (e) (2.0 pt) To which function is the mystery function below equivalent?
   def mystery(arr):
   a = 0
   for item in arr:
   if item != 0:
   a = a + 1
   return a
   Exam generated for zlyu@berkeley.edu 19
   (f) (2.0 pt) The following function foo takes in an array as an argument. What does the following
   function do?
   def foo(input_arr):
   arr = make_array()
   length_input = len(input_arr)
   for index in np.arange(length_input):
   arr = np.append(arr, input_arr.item(length_input-index-1))
   return arr
   Exam generated for zlyu@berkeley.edu 20
7. (13.0 points) Wall Street Bets
   Brett is interested in investing his hard-earned money by buying stocks. His friend Sunny proposes that he does
   some research and data analysis before he believes all the deep dives that he read about on Reddit.
   Right before the stock market closes, Brett collects the daily price data in the table stocks, where each row
   represents one company. Here is a snapshot:
   Symbol Open High Low Close Volume Percent Change %
   GME 128.17 151.53 127.50 137.74 30,733,670 0.407
   BB 9.80 9.85 8.82 9.45 23,723,400 -0.0396
   AMC 8.08 8.27 7.63 8.05 59,734,129 0.0025
   AMD 79.00 79.48 74.20 78.52 58,548,910 0.0099
   TSLA 626.06 627.84 539.49 597.95 89,396,461 -0.0378
   . . . (13851 rows omitted)
   The table contains the following columns:

• Symbol: The abbreviation that denotes a specific company or index (such as the S&P 500 index, which
  consists of a basket of specific stocks)
• Open/Close: The price of one stock unit at the opening/closing of the market (US$)
• High/Low: The highest/lowest price of one stock unit during the day (US$)
• Volume: The number of stock units traded during the day
• Percent Change: The percentage change, from the the prior-day’s close to the current-day’s close (%)
  Brett decides that the best way to analyze the riskiness of a company’s stock is through finding the difference
  between the high and the low of the day, also known as the day’s range.
  Brett’s other friend Natalie argues that he also needs to take into account the distribution of percentage change.
  The histogram looks as follows:
  Exam generated for zlyu@berkeley.edu 21
  (a) (1.0 pt) Natalie wants to know the total percentage of companies for which the stock prices did not change
  by more than 5%. Select the percentage corresponding to this quantity.

30%

10%

50%

90%

(b) (1.0 pt) Sunny realizes that the majority of the companies fall within this small range. It is important
that we make the bins smaller to get a better understanding. We want to divide the bin [0,5) up into three
bins: [0, 1), [1, 3) and [3, 5).
Bin % Within Original [0,5) Bin
[0,1] 25%
[1,3) 70%
[3, 5) 5%
Given the heights (A) 2.5, (B) 12.5, and (C) 17.5, order the heights from left to right to match the order of
the 3 bins above.

A, B, C

A, C, B

B, C, A

B, A, C

(c) (1.0 pt) Kevin tries to help them create a new histogram with the smaller bins, but he has never taken
Exam generated for zlyu@berkeley.edu 22
Data 8. He messes up the histogram by incorrectly specifying the bins argument. Which of the following
graphs could he have generated, given the data above? Select all that apply.
2
2
2
2
(d) (5.0 points)
The four of them together discover an anonymous post on Reddit that claims to have more data about the
absolute value of percentage change in stocks that is not publicly known. However, this post requires them
to solve a puzzle by piecing together a bar chart and table to see the full histogram. Fill in the table below
using the bar chart. (Note: Treat Bin Number as a categorical variable.)
Exam generated for zlyu@berkeley.edu 23
Exam generated for zlyu@berkeley.edu 24
Bin Number Bin Range Height
1 [0, 2.5) a
2 b 10
3 c 10
4 [10,15) d
5 e 2
i. (1.0 pt) a (your answer should be a single number)
ii. (1.0 pt) b (your answer should be a range in the format [x, y))
iii. (1.0 pt) c (your answer should be a range in the format [x, y))
iv. (1.0 pt) d (your answer should be a single number)
v. (1.0 pt) e (your answer should be a range in the format [x, y))
Exam generated for zlyu@berkeley.edu 25

8. (0.0 points) Last Words
   (a) If there was any question on the exam that you thought was ambiguous and required clarification to be
   answerable, please identify the question (including the title of the section, e.g., Visualizations) and state
   your assumptions. Be warned: We only plan to consider this information if we agree that the question was
   erroneous or ambiguous and we consider your assumption reasonable.
   Exam generated for zlyu@berkeley.edu 26
   No more questions.

https://www.data8.org/