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Instructor(s): Janine Tiefenbruck

This exam was administered in-person. Students were allowed one page of double-sided handwritten notes. No calculators were allowed. Students had 50 minutes to take this exam.

Note (groupby / pandas 2.0): Pandas 2.0+ no longer silently drops columns that can’t be aggregated after a groupby, so code written for older pandas may behave differently or raise errors. In these practice materials we use .get() to select the column(s) we want after .groupby(...).mean() (or other aggregations) so that our solutions run on current pandas. On real exams you will not be penalized for omitting .get() when the old behavior would have produced the same answer.

A college mascot is a costumed character that represents the school at athletic competitions and other major campus events. For example, you might see UCSD’s mascot, King Triton, at basketball games and the upcoming Sun God Festival.

College students can apply to serve as the mascot for their school, which is quite competitive! Applicants usually need to fall within a certain height range to fit the costume. Throughout this exam, we will format heights in feet and inches, for example "5ft 7in" or "6ft", omitting inches when the height is a whole number of feet, as in the second example. Recall that there are 12 inches in one foot.

The DataFrame mascots has one row for every college or university in the US with a named mascot. The columns are:

• "school" (str): The name of the school. This column has no repeated values.
• "mascot" (str): The name of the school’s mascot.
• "type" (str): Mascot category, either "human", "animal", or "other".
• "height" (str): The range of heights that fit into the mascot costume. Values consist of two heights, formatted as described above, separated by " - ".
• "team" (str): The general name of the school’s athletic team.
• "colors" (list): A list of the school colors. Each school has at least one school color.

The first few rows of mascots are shown below, though mascots has many more rows than pictured.

Throughout this exam, we will refer to mascots repeatedly. Assume that we have already run import babypandas as bpd and import numpy as np.

Problem 1

Recall that each value in the "height" column of mascots is a string with two heights separated by " - ". Heights are formatted like "5ft 6in" or "6ft".

In this problem, you will need to fill in the blanks in the provided code to add three new columns to mascots:

• "min" (int) The smallest height that fits into the mascot costume, measured in inches.
• "max" (int) The largest height that fits into the mascot costume, measured in inches.
• "range" (int): The difference between the smallest and largest heights that fit into the mascot costume, measured in inches.

After the blanks have been correctly filled in, the first five rows of mascots should appear as follows.

Problem 1.1

To start, complete the implementation of the function inches which takes as input a single height and returns that height in inches, as an int. Example inputs and outputs are given below.

>>> inches("6ft 11in")
83 

>>> inches("5ft")
60

def inches(h):
    parts = h.split(" ")
    output = __(a)__
    if len(parts) == 2:
        output = __(b)__
    return output

Problem 1.2

Fill in the blanks below so that the code adds the three required columns to mascots. Feel free to use the inches function defined in part (a).

def min_height(s):
    return __(c)__

def max_height(s):
    return __(d)__

mascots = mascots.assign(min = mascots.get("height").apply(min_height))
mascots = mascots.assign(max = mascots.get("height").apply(max_height))
mascots = mascots.assign(range = __(e)__)

Problem 2

Which of the following expressions evaluate to the name of the school with the widest height range for its mascot costume (or any such school, in the case of a tie)? Select all that apply.

Hint: .groupby orders rows in ascending order of the values in the index.

• mascots.set_index("school").get("range").max()

• mascots.set_index("school").sort_values(by="range").index[-1]

• mascots.groupby("range").max().get("school").iloc[-1]

• mascots.groupby("school").max().index[-1]

• None of the above.

Problem 3

Sofia defines the variables below. Note that hundred is a DataFrame containing the first 100 rows of mascots.

hundred = mascots.take(np.arange(100))
has_state = hundred.get("school").str.contains("State")
is_animal = hundred.get("type") == "animal"

Problem 3.1

What is the data type of is_animal?

• string

• boolean

• array

• Series

• DataFrame

Problem 3.2

Sofia randomly selects one row from hundred. Which expression evaluates to the conditional probability that she selects a school with an "animal" mascot, given that she selects a school with "State" in its name?

• (has_state & is_animal).sum() / 100

• (has_state & is_animal).sum() / is_animal.sum()

• (has_state & is_animal).sum() / has_state.sum()

• is_animal.sum() / 100

• is_animal.sum() / has_state.sum()

Problem 3.3

The distribution of mascot "type" in hundred is shown in the table below.

Now, Sofia randomly selects two rows from hundred, independently and with replacement. What is the probability that Sofia selects at least one school with a "human" mascot? Give your answer as a mathematical expression, which you do not need to simplify.

Problem 4

Ella creates two histograms as follows.

• Histogram A:

mascots.plot(kind="hist", y="max", density=True, 
             bins=np.arange(48, 85, 8))

• Histogram B:

mascots.plot(kind="hist", y="max", density=True, 
             bins=np.arange(48, 85, 4))

Problem 4.1

How many bars are in Histogram A? Give your answer as an integer.

Problem 4.2

What is the largest value that can be displayed in Histogram B? Give your answer as an integer.

Problem 4.3

Which of the following statements must be true? Select all that apply.

• The total area of Histogram A equals the total area of Histogram B.

• If no mascot has a maximum height of 70 or 71 inches, then in both histograms, the height of the bar that includes the interval [70, 71] is 0.

• The proportion of mascots with maximum height between 65 and 70 inches (inclusive) can be found by adding the areas of all bars that cover any part of the interval [65, 70].

• The tallest bar in Histogram B is the same height as the tallest bar in Histogram A.

• None of the above.

Problem 5

Define two DataFrames single and double as follows.

single = mascots.groupby("range").count()
double = mascots.groupby(["min", "max"]).count()

Problem 5.1

Which statement below evaluates to True?

• single.shape[0] < double.shape[0]

• single.shape[0] == double.shape[0]

• single.shape[0] > double.shape[0]

Problem 5.2

Which of the following statements are true? Select all that apply.

• If two schools are grouped together in single, they must also be grouped together in double.

• If two schools are grouped together in double, they must also be grouped together in single.

• If two schools are in different groups in single, they must also be in different groups in double.

• If two schools are in different groups in double, they must also be in different groups in single.

• None of the above.

Problem 5.3

Which statement below evaluates to True?

• mascots.groupby("height").count().shape[0] < double.shape[0]

• mascots.groupby("height").count().shape[0] == double.shape[0]

• mascots.groupby("height").count().shape[0] > double.shape[0]

Problem 6

Suppose Pranav randomly selects 4 different schools from among those included in mascots. Fill in the blanks below to implement a simulation that estimates the probability that at least two of the schools Pranav selected have a mascot of type "animal".

mascot_types = np.array(mascots.get("type"))

repetitions = 10000
count_event = 0

for i in np.arange(repetitions):
    sample = np.random.choice(__(a)__)
    
    num_animals = np.count_nonzero(__(b)__)
    
    if __(c)__:
        count_event += 1

prob = __(d)__

Problem 6.1

What goes in blank (a)?

• mascot_types, repetitions, replace=True

• mascot_types, repetitions, replace=False

• mascot_types, 4, replace=True

• mascot_types, 4, replace=False

Problem 6.2

What goes in blank (b)?

Problem 6.3

What goes in blank (c)?

Problem 6.4

What goes in blank (d)?

• count_event

• count_event / repetitions

• count_event / 4

• np.mean(count_event)

• count_event.sum() / repetitions

Problem 7

The bar chart below was produced from the data in mascots. It shows how many schools use each color.

Problem 7.1

If you knew the exact heights of each bar, how could you determine the total number of schools in mascots?

• Sum the heights of all bars.

• Sum the heights of all bars and divide by the number of colors (9).

• You could not determine the total number of schools from this information.

Problem 7.2

In the bar chart, the height of the blue bar is 2100 and the height of the gold bar is 1500. Use this information and the first five rows of mascots (provided with the data description) to determine the maximum possible number of schools in mascots whose school colors are blue and gold only. Give your answer as an integer.

Problem 7.3

Write one line of code that uses the mascots DataFrame to calculate the sum of the heights of all bars in the bar chart above.

Problem 8

Austin and Ray are contestants on Season One of America’s Next Top Mascot, a new reality TV show. In each episode, contestants will compete for one of the mascot roles in the DataFrame below, called antm. The data includes the name of each mascot and the minimum and maximum heights, in inches, for the costume.

Problem 8.1

The America’s Next Top Mascot costume director wants to identify every pair of costumes where one costume’s maximum height exactly equals the other costume’s minimum height. She calls these “single-height costume pairs" because there is only a single height that can wear both costumes.

Write one line of code that uses .merge to calculate the number of single-height costume pairs in antm. Your answer should be a Python expression that evaluates to an integer.

Problem 8.2

What is the number of single-height costume pairs? In other words, what number does a correct answer to part (a) evaluate to? Give your answer as an integer.

Problem 8.3

The last episode of the season will reveal the mascot roles to be featured next season. Next season’s mascots are stored in a DataFrame called antm2 which has the same column names as antm, but contains different data (i.e. a different set of mascots).

We don’t have all of antm2 available, but do know some information about it. First, we know that antm2.merge(antm2, on="min") gives a DataFrame with 61 rows.

Additionally, we have the table at right, which shows the number of mascots in antm2 with each minimum height requirement, except one value is missing.How many mascots in antm2 have a minimum height requirement of 66 inches? Give your answer as an integer.

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