# Discussion 2: Arrays and DataFrames

The problems in this worksheet are taken from past exams. Work on them on paper, since the exams you take in this course will also be on paper.

We encourage you to complete this worksheet in a live discussion section. Solutions will be made available after all discussion sections have concluded. You don’t need to submit your answers anywhere.

Note: We do not plan to cover all problems here in the live discussion section; the problems we don’t cover can be used for extra practice.

## Problem 1

prices is an array of prices, in dollars, of different products at the grocery store. Similarly, calories is an array of the calories in these same products, in the same order.

### Problem 1.1

What does type(prices[0]) evaluate to?

• int

• float

• str

• The price of the first product.

Answer: float

prices[0] represents the price in dollars of some product at the grocery store. The data type should be a float because prices are numbers but not necessarily integers.

### Problem 1.2

What does type(calories[0]) evaluate to?

• int

• float

• str

• The calories in the first product.

Answer: int

Similarly, calories[0] represents the calories in some product at the grocery store. The data type should be int because calories in foods are always reported as integers.

### Problem 1.3

When we divide two arrays of the same length, their corresponding elements get divided, and the result is a new array of the same length as the two originals. In one sentence, interpret the meaning of min(prices / calories).

Answer: This is the cost per calorie of the product which has the lowest cost per calorie, which you might say is the cheapest food to fuel up on (like instant ramen or pasta).

### Problem 1.4

True or False: min(prices / calories) is the same as max(calories / price).

The former is measured in dollars per calories (a very small number), whereas the latter is measured in calories per dollar (a very big number).

However, there is a connection between these two values. The product that has the lowest price per calorie is the same product with the most calories per dollar. So these numbers refer to the same grocery store product, and we can convert one value into the other by taking the reciprocal, which swaps the numerator and denominator of a fraction. Therefore, it’s true that min(prices / calories) is the same as 1 / max(calories / price).

## Problem 2

Consider the following four assignment statements.

bass = "5"
tuna = 2
sword = ["4.0", 5, 12.5, -10, "2023"]
gold = [4, "6", "CSE", "doc"]

### Problem 2.1

What is the value of the expression bass * tuna?

Answer: "55"

##### Difficulty: ⭐️⭐️⭐️⭐️

The average score on this problem was 48%.

### Problem 2.2

Which of the following expressions results in an error?

• int(sword[0])

• float(sword[1])

• int(sword[2])

• int(sword[3])

• float(sword[4])

Answer: int(sword[0])

##### Difficulty: ⭐️⭐️⭐️

The average score on this problem was 51%.

### Problem 2.3

Which of the following expressions evaluates to "DSC10"?

• gold[3].replace("o", "s").title() + str(gold[0] + gold[1])

• gold[3].replace("o", "s").upper() + str(gold[0] + int(gold[1]))

• gold[3].replace("o", "s").upper() + str(gold[1] + int(gold[0]))

• gold[3].replace("o", "s").title() + str(gold[0] + int(gold[1]))

Answer: gold[3].replace("o", "s").upper() + str(gold[0] + int(gold[1]))

##### Difficulty: ⭐️

The average score on this problem was 92%.

## Problem 3

Evaluate the expression (np.arange(1, 7, 2.5) * np.arange(8, 2, -2))[2] .

Answer: 24.0

This question although is daunting at first, is best solved by breaking up the question into parts. First, let us think about the first part, np.arange(1, 7, 2.5). In order to answer this, we must figure out what np.arange() does. What np.arange() does is it creates a numpy array that contains regularly spaces values between a start value and an end value (start is inclusive, end is exclusive). So in this first case, our starting value is 1, our end value is 7, and the regular interval or step size is 2.5. So this call, np.arange(1, 7, 2.5), will output the numpy array np.array([1.0, 3.5, 6.0]) because we start at 1, and continue adding 2.5 stopping at the last value that’s less than 7. The reason the resulting np.array([]) containts all float values is because one of the numbers is not an int, and all elements in the array have to have the same data type. Now that we have evaluated the first half, let us now solve for np.arange(8, 2, -2). Now this part may seem a little tricky because of the negative regular interval (step size), but it is the same logic as before. The output will simply be np.array([8, 6, 4]). In order to get that, we start at 8, and continue to decrease our start value by 2 stopping before we reach 2. Now that we have evaluated both np.arange(1, 7, 2.5) and np.arange(8, 2, -2), it is now time to multiply.

Multiplication of two numpy arrays is simply a pair wise multiplication. So in our case, we will be multiplying np.array([1.0, 3.5, 6.0]) * np.array([8, 6, 4]), which results to np.array([8.0, 21.0, 24.0]). Again, paying attention to the datatypes, the reason that np.array([8.0, 21.0, 24.0]) contains float values rather than int values is because when you multiply an int by a float, your answer will be a float. Now that we have evaluated (np.arange(1, 7, 2.5) * np.arange(8, 2, -2)) to be np.array([8.0, 21.0, 24.0]), we now just need to access the element in position 2, which is 24.0.

## Problem 4

For the problems that follow, we will work with a dataset consisting of various skyscrapers in the US, which we’ve loaded into a DataFrame called sky. The first few rows of sky are shown below (though the full DataFrame has more rows):

Each row of sky corresponds to a single skyscraper. For each skyscraper, we have:

• its name, which is stored in the index of sky (string)

• the 'material' it is made up of (string)

• the 'city' in the US where it is located (string)

• the number of 'floors' (levels) it contains (int)

• its 'height' in meters (float), and

• the 'year' in which it was opened (int)

Below, identify the data type of the result of each of the following expressions, or select “error” if you believe the expression results in an error.

### Problem 4.1

sky.sort_values('height')
• int or float

• Boolean

• string

• array

• Series

• DataFrame

• error

sky is a DataFrame. All the sort_values method does is change the order of the rows in the Series/DataFrame it is called on, it does not change the data structure. As such, sky.sort_values('height') is also a DataFrame.

##### Difficulty: ⭐️⭐️

The average score on this problem was 87%.

### Problem 4.2

sky.sort_values('height').get('material').loc[0]
• int or float

• Boolean

• string

• array

• Series

• DataFrame

• error

sky.sort_values('height') is a DataFrame, and sky.sort_values('height').get('material') is a Series corresponding to the 'material' column, sorted by 'height' in increasing order. So far, there are no errors.

Remember, the .loc accessor is used to access elements in a Series based on their index. sky.sort_values('height').get('material').loc[0] is asking for the element in the sky.sort_values('height').get('material') Series with index 0. However, the index of sky is made up of building names. Since there is no building named 0, .loc[0] causes an error.

##### Difficulty: ⭐️⭐️

The average score on this problem was 79%.

### Problem 4.3

sky.sort_values('height').get('material').iloc[0]
• int or float

• Boolean

• string

• array

• Series

• DataFrame

• error

As we mentioned above, sky.sort_values('height').get('material') is a Series containing values from the 'material' column (but sorted). Remember, there is no element in this Series with an index of 0, so sky.sort_values('height').get('material').loc[0] errors. However, .iloc[0] works differently than .loc[0]; .iloc[0] will give us the first element in a Series (independent of what’s in the index). So, sky.sort_values('height').get('material').iloc[0] gives us back a value from the 'material' column, which is made up of strings, so it gives us a string. (Specifically, it gives us the 'material' type of the skyscraper with the smallest 'height'.)

##### Difficulty: ⭐️⭐️

The average score on this problem was 89%.

### Problem 4.4

sky.get('floors').max()
• int or float

• Boolean

• string

• array

• Series

• DataFrame

• error

The Series sky.get('floors') is made up of integers, and sky.get('floors').max() evaluates to the largest number in the Series, which is also an integer.

##### Difficulty: ⭐️

The average score on this problem was 91%.

### Problem 4.5

sky.index[0]
• int or float

• Boolean

• string

• array

• Series

• DataFrame

• error

sky.index contains the values 'Bayard-Condict Building', 'The Yacht Club at Portofino', 'City Investing Building', etc. sky.index[0] is then 'Bayard-Condict Building', which is a string.

##### Difficulty: ⭐️

The average score on this problem was 91%.

## Problem 5

### Problem 5.1

Write a single line of code that evaluates to the name of the tallest skyscraper in the sky DataFrame.

Answer: sky.sort_values(by='height', ascending=False).index[0]

In order to answer this question, we must first sort the values of the column we are interested in. As such, we sort the entire DataFrame by the height column, and because we are interested in the name of the tallest building, we should set the ascending parameter to False because we would like the heights to be ordered in descending order, thus leading to the line sky.sort_values(by='height', ascending=False). After sorting in descending order, we know that the tallest building is going to be the first row of the new sky DataFrame, and thus we now only need to get the name of the skyscraper, which happens to be in the index. In order to access the index of the DataFrame we can use sky.index, and in our case because we know that we want the first index, we would need to write sky.index[0]. Finally, putting it all together, in order to get the name of the tallest skyscraper in the sky DataFrame, we would need to write sky.sort_values(by='Height', ascending=False).index[0].

### Problem 5.2

Write a single line of code that evaluates to the average number of floors across all skyscrapers in the DataFrame.

Answer: sky.get('floors').mean()

In order to answer the question, we must first figure out how to get the number of floors each skyscraper has. We can do this with a line of code like sky.get('floors') which will get the number of floors each skyscraper has. After doing this, we now need to find out the average number of floors each skyscraper has. We can do this by using the .mean() method, which in our case will get the average number of floors each skyscraper has. Putting this all togther, we get a line of code that looks like sky.get('floors').mean().

## Problem 6

Consider the following assignment statement.

puffin = np.array([5, 9, 13, 17, 21])

### Problem 6.1

Provide arguments to call np.arange with so that the array penguin is identical to the array puffin.

penguin = np.arange(____)

Answer: We need to provide np.arange with three arguments: 5, anything in (21, 25], 4. For instance, something line penguin = np.arange(5, 25, 4) would work.

##### Difficulty: ⭐️

The average score on this problem was 90%.

### Problem 6.2

Fill in the blanks so that the array parrot is also identical to the array puffin.
Hint: Start by choosing y so that parrot has length 5.

parrot = __(x)__ * np.arange(0, __(y)__, 2) + __(z)__

• x: 2
• y: anything in (8, 10]
• z: 5

##### Difficulty: ⭐️⭐️⭐️

The average score on this problem was 74%.

## Problem 7

Suppose students is a DataFrame of all students who took DSC 10 last quarter. students has one row per student, where:

• The index contains students’ PIDs as strings starting with "A".

• The "Overall" column contains students’ overall percentage grades as floats.

• The "Animal" column contains students’ favorite animals as strings.

### Problem 7.1

What type is students.get("Overall")? If this expression errors, select “this errors."

• float

• string

• array

• Series

• this errors

##### Difficulty: ⭐️⭐️⭐️

The average score on this problem was 73%.

### Problem 7.2

What type is students.get("PID")? If this expression errors, select “this errors."

• float

• string

• array

• Series

• this errors

##### Difficulty: ⭐️⭐️⭐️

The average score on this problem was 67%.

Vanessa is one student who took DSC 10 last quarter. Her PID is A12345678, she earned the sixth-highest overall percentage grade in the class, and her favorite animal is the giraffe.

### Problem 7.3

Supposing that students is already sorted by "Overall" in descending order, fill in the blanks so that animal_one and animal_two both evaluate to "giraffe".

animal_one = students.get(__(x)__).loc[__(y)__]
animal_two = students.get(__(x)__).iloc[__(z)__]

• x: "Animal"
• y: "A12345678"
• z: 5

##### Difficulty: ⭐️⭐️⭐️

The average score on this problem was 69%.

### Problem 7.4

If students wasn’t already sorted by "Overall" in descending order, which of your answers would need to change?

• Neither y nor z would need to change

• Both y and z would need to change

• y only

• z only

Answer: z only

##### Difficulty: ⭐️⭐️

The average score on this problem was 82%.

## Problem 8

You are given a DataFrame called sports, indexed by 'Sport' containing one column, 'PlayersPerTeam'. The first few rows of the DataFrame are shown below:

Sport PlayersPerTeam
baseball 9
field hockey 11

Which of the following evaluates to 'basketball'?

• sports.loc[1]

• sports.iloc[1]

• sports.index[1]

• sports.get('Sport').iloc[1]

Answer: sports.index[1]

We are told that the DataFrame is indexed by 'Sport' and 'basketball' is one of the elements of the index. To access an element of the index, we use .index to extract the index and square brackets to extract an element at a certain position. Therefore, sports.index[1] will evaluate to 'basketball'.

The first two answer choices attempt to use .loc or .iloc directly on a DataFrame. We typically use .loc or .iloc on a Series that results from using .get on some column. Although we don’t typically do it this way, it is possible to use .loc or .iloc directly on a DataFrame, but doing so would produce an entire row of the DataFrame. Since we want just one word, 'basketball', the first two answer choices must be incorrect.

The last answer choice is incorrect because we can’t use .get with the index, only with a column. The index is never considered a column.

##### Difficulty: ⭐️⭐️

The average score on this problem was 88%.

## Problem 9

Suppose you are given a DataFrame of employees for a given company. The DataFrame, called employees, is indexed by 'employee_id' (string) with a column called 'years' (int) that contains the number of years each employee has worked for the company.

### Problem 9.1

Suppose that the code

employees.sort_values(by='years', ascending=False).index[0]

outputs '2476'.

True or False: The number of years that employee 2476 has worked for the company is greater than the number of years that any other employee has worked for the company.

• True

• False

This is false because there could be other employees who worked at the company equally long as employee 2476.

The code says that when the employees DataFrame is sorted in descending order of 'years', employee 2476 is in the first row. There might, however, be a tie among several employees for their value of 'years'. In that case, employee 2476 may wind up in the first row of the sorted DataFrame, but we cannot say that the number of years employee 2476 has worked for the company is greater than the number of years that any other employee has worked for the company.

If the statement had said greater than or equal to instead of greater than, the statement would have been true.

##### Difficulty: ⭐️⭐️⭐️⭐️⭐️

The average score on this problem was 29%.

### Problem 9.2

What will be the output of the following code?

employees.assign(start=2021-employees.get('years'))
employees.sort_values(by='start').index.iloc[-1]
• the employee id of an employee who has worked there for the most years

• the employee id of an employee who has worked there for the fewest years

• an error message complaining about iloc[-1]

• an error message complaining about something else

The problem is that the first line of code does not actually add a new column to the employees DataFrame because the expression is not saved. So the second line tries to sort by a column, 'start', that doesn’t exist in the employees DataFrame and runs into an error when it can’t find a column by that name.
This code also has a problem with iloc[-1], since iloc cannot be used on the index, but since the problem with the missing 'start' column is encountered first, that will be the error message displayed.