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end string appended after the last value, default a newline. file a file-like object (stream); defaults to the current sys.stdout. flush whether to forcibly flush the stream. You can also use Jupyter to view function documentation inside your notebook. The function must already be defined in the kernel for this to work. Below, click your mouse anywhere on the print block below and use Shift + Tab to view the function’s documentation. [4]: print ( 'Welcome to Data 100.' ) Welcome to Data 100. 1.2.2 Importing Libraries and Magic Commands In Data 100, we will be using common Python libraries to help us process data. By convention, we import all libraries at the very top of the notebook. There are also a set of standard aliases that are used to shorten the library names. Below are some of the libraries that you may encounter throughout the course, along with their respective aliases. [5]: import pandas as pd import numpy as np import matplotlib.pyplot as plt plt . style . use( 'fivethirtyeight' ) % matplotlib inline %matplotlib inline is a Jupyter magic command that configures the notebook so that matplotlib displays any plots that you draw directly in the notebook rather than to a file, al- lowing you to view the plots upon executing your code. (Note: In practice, this is no longer necessary, but we’re showing it to you now anyway.) Another useful magic command is %%time , which times the execution of that cell. You can use this by writing it as the first line of a cell. (Note that %% is used for cell magic commands that apply to the entire cell, whereas % is used for line magic commands that only apply to a single line.) [6]: %%time lst = [] for i in range ( 100 ): lst . append(i) CPU times: user 0 ns, sys: 24 µs, total: 24 µs Wall time: 30 µs 3

[14]: # A regular Python list can store items of different data types [ 1 , '3' ] [14]: [1, '3'] [15]: # Arrays will convert everything to the same data type np . array([ 1 , '3' ]) [15]: array(['1', '3'], dtype='<U21') [16]: # Another example of array type conversion np . array([ 5 , 8.3 ]) [16]: array([5. , 8.3]) Arrays are also useful in performing vectorized operations . Given two or more arrays of equal length, arithmetic will perform element-wise computations across the arrays. For example, observe the following: [17]: # Python list addition will concatenate the two lists [ 1 , 2 , 3 ] + [ 4 , 5 , 6 ] [17]: [1, 2, 3, 4, 5, 6] [18]: # NumPy array addition will add them element-wise np . array([ 1 , 2 , 3 ]) + np . array([ 4 , 5 , 6 ]) [18]: array([5, 7, 9]) 1.3.4 Question 2 1.3.5 Question 2a Write a function summation that evaluates the following summation for 𝑛 ≥ 1 : 𝑛 ∑ 𝑖=1 𝑖 3 + 3𝑖 2 Note : You should not use for loops in your solution. Check the NumPy documentation . If you’re stuck, try a search engine! Searching the web for examples of how to use modules is very common in data science. You may find np.arange helpful for this question! [23]: def summation (n): """Compute the summation i^3 + 3 * i^2 for 1 <= i <= n.""" arr = np . arange( 1 , n +1 ) 6

1.3.7 Question 2c Recall the formula for population variance below: 𝜎 2 = ∑ 𝑁 𝑖=1 (𝑥 𝑖 − 𝜇) 2 𝑁 Complete the functions below to compute the population variance of population , an array of numbers. For this question, do not use built-in NumPy functions, such as np.var . Again, avoid using for loops! For a refresher on what variance is, feel free to read up on it in the Data 8 Textbook here ! [39]: def mean (population): """ Returns the mean of population (mu) Keyword arguments: population -- a numpy array of numbers """ # Calculate the mean of a population return sum (population) / len (population) def variance (population): """ Returns the variance of population (sigma squared) Keyword arguments: population -- a numpy array of numbers """ # Calculate the variance of a population return sum ((population - mean(population)) **2 ) / len (population) [40]: grader . check( "q2c" ) [40]: q2c results: All test cases passed! 1.3.8 Question 2d Given the array random_arr , assign valid_values to an array containing all values 𝑥 such that 2𝑥 4 > 1 . Note : You should not use for loops in your solution. Instead, look at NumPy ’s documentation on Boolean Indexing . Documentation can be very intimidating at first glance, but don’t worry, that’s completely okay, one of the goals of this class is to build familiarity with reading the documentation of data science tools. Ask for help if needed, we’re always there for you! 9

1.4.5 Question 4 (Ungraded) Data science is a rapidly expanding field and no degree program can hope to teach you everything that will be helpful to you as a data scientist. So it’s important that you become familiar with looking up documentation and learning how to read it. Below is a section of code that plots a three-dimensional “wireframe” plot. You’ll see what that means when you draw it. Replace each # Your answer here with a description of what the line above does, what the arguments being passed in are, and how the arguments are used in the function. For example, np.arange(2, 5, 0.2) # This returns an array of numbers from 2 to 5 with an interval size of 0.2 Hint: The Shift + Tab tip from earlier in the notebook may help here. Remember that objects must be defined in order for the documentation shortcut to work; for example, all of the docu- mentation will show for method calls from np since we’ve already executed import numpy as np . However, since z is not yet defined in the kernel, z.reshape(x.shape) will not show documentation until you run the line z = np.cos(squared) . [ ]: from mpl_toolkits.mplot3d import axes3d u = np . linspace( 1.5 * np . pi, -1.5 * np . pi, 100 ) # Your answer here [x, y] = np . meshgrid(u, u) # Your answer here squared = np . sqrt(x . flatten() ** 2 + y . flatten() ** 2 ) z = np . cos(squared) # Your answer here z = z . reshape(x . shape) # Your answer here fig = plt . figure(figsize = ( 6 , 6 )) ax = fig . add_subplot( 111 , projection = '3d' ) # Your answer here ax . plot_wireframe(x, y, z, rstride = 5 , cstride = 5 , lw = 2 ) # Your answer here ax . view_init(elev = 60 , azim = 25 ) # Your answer here plt . savefig( "figure1.png" ) # Your answer here 1.4.6 Question 5 (Ungraded) Do you think a hotdog is a sandwich? Tell us what you think in the following Markdown cell. :) Answer: Yes, its like a po boy 12