Prepare for and practice interview questions from Cognius across topics like Product Metrics, Algorithms, Probability and more.

Cognius Interview Questions

Cognius Interview Guides

Data Structures & Algorithms

Given two sorted lists, write a function to merge them into one sorted list.

Merge Sorted Lists

Find the missing integer from a array of consequtive integers

Find the Missing Number

Find Bigrams

Write a function to create a single dataframe with complete addresses in the format of street, city, state, zip code.

Complete Addresses

Write a function friendship_timeline to generate an output that lists the pairs of friends with their corresponding timestamps of the friendship beginning and then the timestamp of the friendship ending. 

Friendship Timeline

Machine Learning

How would you encode a categorical variable with thousands of distinct values

Encoding Categorical Features

Interpret coefficients of logistic regression for categorical and boolean variables

Coefficients of Logistic Regression

Which model would perform better and why?

Booking Regression

How would you build a job recommendation feed?

Job Recommendation

Write a function calculate_rmse to calculate the root mean squared error from y_pred and y_true

RMS Error

Select the 2nd highest salary in the engineering department

2nd Highest Salary

Write a SQL query to create a histogram of the number of comments per user in the month of January 2020.

Comments Histogram

Write a query that returns all neighborhoods that have 0 users.

Empty Neighborhoods

Calculate the first touch attribution for each `user_id` that converted.

First Touch Attribution

Write a query to return the two students with the closest test scores and the score difference

Closest SAT Scores

Probability

What is the probability that each subsequent card is larger than the previous drawn card when picking three cards from a shuffled deck of 500 cards

500 Cards

First to Six

What is the probability that it's actually raining in Seattle?

Raining in Seattle

What is the probability that item X would be found on Amazon's website?

Found Item

Compute the expected number of good ads in each scenario and the probability a bad rating came from a lazy rater

Ad Raters

Product Sense & Metrics

How would you investigate a decline in the average number of comments per user?

Decreasing Comments

How can we measure the success of a 30-day free trial in acquiring and retaining new Netflix users

Netflix Retention

How would you measure the success of Facebook Groups

Group Success

How would you verify the claim that Facebook is losing young users and what test metrics would you look at

Losing Users

What would you investigate to diagnose what's happening?

WAU vs Open Rates

<p>Write a SQL query to select the 2nd highest salary in the engineering department.</p>

<p><strong>Note:</strong> If more than one person shares the highest salary, the query should select the next highest salary.</p>

<p><strong>Example:</strong></p>

<p><strong>Input:</strong></p>

<p><code>employees</code> table</p>

<table>
<thead>
<tr>
<th>Column</th>
<th>Type</th>
</tr>
</thead>

<tbody>
<tr>
<td><code>id</code></td>
<td>INTEGER</td>
</tr>

<tr>
<td><code>first_name</code></td>
<td>VARCHAR</td>
</tr>

<tr>
<td><code>last_name</code></td>
<td>VARCHAR</td>
</tr>

<tr>
<td><code>salary</code></td>
<td>INTEGER</td>
</tr>

<tr>
<td><code>department_id</code></td>
<td>INTEGER</td>
</tr>
</tbody>
</table>
<p><code>departments</code> table</p>

<table>
<thead>
<tr>
<th>Column</th>
<th>Type</th>
</tr>
</thead>

<tbody>
<tr>
<td><code>id</code></td>
<td>INTEGER</td>
</tr>

<tr>
<td><code>name</code></td>
<td>VARCHAR</td>
</tr>
</tbody>
</table>
<p><strong>Output:</strong></p>

<table>
<thead>
<tr>
<th>Column</th>
<th>Type</th>
</tr>
</thead>

<tbody>
<tr>
<td><code>salary</code></td>
<td>INTEGER</td>
</tr>
</tbody>
</table>


<p>We’re given two tables, a <code>users</code> table with demographic information and the neighborhood they live in and a <code>neighborhoods</code> table.</p>

<p>Write a query that returns all neighborhoods that have 0 users. </p>

<p><strong>Example:</strong></p>

<p><strong>Input:</strong></p>

<p><code>users</code> table</p>

<table>
<thead>
<tr>
<th>Columns</th>
<th>Type</th>
</tr>
</thead>

<tbody>
<tr>
<td><code>id</code></td>
<td>INTEGER</td>
</tr>

<tr>
<td><code>name</code></td>
<td>VARCHAR</td>
</tr>

<tr>
<td><code>neighborhood_id</code></td>
<td>INTEGER</td>
</tr>

<tr>
<td><code>created_at</code></td>
<td>DATETIME</td>
</tr>
</tbody>
</table>
<p><code>neighborhoods</code> table</p>

<table>
<thead>
<tr>
<th>Columns</th>
<th>Type</th>
</tr>
</thead>

<tbody>
<tr>
<td><code>id</code></td>
<td>INTEGER</td>
</tr>

<tr>
<td><code>name</code></td>
<td>VARCHAR</td>
</tr>

<tr>
<td><code>city_id</code></td>
<td>INTEGER</td>
</tr>
</tbody>
</table>
<p><strong>Output:</strong></p>

<table>
<thead>
<tr>
<th>Columns</th>
<th>Type</th>
</tr>
</thead>

<tbody>
<tr>
<td><code>name</code></td>
<td>VARCHAR</td>
</tr>
</tbody>
</table>


<p>Given the <code>employees</code> and <code>departments</code> table, write a query to get the top 3 highest employee salaries by department. If the department contains less that 3 employees, the top 2 or the top 1 highest salaries should be listed (assume that each department has at least 1 employee). </p>

<p><em>Note: The output should include the full name of the employee in one column, the department name, and the salary. The output should be sorted by department name in ascending order and salary in descending order.</em> </p>

<p><strong>Example:</strong></p>

<p><strong>Input:</strong></p>

<p><code>employees</code> table</p>

<table>
<thead>
<tr>
<th>Column</th>
<th>Type</th>
</tr>
</thead>

<tbody>
<tr>
<td><code>id</code></td>
<td>INTEGER</td>
</tr>

<tr>
<td><code>first_name</code></td>
<td>VARCHAR</td>
</tr>

<tr>
<td><code>last_name</code></td>
<td>VARCHAR</td>
</tr>

<tr>
<td><code>salary</code></td>
<td>INTEGER</td>
</tr>

<tr>
<td><code>department_id</code></td>
<td>INTEGER</td>
</tr>
</tbody>
</table>
<p><code>departments</code> table</p>

<table>
<thead>
<tr>
<th>Column</th>
<th>Type</th>
</tr>
</thead>

<tbody>
<tr>
<td><code>id</code></td>
<td>INTEGER</td>
</tr>

<tr>
<td><code>name</code></td>
<td>VARCHAR</td>
</tr>
</tbody>
</table>
<p><strong>Output</strong>:</p>

<table>
<thead>
<tr>
<th>Column</th>
<th>Type</th>
</tr>
</thead>

<tbody>
<tr>
<td><code>employee_nam</code>e</td>
<td>VARCHAR</td>
</tr>

<tr>
<td><code>department_name</code></td>
<td>VARCHAR</td>
</tr>

<tr>
<td><code>salary</code></td>
<td>INTEGER</td>
</tr>
</tbody>
</table>


Get the top 3 highest employee salaries by department

Top Three Salaries

<p>Given two sorted lists, write a function to merge them into one sorted list.</p>

<p><em>Bonus: What’s the time complexity?</em></p>

<p><strong>Example:</strong></p>

<p><strong>Input:</strong></p>

<pre tabindex="0" class="chroma"><code><span class="line"><span class="cl"><span class="n">list1</span> <span class="o">=</span> <span class="p">[</span><span class="mi">1</span><span class="p">,</span><span class="mi">2</span><span class="p">,</span><span class="mi">5</span><span class="p">]</span>
</span></span><span class="line"><span class="cl"><span class="n">list2</span> <span class="o">=</span> <span class="p">[</span><span class="mi">2</span><span class="p">,</span><span class="mi">4</span><span class="p">,</span><span class="mi">6</span><span class="p">]</span>
</span></span></code></pre>

<p><strong>Output:</strong></p>

<pre tabindex="0" class="chroma"><code><span class="line"><span class="cl"><span class="k">def</span> <span class="nf">merge_list</span><span class="p">(</span><span class="n">list1</span><span class="p">,</span><span class="n">list2</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="p">[</span><span class="mi">1</span><span class="p">,</span><span class="mi">2</span><span class="p">,</span><span class="mi">2</span><span class="p">,</span><span class="mi">4</span><span class="p">,</span><span class="mi">5</span><span class="p">,</span><span class="mi">6</span><span class="p">]</span>
</span></span></code></pre>


<p>You have two sorted lists, one with m elements and one with n elements. What would be the time complexity of merging the two lists via merge sort?</p>


You have two sorted lists, one with m elements and one with n elements. What would be the time complexity of merging the two lists via merge sort? 

Merging Lists Complexity

<p>Given a table of students and their SAT test scores, write a query to return the two students with the closest test scores with the score difference.</p>

<p>If there are multiple students with the same minimum score difference, select the student name combination that is higher in the alphabet. </p>

<p><strong>Example:</strong></p>

<p><strong>Input:</strong></p>

<p><code>scores</code> table</p>

<table>
<thead>
<tr>
<th>Column</th>
<th>Type</th>
</tr>
</thead>

<tbody>
<tr>
<td><code>id</code></td>
<td>INTEGER</td>
</tr>

<tr>
<td><code>student</code></td>
<td>VARCHAR</td>
</tr>

<tr>
<td><code>score</code></td>
<td>INTEGER</td>
</tr>
</tbody>
</table>
<p><strong>Output:</strong></p>

<table>
<thead>
<tr>
<th>Column</th>
<th>Type</th>
</tr>
</thead>

<tbody>
<tr>
<td><code>one_student</code></td>
<td>VARCHAR</td>
</tr>

<tr>
<td><code>other_student</code></td>
<td>VARCHAR</td>
</tr>

<tr>
<td><code>score_diff</code></td>
<td>INTEGER</td>
</tr>
</tbody>
</table>


<p>Amy and Brad take turns in rolling a fair six-sided die. Whoever rolls a “6” first wins the game. Amy starts by rolling first.</p>

<p>What’s the probability that Amy wins?</p>


Amy and Brad take turns in rolling a fair six-sided die. Whoever rolls a “6” first wins the game. Amy starts by rolling first.

What’s the probability that Amy wins?

<p>Let’s say that your company is running a standard control and variant AB test on a feature to increase conversion rates on the landing page. The PM checks the results and finds a .04 p-value.</p>

<p>How would you assess the validity of the result?</p>


How would you assess the validity of the result?

Experiment Validity

A/B Testing

<p>Given an integer <code>N</code>, write a function that returns a list of all of the prime numbers up to <code>N</code>.</p>

<p><em>Note: Return an empty list there are no prime numbers less than or equal to <code>N</code>.</em></p>

<p><strong>Example:</strong></p>

<p><strong>Input:</strong></p>

<pre tabindex="0" class="chroma"><code><span class="line"><span class="cl"><span class="n">N</span> <span class="o">=</span> <span class="mi">3</span>
</span></span></code></pre>

<p><strong>Output:</strong></p>

<pre tabindex="0" class="chroma"><code><span class="line"><span class="cl"><span class="k">def</span> <span class="nf">prime_numbers</span><span class="p">(</span><span class="n">N</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="p">[</span><span class="mi">2</span><span class="p">,</span><span class="mi">3</span><span class="p">]</span>
</span></span></code></pre>


Given an integer N, write a function that returns all of the prime numbers up to N

Prime to N

<p>We’re given a table of bank transactions with three columns, <code>user_id</code>, a deposit or withdrawal value (determined if the value is positive or negative), and <code>created_at</code> time for each transaction.</p>

<p>Write a query to get the total three-day rolling average for deposits by day.</p>

<p><em>Note: Please use the format <code>&#39;%Y-%m-%d&#39;</code> for the date in the outout</em></p>

<p><strong>Example:</strong></p>

<p><strong>Input:</strong></p>

<p><code>bank_transactions</code> table</p>

<table>
<thead>
<tr>
<th>Column</th>
<th>Type</th>
</tr>
</thead>

<tbody>
<tr>
<td><code>user_id</code></td>
<td>INTEGER</td>
</tr>

<tr>
<td><code>created_at</code></td>
<td>DATETIME</td>
</tr>

<tr>
<td><code>transaction_value</code></td>
<td>FLOAT</td>
</tr>
</tbody>
</table>
<p><strong>Output:</strong></p>

<table>
<thead>
<tr>
<th>Column</th>
<th>Type</th>
</tr>
</thead>

<tbody>
<tr>
<td><code>dt</code></td>
<td>VARCHAR</td>
</tr>

<tr>
<td><code>rolling_three_day</code></td>
<td>FLOAT</td>
</tr>
</tbody>
</table>


Write a query to get the total three-day rolling average for deposits by day

Rolling Bank Transactions

<p>Write a query to identify customers who placed more than three transactions each in both 2019 and 2020.</p>

<p><strong>Example:</strong></p>

<p><strong>Input:</strong></p>

<p><code>transactions</code> table</p>

<table>
<thead>
<tr>
<th>Column</th>
<th>Type</th>
</tr>
</thead>

<tbody>
<tr>
<td><code>id</code></td>
<td>INTEGER</td>
</tr>

<tr>
<td><code>user_id</code></td>
<td>INTEGER</td>
</tr>

<tr>
<td><code>created_at</code></td>
<td>DATETIME</td>
</tr>

<tr>
<td><code>product_id</code></td>
<td>INTEGER</td>
</tr>

<tr>
<td><code>quantity</code></td>
<td>INTEGER</td>
</tr>
</tbody>
</table>
<p><code>users</code> table</p>

<table>
<thead>
<tr>
<th>Column</th>
<th>Type</th>
</tr>
</thead>

<tbody>
<tr>
<td><code>id</code></td>
<td>INTEGER</td>
</tr>

<tr>
<td><code>name</code></td>
<td>VARCHAR</td>
</tr>
</tbody>
</table>
<p> 
<strong>Output:</strong></p>

<table>
<thead>
<tr>
<th>Column</th>
<th>Type</th>
</tr>
</thead>

<tbody>
<tr>
<td><code>customer_name</code></td>
<td>VARCHAR</td>
</tr>
</tbody>
</table>


<p>Which of the following queries will return a list of customers and the total amount they have spent on orders?</p>


Which of the following queries will return a list of customers and the total amount they have spent on orders?

Customer Orders

Write a query to identify customers who placed more than three transactions each in both 2019 and 2020

<p>Write a SQL query to create a histogram of the number of comments per user in the month of January 2020.</p>

<p><em>Note: Assume bin buckets class intervals of one.</em></p>

<p><em>Note: Comments that were created outside of January 2020 should be counted in a “0” bucket</em></p>

<p><strong>Example:</strong></p>

<p><strong>Input:</strong></p>

<p><code>users</code> table</p>

<table>
<thead>
<tr>
<th>Columns</th>
<th>Type</th>
</tr>
</thead>

<tbody>
<tr>
<td><code>id</code></td>
<td>INTEGER</td>
</tr>

<tr>
<td><code>name</code></td>
<td>VARCHAR</td>
</tr>

<tr>
<td><code>created_at</code></td>
<td>DATETIME</td>
</tr>

<tr>
<td><code>neighborhood_id</code></td>
<td>INTEGER</td>
</tr>

<tr>
<td><code>mail</code></td>
<td>VARCHAR</td>
</tr>
</tbody>
</table>
<p><code>comments</code> table</p>

<table>
<thead>
<tr>
<th>Columns</th>
<th>Type</th>
</tr>
</thead>

<tbody>
<tr>
<td><code>user_id</code></td>
<td>INTEGER</td>
</tr>

<tr>
<td><code>body</code></td>
<td>VARCHAR</td>
</tr>

<tr>
<td><code>created_at</code></td>
<td>DATETIME</td>
</tr>
</tbody>
</table>
<p><strong>Output:</strong></p>

<table>
<thead>
<tr>
<th>Column</th>
<th>Type</th>
</tr>
</thead>

<tbody>
<tr>
<td><code>comment_count</code></td>
<td>INTEGER</td>
</tr>

<tr>
<td><code>frequency</code></td>
<td>INTEGER</td>
</tr>
</tbody>
</table>


<p>Imagine a deck of 500 cards numbered from 1 to 500. If all the cards are shuffled randomly and you are asked to pick three cards, one at a time, what’s the probability of each subsequent card being larger than the previous drawn card?</p>


<p>Imagine a deck of 2000 cards numbered from 1 to 2000. If all the cards are shuffled randomly and you are asked to pick three cards, one at a time, what’s the probability of each subsequent card being larger than the previously drawn card?</p>


Imagine a deck of 2000 cards numbered from 1 to 2000. If all the cards are shuffled randomly and you are asked to pick three cards, one at a time, what's the probability of each subsequent card being larger than the previously drawn card?

2000 cards

<p>Let’s say you work at a file-hosting website. You have information on user’s daily downloads in the <code>download_facts</code> table</p>

<p>Use the window function <code>RANK</code> to display the top three users by downloads each day. Order your data by <code>date</code>, and then by <code>daily_rank</code></p>

<p><strong>Example:</strong></p>

<p><strong>Input:</strong></p>

<p><code>download_facts</code> table</p>

<table>
<thead>
<tr>
<th>Column</th>
<th>Type</th>
</tr>
</thead>

<tbody>
<tr>
<td><code>user_id</code></td>
<td>INTEGER</td>
</tr>

<tr>
<td><code>date</code></td>
<td>DATE</td>
</tr>

<tr>
<td><code>downloads</code></td>
<td>INTEGER</td>
</tr>
</tbody>
</table>
<p><strong>Output:</strong></p>

<table>
<thead>
<tr>
<th>Column</th>
<th>Type</th>
</tr>
</thead>

<tbody>
<tr>
<td><code>daily_rank</code></td>
<td>INTEGER</td>
</tr>

<tr>
<td><code>user_id</code></td>
<td>INTEGER</td>
</tr>

<tr>
<td><code>date</code></td>
<td>DATE</td>
</tr>

<tr>
<td><code>downloads</code></td>
<td>INTEGER</td>
</tr>
</tbody>
</table>


Write a query to display the top three users by downloads each day

Top 3 Users

<p>Given a table of product subscriptions with a subscription start date and end date for each user, write a query that returns true or false whether or not each user has a subscription date range that overlaps with any other completed subscription.</p>

<p>Completed subscriptions have <code>end_date</code> recorded.</p>

<p><strong>Example:</strong></p>

<p><strong>Input:</strong></p>

<p><code>subscriptions</code> table</p>

<table>
<thead>
<tr>
<th>Column</th>
<th>Type</th>
</tr>
</thead>

<tbody>
<tr>
<td><code>user_id</code></td>
<td>INTEGER</td>
</tr>

<tr>
<td><code>start_date</code></td>
<td>DATETIME</td>
</tr>

<tr>
<td><code>end_date</code></td>
<td>DATETIME</td>
</tr>
</tbody>
</table>

<table>
<thead>
<tr>
<th><code>user_id</code></th>
<th><code>start_date</code></th>
<th><code>end_date</code></th>
</tr>
</thead>

<tbody>
<tr>
<td>1</td>
<td>2019-01-01</td>
<td>2019-01-31</td>
</tr>

<tr>
<td>2</td>
<td>2019-01-15</td>
<td>2019-01-17</td>
</tr>

<tr>
<td>3</td>
<td>2019-01-29</td>
<td>2019-02-04</td>
</tr>

<tr>
<td>4</td>
<td>2019-02-05</td>
<td>2019-02-10</td>
</tr>
</tbody>
</table>
<p><strong>Output:</strong></p>

<table>
<thead>
<tr>
<th><code>user_id</code></th>
<th><code>overlap</code></th>
</tr>
</thead>

<tbody>
<tr>
<td>1</td>
<td>1</td>
</tr>

<tr>
<td>2</td>
<td>1</td>
</tr>

<tr>
<td>3</td>
<td>1</td>
</tr>

<tr>
<td>4</td>
<td>0</td>
</tr>
</tbody>
</table>


Write a query to return whether each user's subscription date range overlaps with any other completed subscription

Subscription Overlap

<p>The schema below is for a retail online shopping company consisting of two tables, <code>attribution</code> and <code>user_sessions</code>.</p>

<ul>
<li><p>The attribution table logs a session visit for each row.</p></li>

<li><p>If <code>conversion</code> is <code>true</code>, then the user converted to buying on that session.</p></li>

<li><p>The <code>channel</code> column represents which advertising platform the user was attributed to for that specific session.</p></li>

<li><p>Lastly the <code>user_sessions</code> table maps many to one session visits back to one user.</p></li>
</ul>

<p>First touch attribution is defined as the channel with which the converted user was associated when they first discovered the website.</p>

<p>Calculate the first touch attribution for each <code>user_id</code> that converted. </p>

<p><strong>Example:</strong></p>

<p><strong>Input:</strong></p>

<p><code>attribution</code> table</p>

<table>
<thead>
<tr>
<th>Column</th>
<th>Type</th>
</tr>
</thead>

<tbody>
<tr>
<td><code>session_id</code></td>
<td>INTEGER</td>
</tr>

<tr>
<td><code>channel</code></td>
<td>VARCHAR</td>
</tr>

<tr>
<td><code>conversion</code></td>
<td>BOOLEAN</td>
</tr>
</tbody>
</table>
<p><code>user_sessions</code> table</p>

<table>
<thead>
<tr>
<th>column</th>
<th>type</th>
</tr>
</thead>

<tbody>
<tr>
<td><code>session_id</code></td>
<td>INTEGER</td>
</tr>

<tr>
<td><code>created_at</code></td>
<td>DATETIME</td>
</tr>

<tr>
<td><code>user_id</code></td>
<td>INTEGER</td>
</tr>
</tbody>
</table>
<p><strong>Example output:</strong></p>

<table>
<thead>
<tr>
<th><code>user_id</code></th>
<th><code>channel</code></th>
</tr>
</thead>

<tbody>
<tr>
<td>123</td>
<td>facebook</td>
</tr>

<tr>
<td>145</td>
<td>google</td>
</tr>

<tr>
<td>153</td>
<td>facebook</td>
</tr>

<tr>
<td>172</td>
<td>organic</td>
</tr>

<tr>
<td>173</td>
<td>email</td>
</tr>
</tbody>
</table>


<p>We’re given a table of product purchases. Each row in the table represents an individual user product purchase.</p>

<p>Write a query to get the number of customers that were upsold, or in other words, the number of users who bought additional products after their first purchase.</p>

<p><em>Note: If the customer purchased two things on the same day, that does not count as an upsell, as they were purchased within a similar timeframe.</em></p>

<p><strong>Example:</strong></p>

<p><strong>Input:</strong></p>

<p><code>transactions</code> table</p>

<table>
<thead>
<tr>
<th>Column</th>
<th>Type</th>
</tr>
</thead>

<tbody>
<tr>
<td><code>id</code></td>
<td>INTEGER</td>
</tr>

<tr>
<td><code>user_id</code></td>
<td>INTEGER</td>
</tr>

<tr>
<td><code>created_at</code></td>
<td>DATETIME</td>
</tr>

<tr>
<td><code>product_id</code></td>
<td>INTEGER</td>
</tr>

<tr>
<td><code>quantity</code></td>
<td>INTEGER</td>
</tr>
</tbody>
</table>
<p><strong>Output:</strong></p>

<table>
<thead>
<tr>
<th>Column</th>
<th>Type</th>
</tr>
</thead>

<tbody>
<tr>
<td><code>num_of_upsold_customers</code></td>
<td>INTEGER</td>
</tr>
</tbody>
</table>


Write a query to get the number of customers that were upsold

Upsell Transactions

<p>Given a table called <code>employees</code>, get the largest salary of any employee by department</p>

<p><strong>Example:</strong></p>

<p><strong>Input:</strong></p>

<p><code>employees</code> table</p>

<table>
<thead>
<tr>
<th>Column</th>
<th>Type</th>
</tr>
</thead>

<tbody>
<tr>
<td><code>id</code></td>
<td>INTEGER</td>
</tr>

<tr>
<td><code>department</code></td>
<td>VARCHAR</td>
</tr>

<tr>
<td><code>salary</code></td>
<td>INTEGER</td>
</tr>
</tbody>
</table>
<p><strong>Output:</strong></p>

<table>
<thead>
<tr>
<th>Column</th>
<th>Type</th>
</tr>
</thead>

<tbody>
<tr>
<td><code>department</code></td>
<td>VARCHAR</td>
</tr>

<tr>
<td><code>largest_salary</code></td>
<td>INTEGER</td>
</tr>
</tbody>
</table>


Write a query to get the largest salary of any employee by department

Largest Salary by Department

<p>Write a query to show the number of users, number of transactions placed, and total order amount per month in the year 2020. Assume that we are only interested in the monthly reports for a single year (January-December).</p>

<p><strong>Example:</strong></p>

<p><strong>Input:</strong></p>

<p><code>transactions</code> table</p>

<table>
<thead>
<tr>
<th>Column</th>
<th>Type</th>
</tr>
</thead>

<tbody>
<tr>
<td><code>id</code></td>
<td>INTEGER</td>
</tr>

<tr>
<td><code>user_id</code></td>
<td>INTEGER</td>
</tr>

<tr>
<td><code>created_at</code></td>
<td>DATETIME</td>
</tr>

<tr>
<td><code>product_id</code></td>
<td>INTEGER</td>
</tr>

<tr>
<td><code>quantity</code></td>
<td>INTEGER</td>
</tr>
</tbody>
</table>
<p><code>products</code> table</p>

<table>
<thead>
<tr>
<th>Column</th>
<th>Type</th>
</tr>
</thead>

<tbody>
<tr>
<td><code>id</code></td>
<td>INTEGER</td>
</tr>

<tr>
<td><code>name</code></td>
<td>VARCHAR</td>
</tr>

<tr>
<td><code>price</code></td>
<td>FLOAT</td>
</tr>
</tbody>
</table>
<p><code>users</code> table</p>

<table>
<thead>
<tr>
<th>Column</th>
<th>Type</th>
</tr>
</thead>

<tbody>
<tr>
<td><code>id</code></td>
<td>INTEGER</td>
</tr>

<tr>
<td><code>name</code></td>
<td>VARCHAR</td>
</tr>

<tr>
<td><code>sex</code></td>
<td>VARCHAR</td>
</tr>
</tbody>
</table>
<p><strong>Output:</strong></p>

<table>
<thead>
<tr>
<th>Column</th>
<th>Type</th>
</tr>
</thead>

<tbody>
<tr>
<td><code>month</code></td>
<td>INTEGER</td>
</tr>

<tr>
<td><code>num_customers</code></td>
<td>INTEGER</td>
</tr>

<tr>
<td><code>num_orders</code></td>
<td>INTEGER</td>
</tr>

<tr>
<td><code>order_amt</code></td>
<td>INTEGER</td>
</tr>
</tbody>
</table>


Write a query to show the number of users, transactions, and total order amount per month in 2020

Monthly Customer Report

<p>You are about to get on a plane to Seattle. You want to know if you should bring an umbrella. You call 3 random friends of yours who live there and ask each independently if it’s raining. Each of your friends has a <sup>2</sup>⁄<sub>3</sub> chance of telling you the truth and a <sup>1</sup>⁄<sub>3</sub> chance of messing with you by lying. All 3 friends tell you that “Yes” it is raining.</p>

<p>What is the probability that it’s actually raining in Seattle?</p>


<p>What is the <strong>main</strong> difference between the Frequentist and Bayesian methods of probabilistic analysis?</p>


What is the **main** difference between the Frequentist and Bayesian methods of probabilistic analysis?

Frequentist Vs Bayesian Analysis

<p>Netflix has hired people to rate movies.</p>

<p>Out of all of the raters, 80% of the raters carefully rate movies and rate 60% of the movies as good and 40% as bad. The other 20% are lazy raters and rate 100% of the movies as good.</p>

<p>Assuming all raters rate the same amount of movies, what is the probability that a movie is rated good?</p>


<p>There are two categories of movie raters: careful and lazy. Careful raters make up 80% of the total. They rate 60% of the movies as good and 40% as bad. Lazy raters, constitute 20% of the raters and 100% of the movies as good. Given these parameters, calculate the overall probability of a movie being rated good.</p>

There are two categories of movie raters: careful and lazy. Careful raters make up 80% of the total. They rate 60% of the movies as good and 40% as bad. Lazy raters, constitute 20% of the raters and 100% of the movies as good. Given these parameters, calculate the overall probability of a movie being rated good.

Lazy Raters

What is the probability that a movie is rated good

<p>Let’s say we’re comparing two machine learning algorithms. In which case would you use a bagging algorithm versus a boosting algorithm? </p>

<p>Give an example of the tradeoffs between the two.</p>


<p>In machine learning, when would you use a bagging algorithm over a boosting algorithm?</p>


In machine learning, when would you use a bagging algorithm over a boosting algorithm?

Bagging vs. Boosting

In which case would you use a bagging algorithm versus a boosting algorithm

Bagging vs Boosting

<p>You have an array of integers, <code>nums</code> of length <code>n</code> spanning <code>0</code> to <code>n</code> with one missing. Write a function <code>missing_number</code> that returns the missing number in the array.</p>

<p><em>Note: Complexity of \(O(n)\) required.</em></p>

<p><strong>Example:</strong></p>

<p><strong>Input:</strong></p>

<pre tabindex="0" class="chroma"><code><span class="line"><span class="cl"><span class="n">nums</span> <span class="o">=</span> <span class="p">[</span><span class="mi">0</span><span class="p">,</span><span class="mi">1</span><span class="p">,</span><span class="mi">2</span><span class="p">,</span><span class="mi">4</span><span class="p">,</span><span class="mi">5</span><span class="p">]</span> 
</span></span><span class="line"><span class="cl"><span class="n">missing_number</span><span class="p">(</span><span class="n">nums</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="mi">3</span>
</span></span></code></pre>


<p>Let’s say we have a very naive advertising platform. There is an audience of size <em>A</em> and a limited amount of impressions <em>B</em>.</p>

<p>Each of the impressions goes to just one user, defined at random. Every user in the audience has the same random chance of receiving each impression. </p>

<ol>
<li><p>Compute the probability that a user has exactly 0 impressions. </p></li>

<li><p>What’s the probability that every person has at least 1 impression?</p></li>
</ol>


Compute the probability a user gets exactly 0 impressions, and the probability everyone gets at least 1 impression

Impression Reach

<p>Write a query to identify the manager with the biggest team size.</p>

<p>You may assume there is only one manager with the largest team size.</p>

<p><strong>Example:</strong></p>

<p><strong>Input:</strong></p>

<p><code>employees</code> table</p>

<table>
<thead>
<tr>
<th>Column</th>
<th>Type</th>
</tr>
</thead>

<tbody>
<tr>
<td><code>id</code></td>
<td>INTEGER</td>
</tr>

<tr>
<td><code>name</code></td>
<td>VARCHAR</td>
</tr>

<tr>
<td><code>manager_id</code></td>
<td>INTEGER</td>
</tr>
</tbody>
</table>
<p><code>managers</code> table</p>

<table>
<thead>
<tr>
<th>Column</th>
<th>Type</th>
</tr>
</thead>

<tbody>
<tr>
<td><code>id</code></td>
<td>INTEGER</td>
</tr>

<tr>
<td><code>name</code></td>
<td>VARCHAR</td>
</tr>

<tr>
<td><code>team</code></td>
<td>VARCHAR</td>
</tr>
</tbody>
</table>
<p><strong>Output:</strong></p>

<table>
<thead>
<tr>
<th>Column</th>
<th>Type</th>
</tr>
</thead>

<tbody>
<tr>
<td><code>manager</code></td>
<td>VARCHAR</td>
</tr>

<tr>
<td><code>team_size</code></td>
<td>INTEGER</td>
</tr>
</tbody>
</table>


Manager Team Sizes

<p>Given two strings <code>A</code> and <code>B</code>, write a function <code>can_shift</code> to return whether or not <code>A</code> can be shifted some number of places to get <code>B</code>.</p>

<p><strong>Example:</strong></p>

<p><strong>Input:</strong></p>

<pre tabindex="0" class="chroma"><code><span class="line"><span class="cl"><span class="n">A</span> <span class="o">=</span> <span class="s1">&#39;abcde&#39;</span>
</span></span><span class="line"><span class="cl"><span class="n">B</span> <span class="o">=</span> <span class="s1">&#39;cdeab&#39;</span>
</span></span><span class="line"><span class="cl"><span class="n">can_shift</span><span class="p">(</span><span class="n">A</span><span class="p">,</span> <span class="n">B</span><span class="p">)</span> <span class="o">==</span> <span class="kc">True</span>
</span></span><span class="line"><span class="cl">
</span></span><span class="line"><span class="cl"><span class="n">A</span> <span class="o">=</span> <span class="s1">&#39;abc&#39;</span>
</span></span><span class="line"><span class="cl"><span class="n">B</span> <span class="o">=</span> <span class="s1">&#39;acb&#39;</span>
</span></span><span class="line"><span class="cl"><span class="n">can_shift</span><span class="p">(</span><span class="n">A</span><span class="p">,</span> <span class="n">B</span><span class="p">)</span> <span class="o">==</span> <span class="kc">False</span>
</span></span></code></pre>


Write a function can_shift to return whether or not A can be shifted some number of places to get B

String Shift

<p>Write a function <code>compute_deviation</code> that takes in a list of dictionaries with a key and list of integers and returns a dictionary with the standard deviation of each list.</p>

<p><em>Note: This should be done without using the NumPy built-in functions.</em></p>

<p><strong>Example:</strong></p>

<p><strong>Input:</strong></p>

<pre tabindex="0" class="chroma"><code><span class="line"><span class="cl"><span class="nb">input</span> <span class="o">=</span> <span class="p">[</span>
</span></span><span class="line"><span class="cl">    <span class="p">{</span>
</span></span><span class="line"><span class="cl">        <span class="s1">&#39;key&#39;</span><span class="p">:</span> <span class="s1">&#39;list1&#39;</span><span class="p">,</span>
</span></span><span class="line"><span class="cl">        <span class="s1">&#39;values&#39;</span><span class="p">:</span> <span class="p">[</span><span class="mi">4</span><span class="p">,</span><span class="mi">5</span><span class="p">,</span><span class="mi">2</span><span class="p">,</span><span class="mi">3</span><span class="p">,</span><span class="mi">4</span><span class="p">,</span><span class="mi">5</span><span class="p">,</span><span class="mi">2</span><span class="p">,</span><span class="mi">3</span><span class="p">],</span>
</span></span><span class="line"><span class="cl">    <span class="p">},</span>
</span></span><span class="line"><span class="cl">    <span class="p">{</span>
</span></span><span class="line"><span class="cl">        <span class="s1">&#39;key&#39;</span><span class="p">:</span> <span class="s1">&#39;list2&#39;</span><span class="p">,</span>
</span></span><span class="line"><span class="cl">        <span class="s1">&#39;values&#39;</span><span class="p">:</span> <span class="p">[</span><span class="mi">1</span><span class="p">,</span><span class="mi">1</span><span class="p">,</span><span class="mi">34</span><span class="p">,</span><span class="mi">12</span><span class="p">,</span><span class="mi">40</span><span class="p">,</span><span class="mi">3</span><span class="p">,</span><span class="mi">9</span><span class="p">,</span><span class="mi">7</span><span class="p">],</span>
</span></span><span class="line"><span class="cl">    <span class="p">}</span>
</span></span><span class="line"><span class="cl"><span class="p">]</span>
</span></span></code></pre>

<p><strong>Output:</strong></p>

<pre tabindex="0" class="chroma"><code><span class="line"><span class="cl"> <span class="n">output</span> <span class="o">=</span> <span class="p">{</span><span class="s1">&#39;list1&#39;</span><span class="p">:</span> <span class="mf">1.12</span><span class="p">,</span> <span class="s1">&#39;list2&#39;</span><span class="p">:</span> <span class="mf">14.19</span><span class="p">}</span>
</span></span></code></pre>


Write a function compute_deviation that returns the standard deviation of each list in a list of dictionaries

Compute Deviation

Statistics

<p>A team wants to A/B test multiple different changes through a sign-up funnel.</p>

<p>For example, on a page, a button is currently red and at the top of the page. They want to see if changing a button from red to blue and/or from the top of the page to the bottom of the page will increase click-through.</p>

<p>How would you set up this test?</p>


<p>Your team wants to run an AB test on the color (red or blue) and position (top/bottom of the page) of a button that links to a promotion.</p>

<p>How many different variants of the test should you run to see the effect that a red button has on the bottom of the page, if currently the button is blue and on the top of the page.</p>


Your team wants to run an AB test on the color (red or blue) and position (top/bottom of the page) of a button that links to a promotion.

How many different variants of the test should you run to see the effect that a red button has on the bottom of the page, if currently the button is blue and on the top of the page.

A/B Test Variants

Button AB Test

<p>Given two tables:  <code>accounts</code>, and <code>downloads</code>, find the average number of downloads for free vs paying accounts, broken down by day.</p>

<p><em>Note: You only need to consider accounts that have had at least one download before when calculating the average.</em></p>

<p><em>Note: round <code>average_downloads</code> to 2 decimal places.</em></p>

<p><strong>Example:</strong></p>

<p><strong>Input:</strong></p>

<p><code>accounts</code> table</p>

<table>
<thead>
<tr>
<th>Column</th>
<th>Type</th>
</tr>
</thead>

<tbody>
<tr>
<td><code>account_id</code></td>
<td>INTEGER</td>
</tr>

<tr>
<td><code>paying_customer</code></td>
<td>BOOLEAN</td>
</tr>
</tbody>
</table>
<p><code>downloads</code> table</p>

<table>
<thead>
<tr>
<th>column</th>
<th>type</th>
</tr>
</thead>

<tbody>
<tr>
<td><code>account_id</code></td>
<td>INTEGER</td>
</tr>

<tr>
<td><code>download_date</code></td>
<td>DATETIME</td>
</tr>

<tr>
<td><code>downloads</code></td>
<td>INTEGER</td>
</tr>
</tbody>
</table>
<p><strong>Output:</strong></p>

<table>
<thead>
<tr>
<th>Column</th>
<th>Type</th>
</tr>
</thead>

<tbody>
<tr>
<td><code>download_date</code></td>
<td>DATETIME</td>
</tr>

<tr>
<td><code>paying_customer</code></td>
<td>BOOLEAN</td>
</tr>

<tr>
<td><code>average_downloads</code></td>
<td>FLOAT</td>
</tr>
</tbody>
</table>


Write a query to find the average downloads for free vs paying accounts by day, rounded to 2 decimals

Download Facts

<p>How would you explain what a p-value is to someone who is not technical?</p>


<p>What does a p-value in a statistical test represent?</p>

What does a p-value in a statistical test represent?

P-value to a Layman I

<p>In a statistical test, how does a low p-value (less than 0.05) influence our decision about the null hypothesis?</p>

In a statistical test, how does a low p-value (less than 0.05) influence our decision about the null hypothesis?

P-value to a Layman II

Explain what a p-value is to someone who is not technical

P-value to a Layman

<p>Tell me about a data project that didn’t go the way you expected. What did you set out to do, what surprised you, and how did you handle it?</p>


Calculate Moving Average	SQL	Easy
Predict Customer Churn	Machine Learning	Medium
A/B Test Significance	Statistics	Medium
Optimize Query Performance	SQL	Hard
Feature Importance Analysis	Machine Learning	Medium
Clean Missing Data	Python	Easy
Neural Network Architecture	Deep Learning	Hard
Calculate Cohort Retention	SQL	Medium
Bayesian Probability	Statistics	Easy
Recommend Similar Products	Machine Learning	Hard

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