Prepare for and practice interview questions from The Hanover Insurance Group across topics like Machine Learning, SQL, Statistics and more.

The Hanover Insurance Group Interview Questions

The Hanover Insurance Group Interview Guides

Machine Learning

Which model would perform better and why?

Booking Regression

Lasso vs Ridge

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

Bagging vs Boosting

How does random forest generate the forest and why use it over logistic regression

Random Forest Explanation

How would you justify the complexity of building such a model and explain the predictions to non-technical stakeholders

Justify a Neural Network

Write a query to select the top 3 departments with at least ten employees and rank them according to the percentage of their employees making over 100K in salary.

Employee Salaries

Select the 2nd highest salary in the engineering department

2nd Highest Salary

Duplicate Rows

Write a query to create a pivot table that shows total sales for each branch by year

Branch Sales Pivot

How would you design a data warehouse for a e-commerce company looking to expand internationally?

International e-Commerce Warehouse

Statistics

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

P-value to a Layman

What are the assumptions of linear regression?

Assumptions of Linear Regression

How do you detect and handle correlation between variables in linear regression, and what happens if you ignore it

Correlation in Regression

What is the difference between type I and type II errors?

Type I and II Errors

How would you tackle multicollinearity in multiple linear regression

Multicollinearity in Regression

Data Structures & Algorithms

Given an array and a target integer, write a function that returns the indices of two integers in the array that add up to the target integer.

Target Indices

Given a list of strings, write a Python program to check whether each string has all the same characters or not.

Same Characters

Write a Python function that adds together all combinations of adjacent integers in int_str

Integer String Addition

Swap the values of `a` and `b` in the dictionary without declaring any other variable

Swap Variables

Write a function that returns the shape of an isosceles triangle.

Triangle as Binary Array

Product Sense & Metrics

What would you investigate to diagnose what's happening?

WAU vs Open Rates

Unified Inbox

What are the top five metrics you would start tracking to understand the health of Google Docs

Docs Metrics

The role of A/B testing in measuring the success rate of an analytics experiment

Success Measurement

Vision Setting and Execution Strategy

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?

Describing a data project and its challenges

Hurdles In Data Projects

Behavioral

Write a SQL query to select the 2nd highest salary in the engineering department.

Note: If more than one person shares the highest salary, the query should select the next highest salary.

Example:

Input:

<code>employees</code> table

<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>
<code>departments</code> table

<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>
Output:

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

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

Given a <code>employees</code> and <code>departments</code> table, select the top 3 departments with at least ten employees and rank them according to the percentage of their employees making over 100K in salary.

Example:

Input:

<code>employees</code> table

<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>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>
<code>departments</code> table

<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>
</tbody>
</table>
Output:

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

<tbody>
<tr>
<td><code>percentage_over_100k</code></td>
<td>FLOAT</td>
</tr>

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

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

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

Give an example of the tradeoffs between the two.

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

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

Bagging vs. Boosting

Let’s say we want to build a model to predict booking prices on Airbnb.

Between linear regression and random forest regression, which model would perform better and why?

What are the two key concepts of random forest regression?

What are the two key concepts of random forest regression?

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

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

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

P-value to a Layman I

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

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

Let’s say you work at Allstate. Allstate is running <code>N</code> online ads right now. The table <code>ads</code> contains all those ads, ranked by popularity via the <code>id</code> column (e.g., the entry with <code>id = 1</code> is the most popular, etc.).

Create a subquery or common table expression named <code>top_ads</code> containing the top 3 ads (by popularity) and return the number of rows that would result from the following operations

<ol>
<li><code>ads INNER JOIN top_ads</code></li>
<li><code>ads LEFT JOIN top_ads</code></li>
<li><code>ads RIGHT JOIN top_ads</code></li>
<li><code>ads CROSS JOIN top_ads</code></li>
</ol>

Note: Please make the <code>join_type</code> column in your output have the values <code>inner_join</code>, <code>left_join</code>, etc. for each of their respective join types

Note: Please return only one query with each number in a different row

Example:

Input:

<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>
Output:

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

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

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

Create top_ads with the top 3 ads and return the row counts for inner, left, right, and cross joins with ads

Size of Joins

How does random forest generate the forest? Additionally, why would we use it over other algorithms such as logistic regression?

What happens when you average the output on multiple decision trees?

What happens when you average the output on multiple decision trees?

Average Trees

Let’s say that you’re a data scientist on the engagement team. A product manager comes up to you and says that the weekly active users metric is up 5% but email notification open rates are down 2%.

What would you investigate to diagnose what’s happening?

Email Open Rate

What’s the difference between Lasso and Ridge Regression?

Under what circumstances is it recommended to use Lasso regression over Ridge regression?

Under what circumstances is it recommended to use Lasso regression over Ridge regression?

What are the assumptions of linear regression?

Which assumption of the residuals of the standard linear regression model can not be overcome by increasing the sample size?

Regression assumptions

What are the key differences between classification models and regression models?

What is the MOST important difference between regression and classification models?

What is the MOST important difference between regression and classification models?

Classification vs Regression

Explain the key differences between classification models and regression models

Classification and Regression

One of your favorite sports teams is playing at a local stadium, but you waited until the last minute to buy a ticket.

You can buy a scalped (second-hand) ticket for $50, which has a 20% chance of not working. If the scalped ticket doesn’t work, you’ll have to buy a box office ticket for $70 at the stadium.

<ol>
<li>How much do you expect to pay to go to the sports game?</li>
<li>How much money should you set aside for the game?</li>
</ol>

How much do you expect to pay and how much money should you set aside for the game

Scalped Ticket

Probability

Given a 2-D matrix P of predicted values and actual values, write a function precision_recall to calculate precision and recall metrics.

Return the ordered pair (precision, recall).

Example:

Input:

<pre tabindex="0" class="chroma"><code>
P = [[121, 9],
 [17, 144]]
</code></pre>

where P represents the following table

<table>
<thead>
<tr>
<th></th>
<th>Predicted =TRUE</th>
<th>Predicted =FALSE</th>
</tr>
</thead>

<tbody>
<tr>
<td>Actual =TRUE</td>
<td>121</td>
<td>9</td>
</tr>

<tr>
<td>Actual =FALSE</td>
<td>17</td>
<td>144</td>
</tr>
</tbody>
</table>
Output:

<pre tabindex="0" class="chroma"><code>def precision_recall(P) -&gt; (0.931, 0.877,)
</code></pre>

Write a function to calculate precision and recall metrics.

Precision and Recall

Three zebras are chilling in the desert. Suddenly a lion attacks.
Each zebra is sitting on a corner of a triangle with sides of equal length.
Each zebra randomly picks a direction and only runs along the outline of the triangle to either edge of the triangle.

What is the probability that none of the zebras collide?

Three zebras are chilling in the desert. Suddenly a lion attacks.

Each zebra is sitting on a corner of a triangle with side of equal length. Each zebra randomly picks a direction and only runs along the outline of the triangle to either edge of the triangle.

What is the probability that none of the zebras collide?

Three zebras are chilling in the desert. Suddenly a lion attacks.

Each zebra is sitting on a corner of a triangle with side of equal length.  Each zebra randomly picks a direction and only runs along the outline of the triangle to either edge of the triangle.

What is the probability that none of the zebras collide?



Three Zebras

Brainteasers

You’re a data scientist at YouTube. Leadership wants to revisit how the platform measures success, not for a specific new feature, but for the product as a whole given its current state.

How would you define and measure success for YouTube? Identify your primary and secondary metrics, explain your rationale for each, and discuss how you would choose the right thresholds for any engagement-based metrics you propose.

Given an array and a target integer, write a function <code>sum_pair_indices</code> that returns the indices of two integers in the array that add up to the target integer. If not found, just return an empty list.

Note: Can you do it on $O(n)$ time?

Note: Even though there could be many solutions, only one needs to be returned.

Example 1:

Input:

<pre tabindex="0" class="chroma"><code>array = [1 2 3 4] 
target = 5 
</code></pre>

Output:

<pre tabindex="0" class="chroma"><code>def sum_pair_indices(array, target) -&gt; [0 3] or [1 2]
</code></pre>

Example 2:

Input:

<pre tabindex="0" class="chroma"><code>array = [3]
target = 6 
</code></pre>

Output:

<pre tabindex="0" class="chroma"><code>Do NOT return [0 0] as you can&#39;t use an index twice.
</code></pre>

Write a Python function that adds together all combinations of adjacent integers of a given string of integers named <code>int_str</code>.

Example 1:

Input:

<pre tabindex="0" class="chroma"><code>int_str = &#39;12&#39;
</code></pre>

Output:

<pre tabindex="0" class="chroma"><code>def int_str_addition -&gt; 1 + 2 + 12 = 15
</code></pre>

Example 2:

Input:

<pre tabindex="0" class="chroma"><code>int_str = &#39;123&#39;
</code></pre>

Output:

<pre tabindex="0" class="chroma"><code>def int_str_addition(int_str) -&gt; 1 + 2 + 3 + 12 + 23 + 123 = 164
#in this case, 13 is not part of our sum as 1 and 3 are not adjacent in &#39;123&#39;
</code></pre>

Let’s say that you’re drawing $N$ cards (without replacement) from a standard 52 card poker deck. Each card is unique and part of 4 different suits and 13 different ranks.

Compute the probability that you will get a pair (two cards of the same rank) from a hand of $N$ cards.

When drawing three cards from a standard 52 card deck without replacement, what is the probability that all cards have different ranks?

When drawing three cards from a standard 52 card deck without replacement, what is the probability that all cards have different ranks?

Poker Pair

Compute the probability of getting a pair from a hand of N cards

How would you handle the data preparation for building a machine learning model using imbalanced data?

Addressing imbalanced data in machine learning through carefully prepared techniques.

Data Preparation for Imbalanced Data

Given a <code>users</code> table, write a query to return only its duplicate rows.

Example:

Input:

<code>users</code> table

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

Let’s say that you are leading the development of an internal chatbot for operations support at Thomson Reuters, an internal tooling in their news division for referencing articles.

How would you design a system given a choice between fine-tuning the LLM or using Retrieval-Augmented Generation (RAG)?

Fine-Tuning VS RAG

AI & Agentic Systems

In the context of hypothesis testing, what are type I errors (type one errors) and type II errors (type two errors)? What is the difference between the two?

Bonus: Describe the probability of making each type of error mathematically.

Let’s say that you’re training a classification model.

How would you combat overfitting when building tree-based models?

Let's say that you're training a classification model.   How would you combat overfitting when building tree-based models?

Overfit Avoidance

Let’s say you have a table with a billion rows.

How would you add a column inserting data from the original source without affecting the user experience?

How would you add a column inserting data from the original source without affecting the user experience

Modifying a Billion Rows

Query Optimization

Let’s say you have to draw two cards from a shuffled deck, one at a time.

What’s the probability that the second card is not an Ace?

What's the probability that the second card is not an ace?

Second Ace

Given a list of strings, write a Python program to check whether each string has all the same characters or not. What is the complexity of this program?

<h3>Example</h3>

Input:

<pre tabindex="0" class="chroma"><code>string_list = [&#39;bbbbb&#39;, &#39;abc&#39;, &#39;aaaaaaaab&#39;]
</code></pre>

Output:

<pre tabindex="0" class="chroma"><code>def same_characters(input_list) -&gt; False
</code></pre>

Explanation:

<ul>
<li><code>string bbbbb</code> has all the same characters 
</li>
<li><code>string abc</code> does not have all the same characters 
</li>
<li><code>string aaaaaaaab</code> does not have all the same characters</li>
</ul>

You are given a dictionary with two keys <code>a</code> and <code>b</code> that hold integers as their values.

Without declaring any other variable, swap the value of <code>a</code> with the value of <code>b</code> and vice versa.

Note: Return the dictionary after editing it.

Example:

Input:

<pre tabindex="0" class="chroma"><code>numbers = {
 &#39;a&#39;:3,
 &#39;b&#39;:4
}
</code></pre>

Output:

<pre tabindex="0" class="chroma"><code>def swap_values(numbers) -&gt; {&#39;a&#39;:4,&#39;b&#39;:3}
</code></pre>

How would you tackle multicollinearity in multiple linear regression?

What are time series models? Why do we need them when we have less complicated regression models?

What can happen if a traditional regression model is used on data that has autocorrelation?

What can happen if a traditional regression model is used on data that has autocorrelation?

Why Do We Need Time Series Models? I

Why can't standard regression models be used effectively for data points where current values are influenced by past values?

Why can't standard regression models be used effectively for data points where current values are influenced by past values?

Why Do We Need Time Series Models? II

Explain what time series models are and why they’re needed instead of simpler regression models

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

The Hanover Insurance Group Interview Questions

The Hanover Insurance Group Interview Guides

The Hanover Insurance Group Interview Questions

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