Landing a role as a Data Scientist at top tech companies like Amazon and Meta requires more than just technical know-how—it demands strong problem-solving skills and the ability to explain your reasoning clearly. In this comprehensive guide, we’ll break down some of the most challenging and insightful data scientist interview questions from Amazon, Meta, and similar companies. For each question, you’ll find detailed solutions, conceptual explanations, and practical Python code where appropriate. Whether you’re preparing for an upcoming interview or want to deepen your understanding of advanced data science concepts, this article will help you build the knowledge and confidence to succeed.

Data Scientist Interview Questions from Amazon, Meta and Other Companies: Solutions and Explanations

1. Analyzing Significant Difference in Monthly Time Series Data (Amazon)

Problem Statement

You have monthly time series data with a large number of records. What are some ways you can use to find significant differences between this month and the previous month?

Concepts Involved

• Time Series Analysis
• Statistical Hypothesis Testing
• Change Detection
• Visualization Techniques

Approaches to Detecting Significant Differences

1. Summary Statistics and Descriptive Analysis

Start by comparing high-level statistics between the two months:

• Mean, median, and mode
• Standard deviation and variance
• Count of records
• Quartiles and interquartile range (IQR)

Let \( x_{t-1} \) be the data from the previous month, and \( x_t \) be the data from the current month.

• Difference in Means:
  \( \Delta \mu = \mu_{t} - \mu_{t-1} \)
• Relative Change:
  \( \text{Relative Change} = \frac{\mu_{t} - \mu_{t-1}}{\mu_{t-1}} \)

2. Statistical Hypothesis Testing

To check if the observed difference is statistically significant, use hypothesis testing:

• Two Sample t-test:
  Compare the means of two normally distributed samples.
  
  \( H_0: \mu_{t} = \mu_{t-1} \)
  \( H_a: \mu_{t} \neq \mu_{t-1} \)
  Use when the data is continuous and approximately normal.
• Wilcoxon Rank-Sum Test / Mann-Whitney U Test:
  Non-parametric alternative if data is not normally distributed.
• Chi-Square Test:
  If analyzing categorical frequency data.

from scipy import stats

# Assuming x_prev and x_curr are numpy arrays for previous and current month data
t_stat, p_value = stats.ttest_ind(x_curr, x_prev)

if p_value < 0.05:
    print("Statistically significant difference.")
else:
    print("No significant difference.")

3. Change Point Detection

Identify if and when a significant change occurs in the time series.

• Cumulative Sum (CUSUM): Detects shifts in the mean level.
• Bayesian Change Point Detection: Models abrupt changes.
• Statistical Process Control (SPC) Charts: Visualizes mean and variance over time.

4. Visual Exploration

Visualizations facilitate rapid detection of differences:

• Line charts for trends
• Boxplots for distribution
• Bar charts for summary statistics

import matplotlib.pyplot as plt

plt.boxplot([x_prev, x_curr], labels=['Previous Month', 'Current Month'])
plt.title("Monthly Comparison")
plt.show()

5. Aggregation and Granular Analysis

Drill down by subgroups (e.g., by product, region, customer segment) to find where significant changes are localized.

Summary

• Begin with summary statistics and visualization.
• Use hypothesis testing to establish significance.
• Apply change point detection methods for more advanced analysis.
• Segment data to localize significant differences.

2. Expected Steps for Random Walker on a Cube (Amazon)

Problem Statement

Given a cube and a random walker starting at one vertex, find the expected number of steps to reach the opposite vertex.

Concepts Involved

• Markov Chains
• Symmetry and State Grouping
• Recurrence Relations
• Expected Value Calculation

Cube Structure and State Grouping

A cube has 8 vertices. Each vertex connects to 3 neighbors. Let's label the vertices by their distance (in steps) from the start vertex:

• Distance 0: Start vertex (A) (1 vertex)
• Distance 1: Adjacent vertices (B) (3 vertices)
• Distance 2: Vertices two steps away (C) (3 vertices)
• Distance 3: Opposite vertex (D) (1 vertex, the target)

Expected Steps Notation

• Let \( E_0 \) = Expected steps from distance 0 (start)
• Let \( E_1 \) = Expected steps from distance 1
• Let \( E_2 \) = Expected steps from distance 2
• Let \( E_3 = 0 \) (already at the target)

Setting Up Recurrence Equations

From Distance 0 (Start Vertex):

• All 3 neighbors are at distance 1.
• \( E_0 = 1 + E_1 \)

From Distance 1 (Adjacent Vertices):

• 1 neighbor back to distance 0
• 2 neighbors to distance 2
• Probability to go back to 0: \( \frac{1}{3} \)
  Probability to go to 2: \( \frac{2}{3} \)
• \( E_1 = 1 + \frac{1}{3} E_0 + \frac{2}{3} E_2 \)

From Distance 2:

• 2 neighbors at distance 1
• 1 neighbor at distance 3 (the target)
• Probability to go to 1: \( \frac{2}{3} \)
  Probability to go to 3: \( \frac{1}{3} \)
• \( E_2 = 1 + \frac{2}{3} E_1 + \frac{1}{3} \times 0 \)
  \( E_2 = 1 + \frac{2}{3} E_1 \)

System of Equations

We have:

• \( E_0 = 1 + E_1 \)
• \( E_1 = 1 + \frac{1}{3} E_0 + \frac{2}{3} E_2 \)
• \( E_2 = 1 + \frac{2}{3} E_1 \)

Solving the Equations

Let’s solve step by step:

1. From the third equation:
   \( E_2 = 1 + \frac{2}{3} E_1 \)
2. Substitute \( E_2 \) into the second equation:
   \( E_1 = 1 + \frac{1}{3} E_0 + \frac{2}{3} E_2 \)
   \( E_1 = 1 + \frac{1}{3} E_0 + \frac{2}{3}(1 + \frac{2}{3} E_1) \)
   \( E_1 = 1 + \frac{1}{3} E_0 + \frac{2}{3} + \frac{4}{9} E_1 \)
   \( E_1 - \frac{4}{9} E_1 = 1 + \frac{2}{3} + \frac{1}{3} E_0 \)
   \( \frac{5}{9} E_1 = \frac{5}{3} + \frac{1}{3} E_0 \)
   \( E_1 = \frac{9}{5} \times (\frac{5}{3} + \frac{1}{3} E_0) \)
   \( E_1 = 3 + \frac{3}{5} E_0 \)
3. Substitute \( E_1 \) into \( E_0 = 1 + E_1 \):
   \( E_0 = 1 + 3 + \frac{3}{5} E_0 \)
   \( E_0 = 4 + \frac{3}{5} E_0 \)
   \( E_0 - \frac{3}{5} E_0 = 4 \)
   \( \frac{2}{5} E_0 = 4 \)
   \( E_0 = 10 \)

Final Answers:

• Expected steps from start to opposite vertex: \( E_0 = 10 \)
• Expected steps from adjacent: \( E_1 = 3 + \frac{3}{5} \times 10 = 9 \)
• Expected steps from distance-2: \( E_2 = 1 + \frac{2}{3} \times 9 = 7 \)

Summary Table

Key Takeaways

• Group states by distance due to symmetry.
• Set up recurrence relations for expected steps.
• Solve the system to find the answer: 10 steps expected from start to opposite corner.

3. Counting Distinct Interactions per User (Meta)

Problem Statement

Given an event-level table of interactions between pairs of users (with no duplicate pairs per day), for each possible number of people interacted with, find the count for that group in a given day. For example, 10 people interacted with only one person, 20 with two, etc.

Concepts Involved

• SQL Window Functions and GROUP BY
• Counting Distinct Interactions
• Data Aggregation

Step-by-Step Solution

Assume you have a table interactions with columns:

• user_id1
• user_id2
• date

A row means "user_id1 interacted with user_id2 on that date".

1. Count Interactions Per User

• For a given day, count the number of unique users each user interacted with.

-- Get the count of interactions per user
SELECT
  user_id1 AS user_id,
  COUNT(DISTINCT user_id2) AS num_interacted
FROM interactions
WHERE date = '2024-06-01'
GROUP BY user_id1

2. Aggregate by Number of Interactions

• Now, for each num_interacted, count how many users had that count.

WITH user_counts AS (
  SELECT
    user_id1 AS user_id,
    COUNT(DISTINCT user_id2) AS num_interacted
  FROM interactions
  WHERE date = '2024-06-01'
  GROUP BY user_id1
)
SELECT
  num_interacted,
  COUNT(*) AS user_count
FROM user_counts
GROUP BY num_interacted
ORDER BY num_interacted

3. Python Equivalent Using pandas

import pandas as pd

# Assume df is a DataFrame with columns ['user_id1', 'user_id2', 'date']

day_df = df[df['date'] == '2024-06-01']

# Count distinct interactions peruser_counts = (
    day_df.groupby('user_id1')['user_id2']
    .nunique()
    .reset_index(name='num_interacted')
)

# Now, count number of users for each group size
result = (
    user_counts.groupby('num_interacted')
    .size()
    .reset_index(name='user_count')
    .sort_values('num_interacted')
)

print(result)

Explanation of the Solution

• Step 1: For each user, count how many unique users they interacted with on a given day. This is done using COUNT(DISTINCT user_id2) in SQL or nunique() in pandas.
• Step 2: For each possible value of num_interacted, count how many users have that value. This gives a distribution: how many users interacted with 1 person, 2 people, etc.
• Step 3: Sort and present the results for easy inspection.

Key Points

• This approach generalizes to any day and any size of the dataset.
• Efficient aggregation is critical for large datasets; use indexing and vectorized operations in pandas or appropriate SQL indexes.

4. Python Program to Calculate Tax Given Arbitrary Brackets (Meta)

Problem Statement

Given a salary and a list of tax brackets in the form [[10000, 0.3], [20000, 0.2], [30000, 0.1], [None, 0.1]], write a Python program to compute the total tax owed. You do not know the number of brackets in advance.

Concepts Involved

• Iterative Calculation Through Brackets
• Handling Open-ended Ranges (None)
• Generalization for Any Bracket Structure

Step-by-Step Solution

1. Sort the tax brackets in increasing order.
2. For each bracket, compute the taxable amount (current upper limit minus previous upper limit).
3. For the last bracket (where upper is None), tax all remaining salary.
4. Accumulate the total tax.

def calculate_tax(salary, brackets):
    tax = 0.0
    prev_limit = 0
    for upper, rate in brackets:
        if upper is None:
            # Tax all remaining salary at this rate
            taxable = salary - prev_limit
            if taxable <= 0:
                break
            tax += taxable * rate
            break
        taxable = min(salary, upper) - prev_limit
        if taxable <= 0:
            break
        tax += taxable * rate
        prev_limit = upper
    return tax

# Example usage:
salary = 45000
brackets = [ [10000, .3],[20000, .2], [30000, .1], [None, .1] ]
total_tax = calculate_tax(salary, brackets)
print(f"Total tax: {total_tax:.2f}")

Walkthrough with Example

Let’s calculate for salary = 45,000 and the brackets:

• First 10,000 at 30%
• Next 10,000 (10,001 to 20,000) at 20%
• Next 10,000 (20,001 to 30,000) at 10%
• Everything over 30,000 at 10%

Tax calculation:

• 10,000 * 0.3 = 3,000
• 10,000 * 0.2 = 2,000
• 10,000 * 0.1 = 1,000
• 15,000 * 0.1 = 1,500

Total tax = 3,000 + 2,000 + 1,000 + 1,500 = 7,500

Edge Cases to Consider

• Salary less than first bracket
• Salary exactly on a bracket limit
• Salary within a bracket
• Very large salary extending into None bracket

Generalization

• Program works for any number of brackets and any bracket upper limits, as long as the format is consistent.
• Handles open-ended bracket with None correctly.

Conclusion

Data science interviews at leading tech companies challenge your ability to solve analytical problems, explain your reasoning, and code efficiently. The questions above, from Amazon and Meta, test a range of skills—from statistical analysis and Markov chains to SQL aggregation and algorithmic programming. By mastering the concepts and solutions discussed here, you’ll be well-equipped to tackle similar challenges in real interviews and demonstrate your expertise as a data scientist.

Further Resources

• Meta Data Science Interview Questions
• Amazon Data Scientist Interview Reviews
• Interview Query Practice Problems

Stay curious, keep practicing, and good luck on your data science journey!

Related Articles

• Data Scientist Interview Questions from Uber & Other Tech Companies