HRT Data Scientist Interview Experience — An OA and a Mean-versus-Median Estimation Interview

I recently finished HRT's OA and first Zoom interview. Sharing the questions here—hope this helps people interviewing later!

OA

I received the coding OA invitation a few days ago and finished it today. There were three questions:

Fancy Number

A fancy number is a number that contains only 0 and 1 when written in base 4.

Given n, return the count of fancy numbers smaller than n.

This probably needs some pattern-finding or a digit-DP-type approach. You can't just enumerate from 1 to n.

Reversi simulation

A simulation problem based on Reversi.

It was mainly about simulating the board state according to the given rules. There were quite a few details, but overall it wasn't especially difficult.

Tree

The last question involved a tree structure, mainly merging two trees.

This one went relatively smoothly.

Overall, I got most of the three questions done. The first one, fancy numbers, didn't pass every test case.

HRT First Zoom Interview

We briefly discussed my background, then started on probability and statistics.

The core was a distribution-estimation problem, with follow-up after follow-up.

Consider a distribution:

With 20% probability, X = μ.

With 80% probability, X ∼ N(μ, 1).

Q1: How would you estimate μ?

Given n samples, how would you estimate μ?

Then the question was:

Which is better, the sample mean or the sample median?

The sample mean was a natural first thought, because the whole distribution is symmetric around μ, so both the mean and median are μ.

But the median has a particular advantage here: the distribution has a 20% point mass at X = μ, so the sample median can easily land directly on μ.

Q2: Compare the estimation errors of the mean and median.

Here, error was defined as mean absolute error, or MAE.

The interviewer asked me to write a simulation, using

sample mean

sample median

to estimate μ, then compare their MAEs numerically.

I wrote it and ran it. The sample median's error was clearly much smaller than the sample mean's.

At the time, I mainly understood it in terms of the distribution being symmetric. Looking back, I think the more important reason is the 20% probability mass at μ, which makes the median especially effective for this distribution.

Q3: When n = 80, what is the probability that the error exceeds 0.1?

Now fix n = 80.

The question was

P(|μ̂ - μ| > 0.1)

for the sample mean and sample median, respectively.

Sample median

I didn't have time to work this part out completely.

Intuitively, its probability should be much smaller than the sample mean's, because each sample has a 20% chance of being exactly μ, and the median is very sensitive to those samples concentrated at μ.

There was a little time left at the end for my questions.

I asked about HRT's culture. The interviewer said HRT was generally collaborative, with lots of communication and cooperation, and that people were nice.

Overall, the interview experience was pretty good. The problem itself wasn't especially tricky. It felt like they cared more about whether I could analyze the distribution step by step, propose an estimator, then verify it through calculations or simulation.

Hope I make it to the next round!