Why Data Scientist Candidates Freeze on the Simplest Questions

Interviewer: What is the difference between mean
and median?

Candidate: (thinking: this is too easy, what is the
catch? is it about skewness? distributions? should I
mention mode? geometric mean?)

(eight seconds pass)

Candidate: So... it depends on the distribution...
there are different types of means...

Interviewer: Let's try a concrete case.

Interviewer: What is the difference between mean
and median?

Candidate: The mean is the average, and the median is
the middle value when you sort the data.

For example, five salaries of 3, 4, 4, 5 and 50 lakh:
the mean is 13.2 but the median is 4. One outlier pulls
the mean up a lot.

So for skewed data like income or delivery times, I
usually report the median, or both.

Would you like me to talk about how I check skewness?

import pandas as pd

salaries = pd.Series([3, 4, 4, 5, 50])   # lakh per year, toy data
print("mean  :", salaries.mean())         # 13.2
print("median:", salaries.median())       # 4.0
print("skew  :", round(salaries.skew(), 2))

# Remove the outlier and compare
trimmed = salaries[salaries < 20]
print("mean without outlier  :", trimmed.mean())    # 4.0
print("median without outlier:", trimmed.median())  # 4.0

# The median barely moves; the mean collapses from 13.2 to 4.

from sklearn.datasets import make_classification
from sklearn.model_selection import train_test_split
from sklearn.tree import DecisionTreeClassifier

X, y = make_classification(n_samples=1000, n_features=20,
                           n_informative=5, flip_y=0.05,
                           random_state=0)
X_tr, X_te, y_tr, y_te = train_test_split(X, y, test_size=0.3,
                                          random_state=0)

for depth in [1, 3, 5, 10, None]:
    tree = DecisionTreeClassifier(max_depth=depth, random_state=0)
    tree.fit(X_tr, y_tr)
    print(f"depth={str(depth):5s} train={tree.score(X_tr, y_tr):.3f} "
          f"test={tree.score(X_te, y_te):.3f}")

# With no depth limit, train accuracy reaches 1.0 while test
# accuracy stops improving: that gap is overfitting.

import numpy as np
from scipy import stats

rng = np.random.default_rng(1)
old_page = rng.normal(loc=50, scale=10, size=200)   # time on page, toy data
new_page = rng.normal(loc=52, scale=10, size=200)

t_stat, p_value = stats.ttest_ind(new_page, old_page, equal_var=False)
print(f"t = {t_stat:.2f}, p = {p_value:.4f}")
print(f"difference in means = {new_page.mean() - old_page.mean():.2f}")

# Layered answer:
# 1. "The p-value is how likely a difference this big would be
#     if the two pages really performed the same."
# 2. "Here it tells me whether a gap like this is unusual
#     under 'no real difference'."
# 3. "It does not tell me the size of the effect, so I report
#     the difference and its interval too."

import numpy as np

rng = np.random.default_rng(0)
temperature = rng.normal(30, 5, 1000)
ice_cream = 2.0 * temperature + rng.normal(0, 5, 1000)
swim_accidents = 0.5 * temperature + rng.normal(0, 3, 1000)

print("raw correlation:",
      round(np.corrcoef(ice_cream, swim_accidents)[0, 1], 2))

# Remove the effect of temperature from both variables
def residual(y, x):
    slope, intercept = np.polyfit(x, y, 1)
    return y - (slope * x + intercept)

print("after controlling for temperature:",
      round(np.corrcoef(residual(ice_cream, temperature),
                        residual(swim_accidents, temperature))[0, 1], 2))

# Hot days drive both. Once temperature is removed,
# the correlation drops to roughly zero.

ANSWER EACH IN FOUR LAYERS

1. Mean vs median vs mode
2. Variance vs standard deviation
3. What is a normal distribution?
4. What is a p-value?
5. Type I vs Type II error
6. What is a confidence interval?
7. Correlation vs causation
8. Why does sample size matter?

Layers: define -> example -> nuance -> stop

ANSWER EACH IN FOUR LAYERS

1. What is overfitting? Underfitting?
2. What is the bias-variance trade-off?
3. Precision vs recall
4. Why split into train and test?
5. What does regularisation do?
6. Classification vs regression
7. What is cross-validation?
8. Why scale features for some models?

Rule: no answer may start with 'It depends'.

AFTER RECORDING

[ ] Started speaking within three seconds
[ ] First sentence was a plain definition
[ ] Gave one small, concrete example
[ ] Added exactly one nuance
[ ] Stopped and offered more depth
[ ] Total time under forty seconds
[ ] No textbook phrase I could not explain

Question I froze on: ____________
Rewrite my first sentence: ____________