Data distributions and outliers in ML Python - Practice Problems & Coding Challenges

Challenge - 5 Problems

🧠 Conceptual

intermediate

Understanding the effect of outliers on mean and median

Consider a dataset with values: [10, 12, 14, 15, 100]. Which statement best describes the effect of the outlier (100) on the mean and median?

A The mean is heavily influenced by the outlier, but the median remains relatively stable.

B Both mean and median are equally influenced by the outlier.

C The median is heavily influenced by the outlier, but the mean remains stable.

D Neither mean nor median is influenced by the outlier.

💡 Hint

Think about how mean and median are calculated and how extreme values affect them.

The mean sums all values and divides by count, so a large outlier increases the mean significantly. The median is the middle value when sorted, so one extreme value has little effect.

❓ Predict Output

intermediate

Detecting outliers using the IQR method

What is the output of the following Python code that detects outliers using the interquartile range (IQR)?

ML Python

import numpy as np

data = np.array([5, 7, 8, 12, 15, 18, 22, 100])
Q1 = np.percentile(data, 25)
Q3 = np.percentile(data, 75)
IQR = Q3 - Q1
outliers = data[(data < Q1 - 1.5 * IQR) | (data > Q3 + 1.5 * IQR)]
print(outliers.tolist())

A []

B [5, 7]

C [100]

D [22, 100]

💡 Hint

Calculate Q1, Q3, then find values outside 1.5 times the IQR range.

The IQR is Q3 - Q1. Values below Q1 - 1.5*IQR or above Q3 + 1.5*IQR are outliers. Here, only 100 is above the upper bound.

❓ Model Choice

advanced

Choosing a model robust to outliers

You have a dataset with many outliers. Which regression model is best suited to minimize the effect of outliers on predictions?

A Robust regression using Huber loss

B Ridge regression with L2 regularization

C Linear regression using least squares loss

D Polynomial regression of degree 5

💡 Hint

Consider which loss functions reduce the influence of extreme errors.

Huber loss combines squared loss for small errors and absolute loss for large errors, reducing outlier impact. Least squares and ridge are sensitive to outliers. Polynomial regression can overfit outliers.

❓ Hyperparameter

advanced

Adjusting hyperparameters to handle outliers in clustering

When using DBSCAN clustering on data with noise and outliers, which hyperparameter adjustment helps to better identify outliers as noise points?

A Decrease the epsilon (eps) value to make clusters tighter

B Decrease the minimum samples (min_samples) to form a cluster

C Increase the epsilon (eps) value to include more points in clusters

D Increase the minimum samples (min_samples) to require more points per cluster

💡 Hint

Think about how changing min_samples affects noise detection.

Increasing min_samples means a cluster needs more points, so fewer small groups form clusters, and more points are labeled as noise (outliers). Decreasing eps or min_samples has opposite effects.

❓ Metrics

expert

Evaluating model performance with imbalanced data and outliers

You have a classification dataset with imbalanced classes and some outliers. Which metric is most reliable to evaluate model performance in this scenario?

A Accuracy

B F1-score

C Precision

D Mean Squared Error (MSE)

💡 Hint

Consider metrics that balance false positives and false negatives in imbalanced data.

Accuracy can be misleading with imbalanced data. Precision alone ignores false negatives. F1-score balances precision and recall, providing a better measure. MSE is for regression, not classification.

Practice

1. What is an outlier in a data distribution?

easy

A. A data point that is very different from most other points

B. The average value of all data points

C. The most common value in the data

D. A data point exactly in the middle of the dataset

Solution

1. Step 1: Understand what an outlier means

   An outlier is a point that stands out because it is far from the rest of the data.

2. Step 2: Compare options to definition

   Only A data point that is very different from most other points describes a point very different from others, which matches the outlier definition.

3. Final Answer:

   A data point that is very different from most other points -> Option A

4. Quick Check:

   Outlier = Different point [OK]

Hint: Outliers are points far from the main group [OK]

Common Mistakes:

• Confusing outlier with average
• Thinking outlier is the most common value
• Mixing outlier with median

2. Which of the following Python code snippets correctly calculates the interquartile range (IQR) to detect outliers?

easy

A. iqr = q3 - q1 # where q1 and q3 are 25th and 75th percentiles

B. iqr = mean + std # mean and standard deviation

C. iqr = max(data) - min(data) # range of data

D. iqr = median(data) * 2 # double the median

Solution

1. Step 1: Recall the IQR formula

   IQR is the difference between the 75th percentile (Q3) and 25th percentile (Q1).

2. Step 2: Match code to formula

   iqr = q3 - q1 # where q1 and q3 are 25th and 75th percentiles correctly subtracts q1 from q3. Other options use unrelated statistics.

3. Final Answer:

   iqr = q3 - q1 # where q1 and q3 are 25th and 75th percentiles -> Option A

4. Quick Check:

   IQR = Q3 - Q1 [OK]

Hint: IQR = Q3 minus Q1, not mean or median [OK]

Common Mistakes:

• Using mean or median instead of percentiles
• Confusing IQR with full data range
• Mixing standard deviation with IQR

3. Given the data points [5, 7, 8, 9, 10, 100], which value is most likely an outlier based on the IQR method?

medium

A. 7

B. 100

C. 10

D. 5

Solution

1. Step 1: Calculate Q1 and Q3

   Sorted data: [5,7,8,9,10,100]. Q1 (25th percentile) ≈ 7, Q3 (75th percentile) ≈ 9.5.

2. Step 2: Compute IQR and check outliers

   IQR = 9.5 - 7 = 2.5. Outliers are points below Q1 - 1.5*IQR = 7 - 3.75 = 3.25 or above Q3 + 1.5*IQR = 9.5 + 3.75 = 13.25. Only 100 is above 13.25, so it is an outlier.

3. Final Answer:

   100 -> Option B

4. Quick Check:

   100 > 13.25 means outlier [OK]

Hint: Outliers lie beyond Q1-1.5*IQR or Q3+1.5*IQR [OK]

Common Mistakes:

• Ignoring the large gap and picking smallest value
• Confusing max value as normal
• Not calculating IQR correctly

4. You have this Python code to detect outliers but it gives wrong results:

import numpy as np
q1 = np.percentile(data, 25)
q3 = np.percentile(data, 75)
iqr = q1 - q3
lower_bound = q1 - 1.5 * iqr
upper_bound = q3 + 1.5 * iqr
outliers = [x for x in data if x < lower_bound or x > upper_bound]

What is the error?

medium

A. Percentiles should be 50 and 100, not 25 and 75

B. Outlier condition should use 'and' instead of 'or'

C. IQR calculation is reversed; should be q3 - q1

D. Bounds calculation should add 1.5 to q1 and q3 directly

Solution

1. Step 1: Check IQR calculation

   IQR is the difference between Q3 and Q1, so it must be q3 - q1, not q1 - q3.

2. Step 2: Verify other parts

   Percentiles 25 and 75 are correct. Outlier condition uses 'or' correctly. Bounds use multiplication correctly.

3. Final Answer:

   IQR calculation is reversed; should be q3 - q1 -> Option C

4. Quick Check:

   IQR = Q3 - Q1, not reversed [OK]

Hint: IQR = Q3 minus Q1, watch subtraction order [OK]

Common Mistakes:

• Swapping q1 and q3 in IQR calculation
• Using wrong percentile values
• Confusing 'or' with 'and' in conditions

5. You have a dataset with many outliers skewing the mean. Which method is best to reduce outlier impact before training a machine learning model?

hard

A. Ignore outliers and train directly

B. Replace all values with the mean

C. Use the maximum value as the central measure

D. Remove data points outside 1.5 times the IQR range

Solution

1. Step 1: Understand outlier impact on mean

   Outliers can pull the mean away from the center, causing bias in training.

2. Step 2: Choose method to reduce outlier effect

   Removing points outside 1.5*IQR is a common way to remove outliers. Replacing with mean or ignoring outliers keeps bias. Using max value is not a central measure.

3. Final Answer:

   Remove data points outside 1.5 times the IQR range -> Option D

4. Quick Check:

   Remove outliers using IQR method [OK]

Hint: Cut off points beyond 1.5*IQR to reduce outliers [OK]

Common Mistakes:

• Replacing all data with mean loses information
• Using max value as center is wrong
• Ignoring outliers causes model bias