Study notes and quiz on “Self-Check Assignment 2: Milligan, Chapter 9: Clusters and Distributions

📝 Study Notes
Topic: Clusters and Distributions Source: Milligan, Chapter 9 Field: Data Analysis / Statistics

1. Introduction to Clusters and Distributions
Clusters and distributions are key concepts in data analysis used to understand how data points are grouped and spread across a dataset. They help identify patterns, trends, and anomalies in data.

2. What Are Clusters?
Clusters refer to groups of data points that are similar to each other.

Clustering is a technique used to segment data into meaningful subgroups.

Common clustering methods include hierarchical clustering, k-means clustering, and density-based clustering.

a. Purpose of Clustering
To simplify data analysis

To identify natural groupings in data

To support decision-making and predictive modeling

b. Applications
Market segmentation

Image recognition

Customer profiling

Medical diagnosis

3. What Are Distributions?
A distribution describes how values of a variable are spread or dispersed.

It shows the frequency of different outcomes in a dataset.

a. Types of Distributions
Normal distribution (bell-shaped curve)

Skewed distribution (left or right skew)

Uniform distribution (equal frequency)

Bimodal distribution (two peaks)

b. Key Measures
Mean (average)

Median (middle value)

Mode (most frequent value)

Range, variance, and standard deviation

4. Relationship Between Clusters and Distributions
Clusters may form within specific regions of a distribution.

Analyzing distributions helps determine the spread and central tendency of clusters.

Clustering algorithms often rely on distributional properties to group data.

5. Visualizing Clusters and Distributions
Histograms and box plots show distributions.

Scatter plots and dendrograms show clusters.

Heatmaps and contour plots can reveal density and grouping.

6. Challenges in Clustering and Distribution Analysis
Choosing the right number of clusters

Handling outliers and noise

Interpreting overlapping clusters

Ensuring meaningful segmentation

✅ 15-Question Quiz
Topic: Clusters and Distributions

1. What does a cluster represent in data analysis? A. A single data point B. A group of similar data points C. A random selection of values D. A type of distribution Answer: B

2. Which method is commonly used for clustering? A. Linear regression B. K-means C. ANOVA D. T-test Answer: B

3. What does a distribution describe? A. The number of clusters B. The spread of values in a dataset C. The color of data points D. The size of the sample Answer: B

4. What shape is a normal distribution? A. Flat line B. Zigzag C. Bell curve D. Triangle Answer: C

5. What is the median in a distribution? A. The most frequent value B. The average of all values C. The middle value when data is ordered D. The highest value Answer: C

6. Which distribution has two peaks? A. Normal B. Uniform C. Bimodal D. Skewed Answer: C

7. What is the mode in a dataset? A. The smallest value B. The average value C. The most frequent value D. The middle value Answer: C

8. Which plot is best for visualizing clusters? A. Histogram B. Scatter plot C. Box plot D. Line graph Answer: B

9. What does standard deviation measure? A. The central value B. The frequency of values C. The spread of values around the mean D. The number of clusters Answer: C

10. What is a challenge in clustering analysis? A. Calculating the mean B. Choosing the number of clusters C. Drawing a histogram D. Finding the mode Answer: B

11. What is a skewed distribution? A. A distribution with equal frequencies B. A distribution with two peaks C. A distribution shifted to one side D. A perfectly symmetrical distribution Answer: C

12. Which clustering method builds a tree-like structure? A. K-means B. Hierarchical clustering C. Linear clustering D. Density clustering Answer: B

13. What is the range in a dataset? A. The difference between the highest and lowest values B. The average of all values C. The most frequent value D. The number of clusters Answer: A

14. What does a box plot show? A. Only the mean B. The distribution and outliers C. The number of clusters D. The frequency of values Answer: B

15. Why is clustering useful in business? A. To reduce data size B. To identify customer segments C. To eliminate variables D. To calculate averages Answer: B

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