Why Your Data Might Be Lying to You: The Coefficient of Variation & Skewed Data Problem

Why Your Data Might Be Lying to You: The Coefficient of Variation & Skewed Data Problem

Why Should You Even Care About Data?

Understanding Data is Like Having a Superpower

What This Blog Will Teach You about Data Analysis and Why You Should Stick Around

  • What the Coefficient of Variation is and why people use it
  • Why it sometimes fails, especially with skewed data (Confused about what is left and right skewness? )
  • Some super cool alternatives that are like the next-gen gaming consoles of data analysis

Key Takeaways: What’s in It for You?

  • Decode the Mystery of Coefficient of Variation (CV) : Ever heard of CV and wondered what the hype is all about? We’ll break it down for you in the simplest terms.
  • Why CV Can Be a Drama Queen: Learn why CV sometimes throws a fit and doesn’t play nice with skewed data. Yep, even numbers have their moods!
  • Meet the New Rockstars of Data Analysis : Discover alternative measures that are like the latest iPhone models compared to CV’s old-school flip phone. vs
  • Real-World Hacks for Data Newbies: Get practical tips and tricks that you can use in your daily life, whether you’re shopping online, investing in crypto, or just trying to be the smartest person in the room.
  • Level Up Your Data Game : By the end of this blog, you’ll have enough knowledge to impress not just your friends, but maybe even your boss or professor. Who knows, this could be your first step towards becoming a data scientist!
Data Might Be Lying to You: The Coefficient of Variation & Skewed Data Problem

What’s This Coefficient of Variation Thing Anyway?

Breaking Down the Coefficient of Variation (CV) Like You’re Five

Why Coefficient of Variation is a Go-To Tool

Data Analysis of Instagram Influencers: Food Bloggers vs Comedians

The Scenario

  • Food Bloggers: 1.5, 2, 1.9, 1.7, 2.1, 2.3, 0.3, 0.6, 1.6, 1.4 (in million views)
  • Comedians: 2, 1.9, 7.9, 4.9, 2.9, 0.6, 9.8, 1.6, 2.8, 6.5 (in million views)

The Math Part (Don’t Worry, We’ll Make It Easy!)

Mean (Average) Views

  • Mean (Average) for : (1.5 + 2 + 1.9 + 1.7 + 2.1 + 2.3 + 0.3 + 0.6 + 1.6 + 1.4) / 10 = 1.54 million views
  • Mean (Average) for : (2 + 1.9 + 7.9 + 4.9 + 2.9 + 0.6 + 9.8 + 1.6 + 2.8 + 6.5) / 10 = 4.1 million views
Food Bloggers( x – xbar )( (x – xbar)^2 )Comedians( x – xbar )( (x – xbar)^2 )
1.5-0.040.00162-2.14.41
20.460.21161.9-2.24.84
1.90.360.12967.93.814.44
1.70.160.02564.90.80.64
2.10.560.31362.9-1.21.44
2.30.760.57760.6-3.512.25
0.3-1.241.53769.85.732.49
0.6-0.940.88361.6-2.56.25
1.60.060.00362.8-1.31.69
1.4-0.140.01966.52.45.76
  • Standard Deviation for Food Bloggers: √((0.04 + 0.21 + 0.12 + 0.02 + 0.31 + 0.57 + 1.53 + 0.88 + 0.004 + 0.02)/10) = √(0.366) = 0.605 million views
  • Standard Deviation for Comedians: √((4.41 + 4.84 + 14.44 + 0.64 + 0.04 + 12.25 + 32.49 + 6.25 + 1.69 + 5.76)/10) = √(8.331) = 2.888 million views
  • Coefficient of Variation for Comedians (CV): (2.888 / 4.1) x 100 = 70.44%
  • Coefficient of Variation for Food Bloggers (CV): (0.605 / 1.54) x 100 = 39.28%

What can we conclude from this?

Why Coefficient of Variation is the OG of Data Analysis

How CV Has Been Used in Everything from Stock Markets to Sports Analytics

Coefficient of Variation in Stock Markets

Coefficient of Variation in Sports Analytics

Coefficient of Variation in Healthcare

Coefficient of Variation in Marketing

Coefficient of Variation in Environmental Science

The Coefficient of Variation & Skewed Data

The Plot Twist: Coefficient of Variation Doesn’t Work for All Data

What Happens When Data is as Skewed as a TikTok Algorithm

Real Talk About Outliers and Why They’re the Party Crashers of Data Analysis

Meet the New Kids: Alternatives to Coefficient of Variation

Why Sticking to Just CV is Like Still Using a Flip Phone in 2023

Introducing Quantile-Based Measures That Are the Smartphones to CV’s Flip Phone

  1. Interquartile Range divided by the Median: This is like the iPhone’s portrait mode but for data. It focuses on the middle 50% of your data, giving you a more balanced view.
  2. Median Absolute Deviation divided by the Median: This is like the Night mode on your smartphone camera. Even when things are a bit dark and murky (read: outliers and skewed data), it helps you see clearly.

The Interquartile Range/Median Combo

What It Is and Why It’s Like the Avocado Toast of Data Analysis

Calculations Using the Food Bloggers and Comedians Example

Food Bloggers
  1. Sort the Data: 0.3, 0.6, 1.4, 1.5, 1.6, 1.7, 1.9, 2, 2.1, 2.3
  2. Find the Median: (1.7+1.6)/2 = 1.65 million views
  3. Find the Lower Quartile (Q1): (0.6+1.4)/2 = 1 million views
  4. Find the Upper Quartile (Q3): (2+2.1)/2 = 2.05 million views
  5. Calculate IQR: ( Q3 – Q1 = 2.05 – 1 = 1.05 ) million views
  6. IQR/Median: 1.05/1.65*100 = 63.64%
Comedians
  1. Sort the Data: 0.6, 1.6, 1.9, 2, 2.8, 2.9, 4.9, 6.5, 7.9, 9.8
  2. Find the Median: (2.8 + 2.9)/2 = 2.85 million views
  3. Find the Lower Quartile (Q1): (1.6 + 1.9)/2 = 1.75 million views
  4. Find the Upper Quartile (Q3): (6.5 + 7.9)/2 = 7.2 million views
  5. Calculate IQR: ( Q3 – Q1 = 7.2 – 1.75 = 5.45 ) million views
  6. IQR/Median: 5.45/2.85*100 = 191.23%

Why Choose IQR/Median Over CV in This Case?

The Median Absolute Deviation/Median Duo

What It Is and Why It’s Like the Spotify Playlist That Understands Your Mood

Calculations Using the Food Bloggers and Comedians Example

Food Bloggers (in million views)Deviation (x-median)Absolute DeviationComedians (in million views)Deviation (x-median)Absolute Deviation
1.5-0.150.152-0.850.85
20.350.351.9-0.950.95
1.90.250.257.95.055.05
1.70.050.054.92.052.05
2.10.450.452.90.050.05
2.30.650.650.6-2.252.25
0.3-1.351.359.86.956.95
0.6-1.051.051.6-1.251.25
1.6-0.050.052.8-0.050.05
1.4-0.250.256.53.653.65

Food Bloggers

Comedians

Food Bloggers

Comedians

Why Opt for MAD/Median Over CV?

  1. Outliers: CV is sensitive to outliers. Remember that comedian with 9.8 million views? That’s an outlier and it skews the CV, making it look like comedians are super variable in their popularity. But is that the case for most comedians? Not really.
  2. Skewed Data: CV can be misleading when the data is skewed. In the case of comedians, the data is not evenly distributed, and CV might give you a distorted view of the variability.

The Newbies vs The Veteran

MeasureFood Bloggers (%)Comedians (%)Best ForWorst ForSensitivity to Outliers
Coefficient of Variation (CV)39.2870.44Normally distributed dataSkewed data or outliersHigh
Interquartile Range/Median (IQR/Median)24.2442.11Skewed dataNormally distributed dataLow
Median Absolute Deviation/Median (MAD/Median)15.1533.33Skewed data and outliersNormally distributed dataVery Low

Key Takeaways

  • Coefficient of Variation (CV): The old-school method that’s great for normally distributed data but can get tripped up by outliers or skewed data.
  • Interquartile Range/Median (IQR/Median): The modern method that’s less sensitive to outliers and works well for skewed data, but may not be the best for normally distributed data.
  • Median Absolute Deviation/Median (MAD/Median): The new kid on the block that’s robust against both outliers and skewed data, making it the most “honest” measure of the three.

Coefficient of Variation vs IQR/Median vs MAD/Median

MeasurePositivesNegatives
Coefficient of Variation (CV)– Widely used and understood
– Good for comparing variability across different units
– Sensitive to outliers
– Can be misleading for skewed data
Interquartile Range/Median (IQR/Median)– Less sensitive to outliers compared to CV
– Good for skewed data
– Not as widely understood as CV
– May require more computation
Median Absolute Deviation/Median (MAD/Median)– Robust against outliers
– Excellent for skewed data
– Provides a “honest” view of variability
– Least known among the three
– May require more computation

How to Pick Your Data Hero

Influence Functions: The Spider-Sense

  • CV: Like Iron Man without his suit, it’s vulnerable to outliers.
  • IQR/Median: More like Captain America’s shield, it offers better protection against outliers.
  • MAD/Median: Think of it as Doctor Strange’s time stone; it’s robust and can handle all sorts of data quirks.

Biases: The Loki Effect

  • CV: Can be biased in the presence of outliers, making you think there’s more variability than there actually is.
  • IQR/Median: Less biased, but not entirely immune. It’s like Thor; strong but not invincible.
  • MAD/Median: The least biased of the bunch, akin to Vision, who’s programmed to be as unbiased as possible.

Variances: The Hulk Factor

  • CV: High variance means it can swing wildly with outliers, just like how Bruce Banner can suddenly turn into the Hulk.
  • IQR/Median: More stable, but still has some variance. Think of it as Spider-Man; agile but still human.
  • MAD/Median: The most stable, like Black Widow. No superpowers, but highly trained and reliable.

The Final Pick

  • If your data is clean and well-behaved, CV could be your Iron Man.
  • If you’re dealing with some outliers or skewed data, IQR/Median is your Captain America.
  • And if you want the most robust and reliable measure, MAD/Median is your Doctor Strange.

Real-World Cheat Codes: Practical Applications

Picking a Netflix Show

Investing in Crypto

Choosing a College Major

Planning a Vacation

Online Shopping

Fitness Goals

Flowchart: Your Personal Data Guide

a diagram of a flowchart

Doesn’t matter you are a company or a student!