Data Science & Machine Learning
Kanalga Telegram’da o‘tish
Join this channel to learn data science, artificial intelligence and machine learning with funny quizzes, interesting projects and amazing resources for free For collaborations: @love_data
Ko'proq ko'rsatish
Tarmoq:📈 Telegram kanali Data Science & Machine Learning analitikasi
Data Science & Machine Learning (@datasciencefun) Ingliz til segmentidagi kanali faol ishtirokchi. Hozirda hamjamiyat 77 275 obunachidan iborat bo'lib, Taʼlim toifasida 2 020-o'rinni va Hindiston mintaqasida 4 066-o'rinni egallagan.
📊 Auditoriya ko‘rsatkichlari va dinamika
невідомо sanasidan buyon loyiha tez o‘sib, 77 275 obunachiga ega bo‘ldi.
25 Avgust, 2026 dagi oxirgi ma’lumotlarga ko‘ra kanal barqaror faollikka ega. Oxirgi 30 kunda obunachilar soni 432 ga, so‘nggi 24 soatda esa -7 ga o‘zgardi va umumiy qamrov yuqori darajada qolmoqda.
- Tasdiqlash holati: Tasdiqlanmagan
- Jalb etish (ER): Auditoriya o‘rtacha 2.60% darajada jalb etiladi. Nashrdan keyingi dastlabki 24 soatda kontent odatda umumiy obunachilar sonining 1.13% ini tashkil etuvchi reaksiyalarni to‘playdi.
- Post qamrovi: Har bir post o‘rtacha 2 008 marta ko‘riladi; birinchi sutkada odatda 876 ta ko‘rish yig‘iladi.
- Reaksiyalar va o‘zaro ta’sir: Auditoriya faol: har bir postga o‘rtacha 3 ta reaksiya keladi.
- Tematik yo‘nalishlar: Kontent learning, accuracy, distribution, panda, dataset kabi asosiy mavzularga jamlangan.
📝 Tavsif va kontent siyosati
Muallif resursni shaxsiy fikrni ifoda etish maydoni sifatida ta’riflaydi:
“Join this channel to learn data science, artificial intelligence and machine learning with funny quizzes, interesting projects and amazing resources for free
For collaborations: @love_data”
Yuqori yangilanish chastotasi (oxirgi ma’lumot 26 Avgust, 2026 da olingan) sababli kanal doimo dolzarb va katta qamrovli bo‘lib qoladi. Analitika auditoriya kontent bilan faol hamkorlik qilishini, uni Taʼlim toifasidagi muhim ta’sir nuqtasiga aylantirishini ko‘rsatadi.
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| 4 | Output: 1.0
This indicates a perfect positive linear relationship for this small example.
🔹 18. Common Mistakes
• Thinking correlation must be between 0 and 1 → Correlation can be negative: -1 <= r <= 1
• Thinking r = 0 means absolutely no relationship → It means there is no linear relationship detected by Pearson correlation. A nonlinear relationship may still exist.
• Assuming high correlation proves causation → Correlation only tells us that variables move together. It does not establish cause and effect.
🎯 Practice Questions
•
1. What does positive covariance indicate?
•
1. What is the possible range of Pearson correlation?
•
1. What does a correlation of -0.90 indicate?
•
1. Why is correlation easier to interpret than covariance?
•
1. Why doesn't correlation imply causation?
🎯 Key Takeaways
• Covariance measures how two variables change together.
• Positive covariance indicates that variables tend to move in the same direction.
• Negative covariance indicates that they tend to move in opposite directions.
•
Correlation measures the direction and strength of a linear relationship.
•
Pearson correlation ranges from -1 to +1.
• Correlation is unitless and easier to interpret than covariance.
• A correlation of +1 indicates perfect positive linear association.
• A correlation of -1 indicates perfect negative linear association.
• A correlation of 0 indicates no linear association.
• Correlation does not imply causation.
👉 Double Tap ❤️ For More 📊
-----
1.55 ₽ · /balance_help | 1 004 |
| 5 | • +0.9 → Very strong positive
• +0.5 → Moderate positive
• +0.1 → Weak positive
• 0 → No linear relationship
• -0.1 → Weak negative
• -0.5 → Moderate negative
• -0.9 → Very strong negative
The exact interpretation depends on the domain and context.
🔹 9. Pearson Correlation Coefficient ⭐
The most commonly used correlation measure is the Pearson correlation coefficient.
It is calculated as:
• r = Cov(X,Y) / (StdDev X ** StdDev Y)
Where:
• Cov(X,Y) = Covariance between X and Y
• StdDev X = Standard deviation of X
• StdDev Y = Standard deviation of Y
Because covariance is divided by the standard deviations, the result is standardized between -1 and +1.
🔹 10. Covariance vs Correlation
• Covariance: Measures direction of joint variation, Can have any numerical value, Depends on units, Harder to interpret, Useful mathematically
• Correlation: Measures direction and strength, Always between -1 and +1, Unitless, Easier to interpret, Very useful for EDA
🔹 11. Positive Correlation Example
Suppose: Advertising Spend ↑ → Sales ↑
If higher advertising spending generally corresponds to higher sales, the correlation may be positive.
• For example: r = 0.85 → This indicates a strong positive linear relationship.
🔹 12. Negative Correlation Example
Suppose: Price ↑ → Demand ↓
You might observe: r = -0.80 → This indicates a strong negative linear relationship.
🔹 13. Correlation Does NOT Mean Causation ⭐
This is one of the most important concepts in Data Science.
Suppose we observe: Ice Cream Sales ↑ ↔ Swimming Pool Accidents ↑
There may be a positive correlation. But eating ice cream doesn't necessarily cause swimming accidents.
A third variable — hot weather — could influence both:
• Hot Weather → Ice Cream Sales
• Hot Weather → Swimming Activity → Accidents
Therefore: Correlation does not prove causation.
🔹 14. Correlation and Machine Learning
Correlation is frequently used during Exploratory Data Analysis.
For example, suppose you're predicting house prices. You might examine correlations between:
• House size
• Number of bedrooms
• Location-related variables
• Age of property
• Price
A strong correlation between house size and price may indicate that house size could be a useful predictive feature.
However, correlation alone does not determine whether a feature should be included in a model.
🔹 15. Correlation Matrix ⭐
When a dataset contains many numerical variables, we can calculate correlations between every pair of variables. This produces a correlation matrix.
Example:
• Age | Income | Spending
• Age: 1.00, 0.65, -0.10
• Income: 0.65, 1.00, 0.72
• Spending: -0.10, 0.72, 1.00
The diagonal is always 1.00 because every variable has a perfect correlation with itself.
🔹 16. Detecting Multicollinearity
• Correlation can help identify multicollinearity.
• Multicollinearity occurs when two or more predictor variables are highly correlated with each other.
• For example: Annual Income ↔ Monthly Income — These variables contain very similar information.
• Including highly correlated predictors can create problems for some models, particularly linear regression, because it can make coefficient estimates unstable and harder to interpret.
🔹 17. Python Example
Using Pandas:
import pandas as pd
data = {
"Hours": [2, 4, 6, 8, 10],
"Score": [50, 60, 70, 80, 90]
}
df = pd.DataFrame(data)
print(df["Hours"].corr(df["Score"])) | 687 |
| 6 | 🚀 Data Science Roadmap 2026
📘 Phase 2: Mathematics for Data Science
📖 Topic 8: Covariance and Correlation
Welcome back! 👋
In the previous lesson, you learned about Range, Percentiles, Quartiles, IQR, and the Five-Number Summary.
Now let's learn two extremely important concepts for understanding relationships between variables:
• Covariance
• Correlation
These concepts are used extensively in Exploratory Data Analysis (EDA), feature selection, machine learning, and statistical analysis.
🔹 1. Why Do We Need Covariance and Correlation?
Suppose you're analyzing student data:
• Hours Studied | Exam Score
• 2 | 50
• 4 | 60
• 6 | 70
• 8 | 80
• 10 | 90
You can observe that as study hours increase, exam scores also increase.
But how can we mathematically measure this relationship?
That's where covariance and correlation come in.
🔹 2. What is Covariance?
Covariance measures the direction in which two variables change together.
It tells us whether two variables tend to increase or decrease together.
Three possibilities:
• Positive Covariance: When one variable increases, the other tends to increase. X ↑ → Y ↑. Example: Study hours ↑ → Exam score ↑
• Negative Covariance: When one variable increases, the other tends to decrease. X ↑ → Y ↓. Example: Product price ↑ → Demand ↓
• Covariance Near Zero: There is little or no linear relationship between the variables. X ↑ → No consistent change in Y
🔹 3. Covariance Formula
For population data:
• Cov(X,Y) = Sum of (Xi - Mean X) ** (Yi - Mean Y) / N
Where:
• Xi = Individual X value
• Yi = Individual Y value
• Mean X = Mean of X
• Mean Y = Mean of Y
• N = Number of observations
The calculation essentially asks: When X is above or below its average, is Y also above or below its average?
🔹 4. Simple Covariance Example
Consider:
• X = [1, 2, 3]
• Y = [2, 4, 6]
Means:
• Mean(X) = 2
• Mean(Y) = 4
Now calculate deviations:
• X | X - Mean X | Y | Y - Mean Y | Product
• 1 | -1 | 2 | -2 | 2
• 2 | 0 | 4 | 0 | 0
• 3 | 1 | 6 | 2 | 2
Sum of products: 2 + 0 + 2 = 4
Population covariance: Cov(X,Y) = 4 / 3 = 1.33
So covariance is positive. That makes sense because Y increases whenever X increases.
🔹 5. The Problem with Covariance
• Covariance tells us the direction of a relationship, but its magnitude depends on the units of the variables.
• For example: Height in centimeters, Weight in kilograms
• Changing centimeters to meters can change the numerical value of covariance.
• Therefore, covariance isn't always easy to interpret or compare.
• This leads us to correlation.
🔹 6. What is Correlation? ⭐
• Correlation measures both the direction and strength of a linear relationship between two variables.
• Unlike covariance, correlation is standardized.
• Its value always lies between: -1 <= r <= 1
🔹 7. Interpreting Correlation
• r = +1: Perfect positive linear relationship. X ↑ → Y ↑
• r = -1: Perfect negative linear relationship. X ↑ → Y ↓
• r = 0: No linear relationship.
• Important: r = 0 does not necessarily mean there is no relationship at all. A strong nonlinear relationship can still exist.
🔹 8. Correlation Strength
A rough interpretation: | 650 |
| 7 | Output: 1.0
This indicates a perfect positive linear relationship for this small example.
🔹 18. Common Mistakes
• Thinking correlation must be between 0 and 1 → Correlation can be negative: -1 <= r <= 1
• Thinking r = 0 means absolutely no relationship → It means there is no linear relationship detected by Pearson correlation. A nonlinear relationship may still exist.
• Assuming high correlation proves causation → Correlation only tells us that variables move together. It does not establish cause and effect.
🎯 Practice Questions
•
1. What does positive covariance indicate?
•
1. What is the possible range of Pearson correlation?
•
1. What does a correlation of -0.90 indicate?
•
1. Why is correlation easier to interpret than covariance?
•
1. Why doesn't correlation imply causation?
🎯 Key Takeaways
• Covariance measures how two variables change together.
• Positive covariance indicates that variables tend to move in the same direction.
• Negative covariance indicates that they tend to move in opposite directions.
•
Correlation measures the direction and strength of a linear relationship.
•
Pearson correlation ranges from -1 to +1.
• Correlation is unitless and easier to interpret than covariance.
• A correlation of +1 indicates perfect positive linear association.
• A correlation of -1 indicates perfect negative linear association.
• A correlation of 0 indicates no linear association.
• Correlation does not imply causation.
👉 Double Tap ❤️ For More 📊
-----
1.55 ₽ · /balance_help | 1 |
| 8 | • +0.9 → Very strong positive
• +0.5 → Moderate positive
• +0.1 → Weak positive
• 0 → No linear relationship
• -0.1 → Weak negative
• -0.5 → Moderate negative
• -0.9 → Very strong negative
The exact interpretation depends on the domain and context.
🔹 9. Pearson Correlation Coefficient ⭐
The most commonly used correlation measure is the Pearson correlation coefficient.
It is calculated as:
• r = Cov(X,Y) / (StdDev X ** StdDev Y)
Where:
• Cov(X,Y) = Covariance between X and Y
• StdDev X = Standard deviation of X
• StdDev Y = Standard deviation of Y
Because covariance is divided by the standard deviations, the result is standardized between -1 and +1.
🔹 10. Covariance vs Correlation
• Covariance: Measures direction of joint variation, Can have any numerical value, Depends on units, Harder to interpret, Useful mathematically
• Correlation: Measures direction and strength, Always between -1 and +1, Unitless, Easier to interpret, Very useful for EDA
🔹 11. Positive Correlation Example
Suppose: Advertising Spend ↑ → Sales ↑
If higher advertising spending generally corresponds to higher sales, the correlation may be positive.
• For example: r = 0.85 → This indicates a strong positive linear relationship.
🔹 12. Negative Correlation Example
Suppose: Price ↑ → Demand ↓
You might observe: r = -0.80 → This indicates a strong negative linear relationship.
🔹 13. Correlation Does NOT Mean Causation ⭐
This is one of the most important concepts in Data Science.
Suppose we observe: Ice Cream Sales ↑ ↔ Swimming Pool Accidents ↑
There may be a positive correlation. But eating ice cream doesn't necessarily cause swimming accidents.
A third variable — hot weather — could influence both:
• Hot Weather → Ice Cream Sales
• Hot Weather → Swimming Activity → Accidents
Therefore: Correlation does not prove causation.
🔹 14. Correlation and Machine Learning
Correlation is frequently used during Exploratory Data Analysis.
For example, suppose you're predicting house prices. You might examine correlations between:
• House size
• Number of bedrooms
• Location-related variables
• Age of property
• Price
A strong correlation between house size and price may indicate that house size could be a useful predictive feature.
However, correlation alone does not determine whether a feature should be included in a model.
🔹 15. Correlation Matrix ⭐
When a dataset contains many numerical variables, we can calculate correlations between every pair of variables. This produces a correlation matrix.
Example:
• Age | Income | Spending
• Age: 1.00, 0.65, -0.10
• Income: 0.65, 1.00, 0.72
• Spending: -0.10, 0.72, 1.00
The diagonal is always 1.00 because every variable has a perfect correlation with itself.
🔹 16. Detecting Multicollinearity
• Correlation can help identify multicollinearity.
• Multicollinearity occurs when two or more predictor variables are highly correlated with each other.
• For example: Annual Income ↔ Monthly Income — These variables contain very similar information.
• Including highly correlated predictors can create problems for some models, particularly linear regression, because it can make coefficient estimates unstable and harder to interpret.
🔹 17. Python Example
Using Pandas:
import pandas as pd
data = {
"Hours": [2, 4, 6, 8, 10],
"Score": [50, 60, 70, 80, 90]
}
df = pd.DataFrame(data)
print(df["Hours"].corr(df["Score"])) | 1 |
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| 10 | Which of the following represents the five-number summary? | 1 518 |
| 11 | Which formula is used to calculate the upper bound for potential outliers using the IQR method? | 1 400 |
| 12 | If Q1 = 20 and Q3 = 80, what is the IQR? | 1 255 |
| 13 | Which percentile represents the median? | 1 243 |
| 14 | What is the range of the dataset below?
10, 20, 30, 40, 50 | 1 205 |
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| 17 | Essential Excel Functions for Data Analysts 🚀
1️⃣ Basic Functions
SUM() – Adds a range of numbers. =SUM(A1:A10)
AVERAGE() – Calculates the average. =AVERAGE(A1:A10)
MIN() / MAX() – Finds the smallest/largest value. =MIN(A1:A10)
2️⃣ Logical Functions
IF() – Conditional logic. =IF(A1>50, "Pass", "Fail")
IFS() – Multiple conditions. =IFS(A1>90, "A", A1>80, "B", TRUE, "C")
AND() / OR() – Checks multiple conditions. =AND(A1>50, B1<100)
3️⃣ Text Functions
LEFT() / RIGHT() / MID() – Extract text from a string.
=LEFT(A1, 3) (First 3 characters)
=MID(A1, 3, 2) (2 characters from the 3rd position)
LEN() – Counts characters. =LEN(A1)
TRIM() – Removes extra spaces. =TRIM(A1)
UPPER() / LOWER() / PROPER() – Changes text case.
4️⃣ Lookup Functions
VLOOKUP() – Searches for a value in a column.
=VLOOKUP(1001, A2:B10, 2, FALSE)
HLOOKUP() – Searches in a row.
XLOOKUP() – Advanced lookup replacing VLOOKUP.
=XLOOKUP(1001, A2:A10, B2:B10, "Not Found")
5️⃣ Date & Time Functions
TODAY() – Returns the current date.
NOW() – Returns the current date and time.
YEAR(), MONTH(), DAY() – Extracts parts of a date.
DATEDIF() – Calculates the difference between two dates.
6️⃣ Data Cleaning Functions
REMOVE DUPLICATES – Found in the "Data" tab.
CLEAN() – Removes non-printable characters.
SUBSTITUTE() – Replaces text within a string.
=SUBSTITUTE(A1, "old", "new")
7️⃣ Advanced Functions
INDEX() & MATCH() – More flexible alternative to VLOOKUP.
TEXTJOIN() – Joins text with a delimiter.
UNIQUE() – Returns unique values from a range.
FILTER() – Filters data dynamically.
=FILTER(A2:B10, B2:B10>50)
8️⃣ Pivot Tables & Power Query
PIVOT TABLES – Summarizes data dynamically.
GETPIVOTDATA() – Extracts data from a Pivot Table.
POWER QUERY – Automates data cleaning & transformation.
You can find Free Excel Resources here: https://t.me/excel_data
Hope it helps :)
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