Is chapter main ham statistics of us ki types dekhen gay or sirf Descriptive statistics per focus karen gay.
Angrez kehta hai ka:
โStatistics is the science of collecting, organizing, presenting, analyzing and interpreting numerical data to assist in making more effective decisions.โ
Asan alfaz main:
โStatistics is the science of data.โ
Us se b asan alfaz main:
โStatistics data ka wo ilm hai jo data ko collect karna, usay organize karna, analyse karna, aur phir us se conclusions nikalne mein madad karta hai.โ
Sochiye, aap Lahore ke traffic patterns ya Karachi ke weather trends ko samajhne ke liye data collect kar rahe hain; statistics yahan par aapko yeh samajhne mein madad karega ke data kya keh raha hai.
Broadly, statistics do main types mein divided hai:
Descriptive Statistics data ko samajhne aur present karne ka aik asaan aur effective tareeqa hai. Is mein hum data ke basic features ko describe karte hain aur is se simple summaries about the sample and the measures banate hain. Yeh typically numbers ya graphs ke zariye kiya jata hai. Descriptive statistics mein shamil hain:
Descriptive statistics se aapko fori aur clear understanding milti hai ke aapka data kya keh raha hai, bina kisi complex analysis ke. Ye Lahore ke temperature patterns se le kar Karachi ke shopping trends tak, har tarah ke data ko samajhne mein pehla qadam hota hai. ๐โจ๐
Bilkul population and samples asan hy aik dam. chaliye iss concept ko detail se samajhte hain! ๐๐
Population vs. Sample: Ek Hi Data Set, Do Mukhtalif Tawajjuh ๐๐
Ek hi data set ko kabhi population aur kabhi sample ke taur par dekha ja sakta hai, ye depend karta hai ke aap data ko kyun aur kaise analyze kar rahe hain.
Misal: Farz karein, aap ke pass ek class ke final exam ke grades hain. Agar aapka maqsad sirf is class ke scores ka distribution describe karna hai, toh ye grades aapke liye ek population ban jate hain. Lekin, agar aap in grades se koi inference nikalna chahte hain, maslan, dusre classes ya schools ke students ke scores ke bare mein, toh ye grades aapke liye ek sample ke tor par kaam aate hain.
Jab aap population ko analyze karte hain, iska matlab hai ke aapki data set mein poori population of interest shamil hai. Aap is group ke tamam members par apne calculations kar rahe hote hain, aur aap seedhe taur par iss group ke characteristics ke bare mein statements kar sakte hain.
Is ke baraks, jab aap sample ko analyze karte hain, toh aap ek bade population se liye gaye chhote hisse par kaam kar rahe hote hain. Yahan jo statements aap bade group ke bare mein karte hain, woh probabilistic hote hain, yani ke yeh poore group par bilkul sahi na bhi ho sakte.
Descriptive vs. Inferential Statistics:
Parameters (Population ke Liye): Population ko describe karne wale numbers ko parameters kehte hain, aur inhe Greek letters jaise \(\mu\) (population mean ke liye) aur \(\sigma\) (population standard deviation ke liye) se signify kiya jata hai.
Statistics (Sample ke Liye): Sample ko describe karne wale numbers ko statistics kehte hain, aur inhe Latin letters jaise \(\bar{x}\) (sample mean ke liye) aur \(s\) (sample standard deviation ke liye) se signify kiya jata hai.
Practical wajah se, aksar population ki bajaye samples ka analysis kiya jata hai, kyunki puri population ko direct study karna mumkin nahi ho sakta ya phir bohot mehnga pad sakta hai.
Is distinction ko samajhna statistics mein fundamental hai aur iske liye notational conventions aur terminology develop ki gayi hain. Har author ke yahan thoda farq ho sakta hai, lekin generally, yehi conventions follow kiye jate hain. ๐โจ๐
Statistics main mathematical notations ka bohot istemal hota hai. Is liye, aapko in notations ko samajhna bohot zaroori hai. Yeh rahi descriptive statistics mein istemal hone wali kuch common notations ki list, unke ek line mein explanations ke saath:
Ye notations descriptive statistics mein data ko samajhne aur uski interpretation mein madadgar hoti hain. Har notation ka apna specific maqsad aur use hota hai. ๐โจ๐
Descriptive statistics mein kuch aur bhi notations hote hain jo data ko samajhne aur analyze karne mein madadgar hote hain. Yahan kuch aur examples hain:
Ye additional notations aur bhi insight provide karte hain jab hum kisi data set ko descriptive statistics ke zariye analyze karte hain. Inka istemal data ke various aspects ko better samajhne aur interpret karne mein kiya jata hai. ๐๐๐โจ
Angrez kehta hy:
Measures of central tendency, also known as measures of location, are descriptive statistics that describe the central position of a numeric data set.
quantitative (continuous) data.Bilkul, chaliye baat karte hain โCentral Tendencyโ ke baare mein, Roman Urdu aur emojis ke saath! ๐๐
Central Tendency - Markazi Rujhan ๐ฏ
โCentral Tendencyโ ek statistical term hai jo describe karti hai ke ek data set ke andar values kis jagah concentrate hote hain ya jama hote hain. Yeh basically aapko batati hai ke aapke data ke โmarkazโ ya โcentreโ mein kya hota hai. Central Tendency ke measures data ke typical ya average behavior ko samajhne mein madad karte hain.
Central Tendency Ke Teen Main Measures ๐๐๐ฏ
Mean (Ausat): Yeh sab values ka average hota hai. Misal ke taur par, agar aap Lahore ke kisi college ke students ki umar ka average nikalna chahte hain, toh aap sab students ki age ka total le ke unki taadad se divide karenge.
Average Income ๐ฐ: Farz karein, aap Karachi ke ek mohalle mein rehne walon ki average monthly income janna chahte hain. Aap mohalle ke har ghar se income collect karte hain aur un sab ko jamaa kar ke total gharon ki taadad se divide karte hain. Jo number aata hai, woh is mohalle ki average monthly income hogi. Ye mean ya ausat kehlata hai.
Mean (Ausat) ๐
Mean in python can be calculated as show in Figure 5.2
Mean, ya arithmetic mean, data science aur everyday analysis mein sab se zyada istemal hone wala measure hai. Ye aapko data set ke general trend ko samajhne mein madad karta hai. Business decisions se le kar scientific research tak, mean ka istemal data ke average behaviour ko samajhne aur us par mabni decisions lene ke liye kiya jata hai. Ye simple hai, lekin powerful tool hai jo data ke central tendency ko capture karta hai. ๐โจ๐
Median (Wasti Qeemat): Jab values ko order mein arrange kiya jaye, toh jo value beech mein aati hai, woh median hoti hai. Jaise, agar aap Islamabad mein ghar ki prices ko order mein lagaen, toh jo price beech mein hogi, woh median hogi.
Property Rates ๐ : Lahore ke DHA mein property rates ki range bohot zyada hoti hai. Agar aap sab properties ki values ko order mein arrange karein aur phir beech ki value dekhein, toh woh median property rate hogi. Ye aapko batayega ke aam taur par DHA mein property ki qiymat kya hogi, is se high aur low extremes ka asar kam ho jata hai.
Median (Wasti Qiymat) ๐ - Odd Number of Values: Median woh middle value hai jab values ko ascending order mein arrange kiya jata hai. - Even Number of Values: Middle do values ka average. - Example: Agar aapke paas values hain [10, 20, 30, 40, 50], to median 30 hoga (middle value). Agar values hain [10, 20, 30, 40], to median hoga: \[\frac{20 + 30}{2} = 25\]
Median in python can be calculated as show in Figure 5.2
Median, khaas taur par us waqt ahem ho jata hai jab data skewed ho ya outliers contain karta ho. Jaise, agar aap Lahore mein property prices dekhein aur kuch bahut hi high ya low prices hon, to mean distorted ho sakta hai, lekin median aapko zyada reliable picture deta hai.
Median data ke distribution ko beech se cut karta hai, jis se humein pata chalta hai ke data set ke aadhe values is value se kam hain aur aadhe zyada. Ye especially helpful hota hai market analysis, income surveys, ya real estate prices jaise situations mein, jahan outliers mean ko affect kar sakte hain. ๐โจ๐
Mode (Aksar Aane Wali Qiymat): Wo value jo data set mein sab se zyada bar repeat hoti hai. Maan lijiye, Karachi ke ek area mein agar aap dekhein ke zyadatar log konsi car drive kar rahe hain, toh jo car model sab se zyada nazar aaye, woh mode hoga.
Most Common Car ๐: Islamabad ke F-10 sector mein, agar aap notice karein ke zyadatar log Honda Civic drive kar rahe hain, to Honda Civic is sector ka mode hoga. Yani yeh woh car hai jo is area mein sab se zyada common hai.
Mode (Aksar Aane Wali Qiymat) ๐ฏ - Formula: Mode woh value hai jo data set mein sab se zyada bar aati hai. - Example: Agar aapke paas values hain [1, 2, 2, 3, 4], to mode 2 hoga (kyunki 2 do dafa aaya hai aur baaki sab ek ek bar).
Mode in python can be calculated as follows:
# Import libraries
import numpy as np
import matplotlib.pyplot as plt
import pandas as pd
# Create a dataset
data = np.array([1, 2, 2, 3, 4, 4, 4, 5, 5, 6, 6, 6, 6, 7, 8, 9, 9, 9, 9, 9, 10])
# Calculate the mode
modes = pd.Series(data).mode()
# Plot the dataset and mode
plt.figure(figsize=(6, 5))
plt.plot(data, 'ko', label='Data')
for mode in modes:
plt.axhline(mode, color='red', label=f'Mode {mode}')
plt.legend()
plt.title('Data with Multiple Modes')
plt.show()
Mode ka use data ke distribution aur uske most common ya repeated elements ko samajhne ke liye hota hai. Ye aksar categorical data, jaise favorite items, categories, ya classes ko analyze karne mein madadgar hota hai. Mode se humein yeh insight milta hai ke kis cheez ko log sab se zyada pasand karte hain ya sab se zyada istemal karte hain, jo ke market research, public opinion surveys, aur social sciences mein khaas taur par useful hota hai. ๐๐โจ๐ฏ
Central Tendency humein data sets ke baare mein aham insights deti hai. Yeh batata hai ke aam taur par data kis tarah distribute hua hai. Business decisions se le kar scientific research tak, har jagah Central Tendency ka analysis crucial hota hai. Is se hum data ke general pattern ko samajh sakte hain aur complex data sets ko asaan tareeqe se summarize kar sakte hain.
Central Tendency ka sahi istemal aapko aapke data ke markaz ya central point ki deep understanding provide karta hai, jo ke kisi bhi statistical analysis ya data science project ke liye foundation ka kaam karta hai. ๐โจ๐
Median is Better than Mean: Jab data set mein outliers ya extreme values hain, toh median mean se zyada reliable hota hai. Is liye, jab aap data set ko analyze kar rahe hain aur aapko pata hai ke data mein extreme values hain, toh aap median ka istemal karen.
Letโs see an example to understand this better. ๐โจ๐
# Import libraries
import numpy as np
import matplotlib.pyplot as plt
import pandas as pd
# Create a dataset with some outliers
data = np.array([1, 2, 3, 4, 5, 6, 7, 8, 9, 10])
# Calculate the mean and median of the dataset
mean = np.mean(data)
median = np.median(data)
# Plot the dataset, mean, and median
plt.figure(figsize=(6, 5))
plt.plot(data, 'ko', label='Data')
plt.axhline(mean, color='red', label='Mean')
plt.axhline(median, color='blue', label='Median')
plt.legend()
plt.title('Data without Outliers')
plt.show()
# Import libraries
import numpy as np
import matplotlib.pyplot as plt
import pandas as pd
# Create a dataset with some outliers
data = np.array([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 100])
# Calculate the mean and median of the dataset
mean = np.mean(data)
median = np.median(data)
# Plot the dataset, mean, and median
plt.figure(figsize=(6, 5))
plt.plot(data, 'ko', label='Data')
plt.axhline(mean, color='red', label='Mean')
plt.axhline(median, color='blue', label='Median')
plt.legend()
plt.title('Data with Outlier')
plt.show()
# Add some outliers to the dataset
data_with_outliers = np.append(data, [1000, 2000, 3000])
# Calculate the new mean and median
new_mean = np.mean(data_with_outliers)
new_median = np.median(data_with_outliers)
# Plot the updated dataset, mean, and median
plt.figure(figsize=(6, 5))
plt.plot(data_with_outliers, 'ko', label='Data with Outliers')
plt.axhline(new_mean, color='red', label='Mean')
plt.axhline(new_median, color='blue', label='Median')
plt.legend()
plt.title('Data with More Outliers')
plt.show()
Variability ya Tabdeeli, statistics mein data points ke darmiyan hone wale ikhtilaaf ya farq ko bayan karta hai. Yeh aapko batata hai ke aapke data mein diversity ya inconsistency kitni hai. Iska matlab hai ke aapke data points kitne similar ya dissimilar hain ek dusre se.
Variability is also known as dispersion ya spread.
Variability Ke Main Measures ๐
Bilkul, yeh raha ek aam zindagi se related example jis se โvariabilityโ ka concept samajh mein aayega, Roman Urdu aur emojis ke saath! ๐๐
Coefficient of Variation (CV), ya Tabdeeli Ka Coefficient, ek statistical measure hai jo data ke variability ko quantify karta hai, lekin isey standard deviation ke relative terms mein express kiya jata hai. Ye batata hai ke data ke standard deviation ka mean ke sath kya rishta hai.
CV ka formula hai: \[CV = \frac{\sigma}{\bar{x}} \times 100\%\] Jahan \(\sigma\) standard deviation hai aur \(\bar{x}\) mean hai.
CV ek versatile tool hai jo data ke spread ya variability ko relative terms mein samajhne mein madad karta hai, aur ye kai fields mein, jaise finance, research, aur marketing mein, insights provide karne ke liye istemal hota hai. ๐๐ฌโจ๐
School Ki Performance ๐ซ๐
Situation: Aap ek education board ke analyst hain aur aapko Lahore ke alag-alag schools ke matriculation ke exam results ka analysis karna hai. Aap dekh rahe hain ke har school ke students ke marks mein kitna farq hai.
Data Collection: Aap paanch different schools se students ke matric ke exam scores collect karte hain. Yeh scores kuch is tarah hain:
Analyzing Variability:
Conclusion: Is analysis se aapko yeh insight milti hai ke kuch schools mein students ke marks mein zyada variability hai (jaise School A, B, aur E), jabke School C mein students ke performance mein kam variability hai. Is se education board ko yeh samajhne mein madad milti hai ke kis school mein teaching methods zyada consistent results la rahe hain aur kahan par student performance mein zyada variation hai.
Is tarah ke analysis se stakeholders ko valuable insights milte hain jo unhe policies aur interventions design karne mein madad karte hain. Variability ka yeh analysis business, health, sports, aur bhi bohot se fields mein useful hota hai. ๐๐ซโจ๐
import numpy as np
import matplotlib.pyplot as plt
# Step 2: Create a dataset
data = np.random.normal(loc=0, scale=1, size=1000)
# Step 3: Calculate the range of the dataset
data_range = [np.min(data), np.max(data)]
# Step 4: Plot the histogram of the dataset
plt.hist(data, bins=30, alpha=0.5)
# Step 5: Highlight the range on the histogram
plt.axvline(data_range[0], color='red', linestyle='dashed', linewidth=2)
plt.axvline(data_range[1], color='red', linestyle='dashed', linewidth=2)
plt.title('Histogram with Range Highlighted')
plt.show()
# Step-1: Import libraries
import numpy as np
import matplotlib.pyplot as plt
# Step 2: Create a dataset
data = np.random.normal(loc=0, scale=1, size=1000)
# Step 3: Calculate the Interquartile Range (IQR) of the dataset
Q1 = np.percentile(data, 25)
Q3 = np.percentile(data, 75)
IQR = Q3 - Q1
# Step 4: Plot the boxplot of the dataset
plt.figure(figsize=(6, 4))
plt.boxplot(data, vert=False)
plt.title('Boxplot with IQR')
# Annotate Q1, Q3, and IQR
plt.annotate(f'Q1\n{Q1:.2f}', (Q1, 1.1), textcoords="data",
va='center', ha='center', fontsize=10, color='blue')
plt.annotate(f'Q3\n{Q3:.2f}', (Q3, 1.1), textcoords="data",
va='center', ha='center', fontsize=10, color='blue')
plt.annotate(f'IQR\n{IQR:.2f}', ((Q1+Q3)/2, 1.2), textcoords="data",
va='center', ha='center', fontsize=10, color='red')
plt.show()
print(f"The Interquartile Range (IQR) is: {IQR}")
print("")
The Interquartile Range (IQR) is: 1.311518777203355
# Step-1: Import libraries
import numpy as np
import matplotlib.pyplot as plt
# Step 2: Create a dataset following a normal distribution
data = np.random.normal(loc=0, scale=1, size=1000)
# Step 3: Calculate the variance and standard deviation of the dataset
variance = np.var(data)
std_dev = np.sqrt(variance)
mean = np.mean(data)
# Step 4: Plot the histogram of the dataset
plt.hist(data, bins=30, alpha=0.5)
# Step 5: Highlight the variance on the histogram
plt.axvline(mean - std_dev, color='red', linestyle='dashed', linewidth=2)
plt.axvline(mean + std_dev, color='red', linestyle='dashed', linewidth=2)
plt.title('Histogram with Variance Highlighted')
plt.annotate(f'Variance: {variance:.2f}', xy=(0.05, 0.95), xycoords='axes fraction')
plt.show()
print(f"The variance is: {variance}")
The variance is: 1.049007173333975# Step-1: Import libraries
import numpy as np
import matplotlib.pyplot as plt
# Step 2: Create a dataset following a normal distribution
data = np.random.normal(loc=0, scale=1.70, size=1000)
# Step 3: Calculate the standard deviation and mean of the dataset
std_dev = np.std(data)
mean = np.mean(data)
# Step 4: Plot the histogram of the dataset
plt.hist(data, bins=30, alpha=0.5)
# Step 5: Highlight the standard deviation on the histogram
plt.axvline(mean - std_dev, color='red', linestyle='dashed', linewidth=2)
plt.axvline(mean + std_dev, color='red', linestyle='dashed', linewidth=2)
plt.title('Histogram with Standard Deviation Highlighted')
plt.annotate(f'Standard Deviation: {std_dev:.2f}', xy=(0.05, 0.95), xycoords='axes fraction')
plt.show()
print(f"The standard deviation is: {std_dev}")
The standard deviation is: 1.7033920898240134# Step 1: Import necessary libraries
import pandas as pd
import matplotlib.pyplot as plt
import seaborn as sns
# Step 2: Load the Titanic dataset
titanic = sns.load_dataset('titanic')
# Step 3: Calculate the mean fare for each class
mean_fare = titanic.groupby('class', observed = True)['fare'].mean()
# Step 4: Calculate the standard error for each class
std_error = titanic.groupby('class', observed = True)['fare'].sem()
# creata a dataframe from mean_fare and std_error
df = pd.DataFrame({'Mean Fare': mean_fare,
'Standard Error': std_error}).reset_index()
# Assuming fare_stats is already defined as per previous steps
# Step 5: Plot a bar plot with error bars representing the standard error
plt.figure(figsize=(10, 6))
# Create a bar plot
plt.bar(df['class'], df['Mean Fare'], yerr=df['Standard Error'], capsize=5)
# Adding labels and title
plt.xlabel('Class')
plt.ylabel('Mean Fare')
plt.title('Mean Fare by Class with Standard Error')
# Show the plot
plt.show()
# silence all warnings
import warnings
warnings.filterwarnings('ignore')
Data Science mein, variability ya tabdeeli ka kirdar bohot ahem hota hai. Ye measure karta hai ke data points kitne alag hain ek dusre se aur ye insights provide karta hai ke data kis tarah distribute hua hai.
In sab examples se clear hota hai ke Data Science mein variability ko samajhna essential hai. Ye aapko data ke nature ko samajhne, risks ko manage karne, aur better decisions lene mein madad karta hai. ๐๐ก๐โจ๐ฉโ๐ป
Aaiye baat karte hain โOutliersโ ke baare mein Data Science aur statistics mein! ๐๐
Outliers, ya intehai qiymat, woh data points hote hain jo baqi data se bohot alag hote hain. Ye aise values hoti hain jo ya to bohot zyada bari ya chhoti hoti hain baqi data ke comparison mein. In points ko outliers kehte hain kyunki ye โnormalโ ya expected range se bahar hote hain.
Outliers ko handle karna carefully kiya jana chahiye. Kabhi-kabhi inhe data set se hata diya jata hai, lekin kabhi-kabhi inhe analyze karna bhi zaroori hota hai, khas taur par jab ye kisi real phenomenon ya important information ko represent karte hain. Outliers ko identify karne ke liye various methods jaise scatter plots, box plots, aur statistical tests (e.g., Z-score, IQR) ka use kiya jata hai. ๐๐ฌโจ๐
Detecting and removing outliers is a crucial step in data preprocessing, especially in data science and machine learning projects. Python, with its libraries like Pandas, NumPy, and SciPy, provides efficient tools to handle this task. Hereโs a general approach to detect and remove outliers in Python:
The Z-score method is a statistical technique used to measure how far away a data point is from the mean, relative to the standard deviation of the dataset. The equation for calculating the Z-score of a data point is:
\[Z = \frac{(X - \mu)}{\sigma}\]
Where:
\(Z\) is the Z-score.
\(X\) is the value of the data point.
\(\mu\) is the mean of the dataset.
\(\sigma\) is the standard deviation of the dataset.
Explanation of the Z-score Formula:
\((X - \mu)\): This part of the formula calculates the difference between the data point and the mean of the dataset. It shows how far the data point is from the mean.
Division by \(\sigma\): This step normalizes the difference based on the standard deviation of the dataset. It essentially tells you how many standard deviations away from the mean your data point is.
Use of Z-score:
This method is widely used in statistics and data science to identify outliers and understand the distribution of data points within a dataset.
import numpy as np
data = np.array([10, 12, 12, 13, 12, 11, 14, 13, 15, 102, 12, 14, 14, 17, 19, 107, 10, 13, 12, 14, 12])
z_scores = np.abs((data - np.mean(data)) / np.std(data))
outliers = data[z_scores > 3]
print(outliers)[107]25th percentile - 1.5 * IQR or above 75th percentile + 1.5 * IQR are typically considered outliers.import numpy as np
data = np.array([2, 10, 12, 12, 13, 12, 11, 14, 13, 15, 102, 12, 14, 14, 17, 19, 107, 10, 13, 12, 14, 12, 207]) # Your data array
Q1 = np.quantile(data, 0.25)
Q3 = np.quantile(data, 0.75)
IQR = Q3 - Q1
outliers = data[(data < (Q1 - 1.5 * IQR)) | (data > (Q3 + 1.5 * IQR))]
print(outliers)[ 2 102 19 107 207]import numpy as np
import matplotlib.pyplot as plt
data = np.array([2, 10, 12, 12, 13, 12, 11, 14, 13, 15, 102, 12, 14, 14, 17, 19, 107, 10, 13, 12, 14, 12, 207]) # Your data array
plt.boxplot(data)
plt.show()
Once outliers are identified, you can choose to remove them to clean your dataset. This can be done by filtering the data.
#import libraries
import pandas as pd
import numpy as np
import seaborn as sns
data = sns.load_dataset('titanic')
# show the content of the 'age' column
print(f"the length of age column in Data is {len(data['age'])}")
# Remove outliers from the 'age' column
Q1 = data['age'].quantile(0.25)
Q3 = data['age'].quantile(0.75)
IQR = Q3 - Q1
filtered_data = data[~((data['age'] < (Q1 - 1.5 * IQR)) |(data['age'] > (Q3 + 1.5 * IQR)))]
# data without outliers
print(f"The length of age column in Data without outliers is {len(filtered_data['age'])}")the length of age column in Data is 891
The length of age column in Data without outliers is 880Here is an example before and after outliers are removed, you can also unfold the code to see the output.
import numpy as np
import matplotlib.pyplot as plt
import seaborn as sns
data = np.array([2, 10, 12, 12, 13, 12, 11, 14, 13, 15, 102, 12, 14, 14, 17, 19, 107, 10, 13, 12, 14, 12, 207]) # Your data array
plt.figure(figsize=(4, 5))
fig1=sns.boxplot(data)
# Remove outliers
Q1 = np.quantile(data, 0.25)
Q3 = np.quantile(data, 0.75)
IQR = Q3 - Q1
filtered_data = data[~((data < (Q1 - 1.5 * IQR)) | (data > (Q3 + 1.5 * IQR)))]
plt.figure(figsize=(4, 5))
fig2 = sns.boxplot(filtered_data)
fig1
fig2
plt.show()
Using these methods in Python, you can effectively detect and handle outliers, ensuring that your data analysis or machine learning models are robust and reliable.
Graphical methods are a simple yet effective way to visualize the distribution of numerical variables. They show the number of observations in each category of a variable. Graphical methods are also known as graphical displays.
There are mny different types of graphical methods, including: 1. Frequency Tables 2. Bar Charts 3. Histograms 4. Box Plots 5. Scatter Plots 6. Line Plots 7. Pie Charts 8. Heat Maps 9. Venn Diagrams 10. Tree Maps 11. Word Clouds 12. Sankey Diagrams 13. Network Diagrams 14. Flow Charts 15. Cartograms 16. Choropleth Maps 17. Geographical Maps 18. and many more!
I would suggest you to explore the Andrew Abelaโs Chart Suggestions to get a better understanding of which chart to use for which type of data.
Python mein bohot se libraries hain jo data visualization ke liye use kiye jate hain. Kuch popular libraries hain:
Is section main ham kuch popular libraries ko use kar ke data visualization ke examples dekhenge. ๐๐โจ๐ or graphical methods se data ko understand karna seekhen gay.
Frequency tables are a simple way to visualize the distribution of categorical variables. They show the number of observations in each category of a variable. Frequency tables are also known as contingency tables.
Frequency tables ka formula hai:
\[\text{Frequency} = \frac{\text{Number of Observations in a Category}}{\text{Total Number of Observations}} \times 100\%\]
Frequency Tables, ya Tadaad Ki Tables, aik aham tool hain statistics aur data analysis mein. Ye tables data ko organize aur summarize karne ke liye use kiye jate hain, khaas taur par jab aapko data ke distribution ya patterns ko quickly samajhna ho.
Example: Maan lijiye aap ek survey conduct kar rahe hain Islamabad ke ek school mein aur aapko yeh janna hai ke students rozana kitni dair TV dekhte hain. Aap categories bana sakte hain jaise โ1 ghantaโ, โ2 ghanteโ, โ3 ghanteโ, etc., aur phir count karte hain ke har category mein kitne students aate hain.
Frequency Tables in Python
import pandas as pd
# Example dataset: student survey on hours spent on social media daily
data = {
'Hours on Social Media': ['<1 hour', '1-2 hours', '2-3 hours', '3-4 hours', '>4 hours'],
'Number of Students': [15, 30, 25, 10, 5]
}
# Creating a DataFrame
df = pd.DataFrame(data)
# Displaying the DataFrame as a Frequency Table
df| Hours on Social Media | Number of Students | |
|---|---|---|
| 0 | <1 hour | 15 |
| 1 | 1-2 hours | 30 |
| 2 | 2-3 hours | 25 |
| 3 | 3-4 hours | 10 |
| 4 | >4 hours | 5 |
Letโs have another example of titanic dataset.
# Example dataset: titanic dataset
import seaborn as sns
import pandas as pd
import matplotlib.pyplot as plt
# Load the titanic dataset
titanic = sns.load_dataset('titanic')
# Create a DataFrame with the frequency table
df = pd.DataFrame({'Survived': titanic['survived'].value_counts(),
'Percentage': titanic['survived'].value_counts(normalize=True) * 100})
# Display the DataFrame
df| Survived | Percentage | |
|---|---|---|
| survived | ||
| 0 | 549 | 61.616162 |
| 1 | 342 | 38.383838 |
In this table you can see that 61.6% of the passengers did not survive the Titanic disaster, while 38.4% survived.
Frequency tables simple yet powerful tools hain jo data ko samajhne aur us par based decisions lene mein bohot madadgar sabit hote hain. Ye especially tab useful hote hain jab data sets bade hote hain ya jab aapko quick insights chahiye hote hain. ๐๐โจ๐
Bar charts are a simple yet effective way to visualize the distribution of categorical variables. They show the number of observations in each category of a variable. Bar charts are also known as bar graphs.
The bar chart is particularly appropriate for displaying discrete data with only a few categories. The bars can be plotted vertically or horizontally. The height or length of each bar is proportional to the number of observations in the category.
The Figure 5.14 shows the bar chart of the Titanic dataset, you can also unfold the code to see the output. The barchart shows the number of passengers who survived and who did not survive the Titanic disaster.
# Example dataset: titanic dataset
import seaborn as sns
import pandas as pd
import matplotlib.pyplot as plt
# Load the titanic dataset
titanic = sns.load_dataset('titanic')
# Create a DataFrame with the frequency table
df = pd.DataFrame({'Survived': titanic['survived'].value_counts(),
'Percentage': titanic['survived'].value_counts(normalize=True) * 100})
# Plot the bar chart
df.plot(kind='bar', rot=0, title='Titanic Survival Rate', figsize=(6, 4))
# Show the plot
plt.show()
Ap bar chart ko horizontal bhi bana sakte hain, jaisa ke Figure 5.15 mein dikhaya gaya hai.
# Example dataset: titanic dataset
import seaborn as sns
import pandas as pd
import matplotlib.pyplot as plt
# Load the titanic dataset
titanic = sns.load_dataset('titanic')
# Create a DataFrame with the frequency table
df = pd.DataFrame({'Survived': titanic['survived'].value_counts(),
'Percentage': titanic['survived'].value_counts(normalize=True) * 100})
# Plot the bar chart
df.plot(kind='barh', rot=0, title='Titanic Survival Rate', figsize=(6, 4))
# Show the plot
plt.show()
Bar charts ka formula hai:
\[\text{Bar Height} = \frac{\text{Number of Observations in a Category}}{\text{Total Number of Observations}} \times 100\%\]
Bar Charts, ya Bar Graphs, aik aham tool hain statistics aur data analysis mein. Ye graphs data ko organize aur summarize karne ke liye use kiye jate hain, khaas taur par jab aapko data ke distribution ya patterns ko quickly samajhna ho.
You can also make stacked bar charts in Python. Stacked bar charts are used to show how a larger category is divided into smaller categories and what the relationship of each part has on the total amount. The Figure 5.16 shows the stacked bar chart of the Titanic dataset, you can also unfold the code to see the output.
# Example dataset: titanic dataset
import seaborn as sns
import pandas as pd
import matplotlib.pyplot as plt
# Load the titanic dataset
titanic = sns.load_dataset('titanic')
# Create a DataFrame with the frequency table
df = pd.DataFrame({'Survived': titanic['survived'].value_counts(),
'Percentage': titanic['survived'].value_counts(normalize=True) * 100})
# Plot the bar chart
df.plot(kind='bar', rot=0, title='Titanic Survival Rate', stacked=True, figsize=(6, 4))
# Show the plot
plt.show()
We can also draw bar charts using plotly library. The Figure 5.17 shows the bar chart of the Titanic dataset using plotly library, you can also unfold the code to see the output.
# Example dataset: titanic dataset
import seaborn as sns
import pandas as pd
import matplotlib.pyplot as plt
import plotly.express as px
# Load the titanic dataset
titanic = sns.load_dataset('titanic')
# Create a DataFrame with the frequency table
df = pd.DataFrame({'Survived': titanic['survived'].value_counts(),
'Percentage': titanic['survived'].value_counts(normalize=True) * 100})
# Plot the bar chart for both the columns Survived and Percentage
fig = px.bar(df, x=df.index, y=['Survived', 'Percentage'], title='Titanic Survival Rate')
fig.show()Histograms are a simple yet effective way to visualize the distribution of numerical variables. They show the number of observations in each category of a variable. Histograms are also known as frequency histograms.
The histogram is a graphical representation of the distribution of numerical data. It is an estimate of the probability distribution of a continuous variable. To construct a histogram, the first step is to โbinโ (or โbucketโ) the range of valuesโthat is, divide the entire range of values into a series of intervalsโand then count how many values fall into each interval. The bins are usually specified as consecutive, non-overlapping intervals of a variable. The bins (intervals) must be adjacent, and are often (but are not required to be) of equal size.
The Figure 5.18 shows the histogram of the Titanic dataset, you can also unfold the code to see the output. The histogram shows the number of passengers who survived and who did not survive the Titanic disaster based on their age.
# Example dataset: titanic dataset
import seaborn as sns
import pandas as pd
import matplotlib.pyplot as plt
# Load the titanic dataset
titanic = sns.load_dataset('titanic')
sns.histplot(data=titanic, x='age', kde=True)
plt.show()
# Plot the histogram
sns.histplot(data=titanic, x='age', hue='survived', multiple='stack', kde=True)
# Show the plot
plt.show()
Pie charts are a simple yet effective way to visualize the distribution of categorical variables. They show the number of observations in each category of a variable. Pie charts are also known as pie graphs.
The pie chart is a circular statistical graphic, which is divided into slices to illustrate numerical proportion. In a pie chart, the arc length of each slice (and consequently its central angle and area), is proportional to the quantity it represents. While it is named for its resemblance to a pie which has been sliced, there are variations on the way it can be presented. The earliest known pie chart is generally credited to William Playfairโs Statistical Breviary of 1801.
The Figure 5.19 shows the pie chart of the Titanic dataset, you can also unfold the code to see the output. The pie chart shows the number of passengers who survived and who did not survive the Titanic disaster.
# Example dataset: titanic dataset
import seaborn as sns
import pandas as pd
import matplotlib.pyplot as plt
# Load the titanic dataset
titanic = sns.load_dataset('titanic')
# Create a DataFrame with the frequency table
df = pd.DataFrame({'Survived': titanic['survived'].value_counts(),
'Percentage': titanic['survived'].value_counts(normalize=True) * 100})
# Plot the pie chart
df.plot(kind='pie', y='Survived', figsize=(6, 4), autopct='%1.1f%%', startangle=90, title='Titanic Survival Rate')
# Show the plot
plt.show()
We can also create pie chart using plotly to show the rate of survival of passengers in the Titanic disaster. The Figure 5.20 shows the pie chart of the Titanic dataset using plotly library where data was grouped based on the class of travelling on titanic dataset.You can also unfold the code to see the output.
# Example dataset: titanic dataset
import seaborn as sns
import pandas as pd
import plotly.express as px
# Load the titanic dataset
titanic = sns.load_dataset('titanic')
# Group the data by 'class' and count the number of survivors
class_survived = titanic.groupby('class')['survived'].sum().reset_index()
# Create a pie chart
fig = px.pie(class_survived, values='survived', names='class', title='Titanic Survival Rate by Class')
fig.show()Box plots are a simple yet effective way to visualize the distribution of numerical variables. They show the number of observations in each category of a variable. Box plots are also known as box and whisker plots.
The box plot is a standardized way of displaying the distribution of data based on the five number summary: minimum, first quartile, median, third quartile, and maximum. It is also known as a box and whisker plot. The box plot is compact and efficient, displaying only the most important summary statistics. It also allows for easy identification of any outliers and a visual representation of the data symmetry and skewness.
The Figure 5.21 shows the box plot of the Titanic dataset, you can also unfold the code to see the output. The box plot shows the number of passengers who survived and who did not survive the Titanic disaster based on their age.
# Example dataset: titanic dataset
import seaborn as sns
import pandas as pd
import matplotlib.pyplot as plt
# Load the titanic dataset
titanic = sns.load_dataset('titanic')
# Plot the box plot
sns.boxplot(data=titanic, x='survived', y='age')
# Show the plot
plt.show()
We can also show the box plot using plotly library. The Figure 5.22 shows the box plot of the Titanic dataset using plotly library, you can also unfold the code to see the output. The box plot shows the number of passengers who survived and who did not survive the Titanic disaster based on their class.
# Example dataset: titanic dataset
import seaborn as sns
import pandas as pd
import plotly.express as px
# Load the titanic dataset
titanic = sns.load_dataset('titanic')
# Plot the box plot
fig = px.box(titanic, x='survived', y="age", color='class', notched=True, title='Titanic Survival Rate by Class and Age')
# Show the plot
fig.show()Bi-variate charts are a simple yet effective way to visualize the relationship between two numerical variables. They show the number of observations in each category of a variable. Bi-variate charts are also known as scatter plots.
The scatter plot is a type of plot or mathematical diagram using Cartesian coordinates to display values for typically two variables for a set of data. If the points are color-coded, one additional variable can be displayed. The data is displayed as a collection of points, each having the value of one variable determining the position on the horizontal axis and the value of the other variable determining the position on the vertical axis.
The Figure 5.23 shows the scatter plot of the Titanic dataset, you can also unfold the code to see the output. The scatter plot shows the relationship between the age and fare of the passengers who survived and who did not survive the Titanic disaster.
# Example dataset: titanic dataset
import seaborn as sns
import pandas as pd
import matplotlib.pyplot as plt
# Load the titanic dataset
titanic = sns.load_dataset('titanic')
# Plot the scatter plot
sns.scatterplot(data=titanic, x='age', y='fare')
# Show the plot
plt.show()
IN 2 variables ko ham further group kar sakte hain aur unke relationship ko visualize kar sakte hain. The Figure 5.24 shows the scatter plot of the Titanic dataset, you can also unfold the code to see the output. The scatter plot shows the relationship between the age and fare of the passengers who survived and who did not survive the Titanic disaster based on their class.
# Example dataset: titanic dataset
import seaborn as sns
import pandas as pd
import matplotlib.pyplot as plt
# Load the titanic dataset
titanic = sns.load_dataset('titanic')
# Plot the scatter plot
sns.scatterplot(data=titanic, x='age', y='fare', hue='survived')
# Show the plot
plt.show()
We can also draw scatter plots using plotly library. The Figure 5.25 shows the scatter plot of the Titanic dataset using plotly library, you can also unfold the code to see the output. The scatter plot shows the relationship between the age and fare of the passengers who survived and who did not survive the Titanic disaster based on their class.
# Example dataset: titanic dataset
import seaborn as sns
import pandas as pd
import plotly.express as px
# Load the titanic dataset
titanic = sns.load_dataset('titanic')
# Plot the scatter plot
fig = px.scatter(titanic, x='age', y='fare', color='class', title='Titanic Survival Rate by Class and Age')
# Show the plot
fig.show()Line plots are a simple yet effective way to visualize the relationship between two numerical variables. They show the number of observations in each category of a variable. Line plots are also known as line graphs.
The line chart or line graph is a type of chart that displays information as a series of data points called โmarkersโ connected by straight line segments. It is a basic type of chart common in many fields. It is similar to a scatter plot except that the measurement points are ordered (typically by their x-axis value) and joined with straight line segments. A line chart is often used to visualize a trend in data over intervals of time โ a time series โ thus the line is often drawn chronologically.
The Figure 5.26 shows the line plot of the Titanic dataset, you can also unfold the code to see the output. The line plot shows the relationship between the age and fare of the passengers who survived and who did not survive the Titanic disaster.
# Example dataset: titanic dataset
import seaborn as sns
import pandas as pd
import matplotlib.pyplot as plt
# Load the titanic dataset
titanic = sns.load_dataset('titanic')
# Plot the line plot
sns.lineplot(data=titanic, x='age', y='fare')
# Show the plot
plt.show()
Ham line plot ko group kar ke bhi visualize kar sakte hain. The Figure 5.27 shows the line plot of the Titanic dataset, you can also unfold the code to see the output. The line plot shows the relationship between the age and fare of the passengers who survived and who did not survive the Titanic disaster based on their class.
# Example dataset: titanic dataset
import seaborn as sns
import pandas as pd
import matplotlib.pyplot as plt
# Load the titanic dataset
titanic = sns.load_dataset('titanic')
# Plot the line plot
sns.lineplot(data=titanic, x='age', y='fare', hue='survived')
# Show the plot
plt.show()
flowchart LR A((Data)) --> B[Composition] A --> C[Distribution] A --> D[Relationship] A --> E[Comparison] B --> F[Bar Chart] B --> G[Pie Chart] B --> H[Tree Map] B --> I[Word Cloud] B --> K[Network Diagram] C --> L[Histogram] C --> M[Box Plot] C --> N[Scatter Plot] C --> O[Line Plot] D --> P[Scatter Plot] D --> Q[Bubule Chart] E --> R[Bar Chart] E --> S[Line Plot] E --> T[Box Plot]
Another Idea of Descriptive Statistics:
graph TD
A[Start: Choose a Chart] --> B(Do you have time series data?)
B -- Yes --> C[Use Line Chart]
B -- No --> D(Do you need to compare parts to a whole?)
D -- Yes --> E[Use Pie Chart or Bar Chart]
D -- No --> F(Do you need to compare items?)
F -- Yes --> G[Use Bar Chart or Column Chart]
F -- No --> H(Do you have relational data?)
H -- Yes --> I[Use Scatter Plot]
H -- No --> J(Need to show distribution?)
J -- Yes --> K[Use Histogram or Box Plot]
J -- No --> L[Consider other types of charts or revise data presentation needs]
Main umeed karta hun k ap ko ye chapter ne bht kuch seekhaya ho ga, or agar sach main seekhaya hy then please do support us by sharing this book with your friends and colleagues. Also, do share your feedback with us, so that we can improve our work in future.
