Statistics Data Science

 Types of Data: -

Majorly deal with 2 types of data : 1) Numberical Data[continuos data] ex: age, salary, height
                                                            Objective: Quantative Study 

                                                            2) Categorical Data[Dispreet Data]: ex: Gender, City etc
                                                            Objective: Qualitative Study

Types of Statistic;;; Basically Statistic is a branch of mathematics which helps u to study data distribution

✅ 1. Descriptive Statistics (वर्णनात्मक सांख्यिकी)

Is type me data ko collect, organize aur summarize kiya jaata hai — taaki data ko aasaan tareeke se samjha ja sake.
Isme sirf jo data diya hota hai usi ka description hota hai, koi prediction nahi hoti.

🔹 Isme kya-kya aata hai:

• Mean (औसत)

• Median (मध्यिका)

• Mode (बहुलक)

• Range

• Standard Deviation

• Tables, Graphs, Charts

🔹 Example:

Agar 10 students ke marks diya ho aur aap:

• Average nikal rahe ho

• Highest–lowest value bata rahe ho
  → Ye Descriptive Statistics hai.

🔹 Use kaha hota hai:

• School/college result analysis

• Business reports

• Government surveys ki summary

• Data visualization

✅ 1. Population (समष्टि / जनसंख्या)

Population = Study ke liye liye gaye sabhi individuals ya sabhi data ka poora group.

Yaani:

Jitne bhi units aapke study ke under aate hain, wo population kehlate hain.

🔹 Example:

• Agar aap poore India ke voters ka study kar rahe ho → Ye Population hai

• Ek college ke sabhi 2000 students → Ye Population hai

• Factory me sabhi workers → Population

🔹 Symbol:

Population ka size usually N se denote hota hai.

✅ 2. Sample (नमूना)

Sample = Population ka chhota hissa jise study ke liye select kiya jaata hai.

Yaani:

Poore group me se thode log/data jo research ke liye liye jaate hain, wo sample hote hain.

🔹 Example:

• 2000 students me se sirf 100 students ka survey → Ye Sample

• 1 lakh voters me se 1000 voters ka survey → Sample

🔹 Symbol:

Sample ka size n se denote hota hai.

✅ 2. Inferential Statistics (निर्णायक / अनुमानात्मक सांख्यिकी)

Isme sample data ke base par poori population ke baare me conclusion ya prediction nikala jaata h

Yaani:

“Thode data se poore group ka andaaza lagana”

🔹 Isme kya-kya aata hai:

• Probability

• Hypothesis Testing

• t-test, z-test

• Chi-square test

• Regression Analysis

• ANOVA

• Confidence Interval

🔹 Example:

Agar aap 100 logon ka survey karke yeh conclude karo ki
“Is shehar me 60% log smartphone use karte hain”
→ Ye Inferential Statistics hai.

🔹 Use kaha hota hai:

• Research

• Medical studies

• Government policies

• Data Science & AI

• Market prediction

✅ SCALE OF MEASUREMENT OF DATA

Data ko measure ya classify karne ke tareeke ko Scale of Measurement kehte hain.
Isse pata chalta hai ki data par kaun-kaun si mathematical operations lag sakti hain.

✅ TYPES OF SCALE OF MEASUREMENT

Statistics me 4 prakar ke scale hote hain:

👉 Nominal

Jisme data sirf naam ya category ke roop me hota hai, use Nominal Scale kehte hain.

🔹 विशेषताएँ:

• Sirf classification

• Order nahi hota

• Zero ka koi matlab nahi

• +, −, ×, ÷ possible nahi

🔹 उदाहरण:

• Gender (Male, Female)

• Blood Group (A, B, AB, O)

• Religion

• City Name

🔹 उपयोग:

• Classification

• Frequency count

👉 Ordinal

Jisme data rank ya order me arrange hota hai, lekin exact difference pata nahi hota.

🔹 विशेषताएँ:

• Order hota hai

• Difference measure nahi hota

• Zero meaningful nahi

• Mathematical operations possible nahi

🔹 उदाहरण:

• Class Rank (1st, 2nd, 3rd)

• Grades (A, B, C)

• Satisfaction level (Low, Medium, High)

• Economic Status (Poor, Middle, Rich)

👉 Interval

🔹 परिभाषा:

Jisme order aur exact difference dono hote hain, lekin true zero nahi hota.

🔹 विशेषताएँ:

• Order ✔

• Difference ✔

• True Zero ❌

• +, − possible

• ×, ÷ meaningful nahi

🔹 उदाहरण:

• Temperature (°C, °F)

• Calendar Year (2020, 2021)

• IQ Score

👉 Ratio

Jisme order, difference aur true zero teeno hote hain, use Ratio Scale kehte hain.

🔹 विशेषताएँ:

• Order ✔

• Difference ✔

• True Zero ✔

• +, −, ×, ÷ sab possible

🔹 उदाहरण:

• Height

• Weight

• Age

• Income

• Distance

• Marks

✅ ONE-LINE REVISION POINTS

• Nominal → Sirf naam

• Ordinal → Sirf order

• Interval → Order + difference

• Ratio → Order + difference + true zero

 

✅ SAMPLING METHOD – NOTES

🔷 अर्थ (Meaning)

Population me se kuch representative units ko chune jaane ki prakriya ko Sampling kehte hain.

RANDOM SAMPLING – NOTES

🔷 अर्थ (Meaning)

Random Sampling wo method hota hai jisme population ke har unit ko sample banne ka barabar (equal) chance milta hai.

FEATURES (विशेषताएँ):

• Har unit ko equal chance

• Bias minimum hota hai

• Scientific aur most reliable method

• Probability known hoti hai

• Statistical tests apply kiye ja sakte hain

STRATIFIED SAMPLING – NOTES

🔷 अर्थ (Meaning)

Stratified Sampling wo method hai jisme poori population ko chhote-chhote homogeneous groups (strata) me baant diya jaata hai,
aur phir har strata se random tarike se sample liya jaata hai.

FEATURES (विशेषताएँ):

• Population ko homogeneous strata me baanta jata hai

• Har strata se random selection

• High accuracy

• Representation balanced hota hai

• Sampling error kam hota hai

• Probability sampling ka hi type hai

CLUSTER SAMPLING – NOTES

🔷 अर्थ (Meaning)

Cluster Sampling wo method hai jisme population ko chhote-chhote groups (clusters) me baant kar
kuch clusters ko randomly select kiya jaata hai,
aur select kiye gaye poore cluster ke sabhi units ko sample maana jaata hai.

FEATURES (विशेषताएँ):

• Population ko natural groups (clusters) me baanta jata hai

• Pure cluster ka data liya jata hai

• Probability sampling ka type hai

• Low cost & time saving

• Large population ke liye suitable

• Accuracy Stratified se kam hoti hai

EXAMPLES (Exam Type):

• Shehar ke sab wards me se 5 wards chun kar unke sab logon ka survey

• Rajya ke sab schools me se 10 schools select karna

• Poore district me se kuch gaon chunna

✅ SYSTEMATIC SAMPLING – NOTES

🔷 अर्थ (Meaning)

Systematic Sampling wo method hai jisme population ko ek order me arrange karke
har ‘kth’ unit ko sample ke roop me select kiya jaata hai.

“Har fix gap (interval) par ek unit ka selection.”

FORMULA (बहुत महत्वपूर्ण)

$$k = \frac{N}{n}$$

• N = Population size

• n = Sample size

• k = Sampling Interval

PROCESS / STEPS:

1. Population ke sabhi units ko 1 se N tak number do

2. k = N/n se interval nikaalo

3. Randomly 1 se k ke beech ek number lo (r)

4. Phir har k ke baad selection karo:
   r, r+k, r+2k, r+3k … jab tak sample complete na ho

 

EXAMPLE (Numerical Type):

Agar
N = 1000, n = 100

$$k = 1000/100 = 10$$

Matlab:
Har 10va unit select hoga:
5, 15, 25, 35, 45 … (agar r = 5 ho)

DATA SOURCES:

1) Survey/Questions

Is method me data questions puchh kar logon se directly collect kiya jaata hai — ya to form (questionnaire) ke through ya interview ke through.

🔹 तरीके:

• Online Survey (Google Form, App)

• Offline Questionnaire

• Face-to-face Interview

• Telephonic Survey

🔹 उदाहरण:

• Students se exam feedback lena

• Voters se opinion poll

• Customers se product review lena

✅ Merits (लाभ):

✔ Large data collection possible
✔ Opinion & behavior ka pata chalta hai
✔ Flexible method

❌ Demerits (हानियाँ):

❌ False answers mil sakte hain
❌ Response rate kam ho sakta hai
❌ Time consuming

2) Experimental Data

Jab data experiment (प्रयोग) karke, controlled environment me collect kiya jaata hai, use Experimental Data kehte hain.

“Cause–effect relationship check karne ke liye.”

🔹 Features:

• Controlled conditions

• Variables ko manipulate kiya jaata hai

• Scientific testing hoti hai

🔹 उदाहरण:

• Medicine ka clinical trial

• Fertilizer ka crop par experiment

• New teaching method ka test

✅ Merits (लाभ):

✔ High accuracy
✔ Cause–effect clear hota hai
✔ Scientific validity zyada

❌ Demerits (हानियाँ):

❌ Cost zyada hoti hai
❌ Artificial environment
❌ Ethical issues ho sakte hain

3) Observation Study

Isme data sirf dekh kar (observe karke) collect kiya jaata hai, bina direct sawal puche.

🔹 Types:

• Direct Observation

• Indirect Observation

• Participant Observation

• Non-Participant Observation

🔹 उदाहरण:

• Traffic count at a signal

• Classroom me students ka behavior

• Factory me machine performance

✅ Merits (लाभ):

✔ Real behavior ka data
✔ No response bias
✔ Useful when questioning not possible

❌ Demerits (हानियाँ):

❌ Observer bias
❌ Limited information
❌ Hidden factors ka pata nahi chalta

SAMPLING BIAS – NOTES

🔷 अर्थ (Meaning)

Sampling Bias tab hota hai jab sample population ka sahi aur poora representation nahi karta,
aur kuch groups ko zyada ya kam chance mil jata hai.

“Galat sample = Galat result”
“When sample is not truly representative of population.”

RESPONSE BIAS – NOTES

🔷 अर्थ (Meaning)

Response Bias tab hota hai jab respondent (उत्तरदाता) jaan-bujhkar ya anjaane me galat, adhura ya socially acceptable jawab deta hai,
jiski wajah se data accurate nahi rehta.

“Galat ya jhootha response = Response Bias”

CAUSES OF RESPONSE BIAS (कारण)

• Social pressure (samaj ka darr)

• Personal sharm/hesitation

• Fear of authority

• Question ka unclear hona

• Interviewer ka influence

• Sensitive questions (income, crime, habits)

• Memory error (yaad na rehna)

 

BIAS = Error in Statistics 

✅ SELECTION BIAS – NOTES

🔷 अर्थ (Meaning)

Selection Bias tab hota hai jab sample ko choose karne ki process hi galat ho jaaye,
jisse population ke kuch groups ko zyada chance mil jaata hai aur kuch ko kam ya bilkul nahi.

“Galat selection process = Selection Bias”

📌 Example:
Sirf urban area se survey karke poore district ka result banana.

✅ RESPONSE BIAS – NOTES

Participants intentionally  give wrong answer 

Response Bias tab hota hai jab respondent survey / questionnaire me sachcha jawab na dekar
galat, adhura ya socially acceptable jawab deta hai.

“Galat jawab dene se hone wali error = Response Bias”

🔷 Response Bias kyon hota hai? (Causes)

• Social pressure (samaj ka darr)

• Fear of authority

• Sensitive questions (income, crime, habits)

• Interviewer ka influence

• Question ka unclear hona

• Memory problem (recall error)

• Jaan-bujhkar jhooth bolna

🔷 Effects / Impact

• Data inaccurate ho jata hai

• Research unreliable ho jaati hai

• Galat conclusions nikalte hain

• Policy & decision making me problem

 

🔷 How to Reduce Response Bias

✔ Anonymous survey conduct karein
✔ Simple, clear & neutral questions
✔ Leading questions avoid karein
✔ Interviewer ko proper training
✔ Sensitive questions carefully puchhein
✔ Multiple questions se cross-check

📘 PROBABILITY

Measure of chances of occurence 

Ex: tossing a coin = random process

🔷 Formula of Probaility

$$P(E) = \frac{\text{Number of favourable outcomes}}{\text{Total number of possible outcomes}}$$

===== Kitne times aa skta hai / Total Kitne hai 

Ex: Ek bag me Green color 3 hai aur blue color 4 hai to ab green kitne bar aa sakta hai ? = 3 and total kitne hai 4 then formula will be = 3/7

🔷 Range of Probability

$$0 \le P(E) \le 1$$

• P(E) = 0 → Event impossible

• P(E) = 1 → Event sure (certain)

​

🔷 Types of Probability

1️⃣ Classical Probability

Jab sab outcomes equally likely ho
📌 Coin, dice problems

---

🔷 Code Given

import random
c_prob = 1/6
print("Classical probability:", round(c_prob,2))
🔷 Concept Used
👉 Classical Probability

Jab sab outcomes equally likely hote hain, to probability:

$$P(E) = \frac{\text{Favourable outcomes}}{\text{Total outcomes}}$$

2️⃣ Empirical (Experimental) Probability

Actual experiment ke results par based
📌 Toss 100 baar karke data

🔷 Code Given

n = 10000
die_rolls = [random.randint(1,6) for x in range(n)]
e_prob = sum([1 for i in die_rolls if i == 6]) / n
print("Empirical probability:", round(e_prob,2))
🔷 Concept Used
👉 Empirical (Experimental) Probability
Jab probability actual experiments ya observations se calculate ki jaati hai, use Empirical Probability kehte hain.
$$P(E) = \frac{\text{Number of times event occurred}}{\text{Total number of trials}}$$