Notes

Statistics

Statistics ka matlab hota hai data ko collect karna, organize karna, present karna aur analyze karna. Real life examples: Class ke marks ka analysis Cricket scores Temperature records Population data

Important Terms:

Observation Har individual value ko observation kehte hain. Example: 10, 20, 30 mein 10 ek observation hai. Frequency (f) Koi value kitni baar aati hai. Example: 5, 5, 7, 8 mein 5 ki frequency = 2 Class Interval Data ko groups mein divide karna. Example: 0–10, 10–20, 20–30 Class Size Upper limit - Lower limit Example: 20–30 ka class size = 10 Class Mark (Mid Value)

Class Mark= 2 Lower Limit+Upper Limit ​

Example: 20–30 ka class mark = 25 Cumulative Frequency (cf) Frequencies ka running total. Example: 4, 6, 3 → cf = 4, 10, 13

Measures of Central Tendency:

Mean (Average)

x ˉ

n ∑x ​

Grouped data ke liye:

x ˉ

∑f i ​

∑f i ​

x i ​

​

Where:

fi = frequency xi = class mark Median Arranged data ka middle value.

Ungrouped Data:

Odd observations → middle value Even observations → do middle values ka average

Grouped Data:

Median=l+( f 2 N ​

−cf ​

)h

Where:

l = median class ka lower boundary N = total frequency cf = preceding cumulative frequency f = median class frequency h = class size Mode Sabse zyada baar aane wali value.

Graphical Representation:

Histogram Frequency Polygon Ogive (Cumulative Frequency Curve)

Important Steps to Find Median in Grouped Data:

Cumulative frequency banao N/2 nikalo Median class identify karo Formula apply karo

Important Points:

Mean = Average value Median = Middle value Mode = Most frequent value Median outliers se kam affected hota hai

Common Mistakes:

Median ke liye data sort na karna Class mark galat nikalna Cumulative frequency galat banana Formula me wrong substitution

Quick Comparison:

Mean → All values use karta hai Median → Middle value par based Mode → Frequency par based

Exam Tips:

Formula yaad rakho Table neatly banao cf carefully calculate karo Final answer with units (if required)

Summary:

Statistics chapter mainly Mean, Median aur Mode par based hai. Grouped data median JAC Board mein bahut important hai. Agar formula aur steps yaad hain to ye chapter bahut scoring hai.