Chapter 14 Statistics

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…