ststs

1. STATISTICS FORMULA
Raj KUMAR
17PBA037
Baddi University of emerging
sciences and technology

2. Mean
 Individual
1. Direct=
𝛴𝑋
𝑁
2. Short cut = A+
𝛴𝑑
𝑁
 Discreet and continuous
1. Direct=
𝛴𝑓𝑋
𝑁
2. Short cut = A+
𝛴𝑓𝑑
𝑁

3. Mean
 COMBINED MEAN
𝑵 𝟏X͞ 𝟏+𝑵 𝟐X͞ 𝟐
𝑵𝟏+𝑵𝟐
,
 WEIGHTED MEAN
∑𝑾𝑿
∑𝑾

4. Median
Individual
N+1/2 (when in points add
L+U/2)
Continuous
M= L+
𝑁
2
−𝑐𝑓
𝑓
∗ 𝑖

5. MODE
Z=𝐿1 +
𝑓1−𝑓0
2𝑓1−𝑓0−𝑓2
*I
 OR
Z=3M-2X͞

6. QUARTILE DEVIATION
Individual
Q1= 𝑁+1
4
Q3= 3 𝑁+1
4
QD= 𝑄3−𝑄1
2
,
Continuous
QD=
𝐿 +
𝑁
4
−𝑐𝑓
𝑓
∗ 𝑖
Coeff. = 𝑄3−𝑄1
𝑄3+𝑄1

7. STANDARD DEVIATION
 Individual Series
 DIRECT
 =SD= 𝚺𝐗 𝟐
𝐍
OR 𝚺(𝐗−𝐗͞
𝐍
 SHORT CUT

𝚺𝐝𝐱 𝟐
𝐍
− (
𝚺𝐝𝐱
𝐍
)²

8. STANDARD DEVIATION
 Discrete & continuous
 SHORT CUT

𝚺𝐟𝐝𝐱²
𝐍
− (
𝚺𝐟𝐝𝐱
𝐍
)²

9. STANDARD DEVIATION
 Coefficient of SD=
ϭ
𝑋
AND
 Coefficient of variation or C.V =
ϭ
𝑋
∗ 100
 Combined SD=
𝑵 𝟏ϭ 𝟏+𝑵 𝟐ϭ 𝟐+𝑵 𝟏 𝒅 𝟏+𝑵₂𝒅₂
𝑵 𝟏+𝑵₂

10. MEAN DEVIATION
 Individual
MD= 𝛴│𝑑
𝑁
 Discrete & CONTINOUS
MD= 𝛴𝑓│𝑑│
𝑁
 COFFICENT
 𝑀𝐷
𝑀𝐸𝐷𝐼𝐴N 𝑂𝑅 𝑀𝐸𝐴𝑁

11. SKEWNESS
 Karl pearson
𝐦𝐞𝐚𝐧 − 𝐦𝐨𝐝𝐞
𝑺𝑫
 Bowley
𝑸𝟑+𝑸𝟏−𝟐 𝑴𝑬𝑫𝑰𝑨𝑵
𝑸𝟑−𝑸𝟏
 Kelly
𝒅𝟗 + 𝒅𝟏 − 𝟐𝒎𝒆𝒅
𝒅𝟗 − 𝒅𝟏

12. Price index
 Formula
 Laspeyre’s
 Σp1q0
Σp0q0
∗ 100
 Paaschee’s
 Σp1q1
Σp0q1
∗ 100
 Fisher’s
 L ∗ 𝑝 ∗ 100

13. Price index
 Dorbish & Bowley’s
 L+P∗100
2
 Marshall edgeworth’s
 Σp1q0+Σp1q1
p0q0+p0q1
∗ 100

14. INDEX NUMBERS
 Time Reversal Test : P01 X P10 = 1
 Factor Reversal Test P01 XQ01 = ΣP1q1/ΣP0q0

15. CORELATION
 Actual mean
r= 𝛴𝑥𝑦
𝛴𝑥2.𝛴𝑦2
 Assumed mean
r= 𝑁.𝛴𝑑𝑥𝑑𝑦−𝛴𝑑𝑥.𝛴𝑑𝑦
𝑁𝛴𝑑𝑥²− 𝛴𝑑𝑥 2. 𝑁.𝛴𝑑𝑦²−(𝛴𝑑𝑦)²
 Actual data
r= 𝑁.𝛴𝑋𝑌−𝛴𝑋.𝛴𝑌
𝑁.𝛴𝑋²− 𝛴𝑋 2. 𝛴𝑌²−(𝛴𝑌)²

16. When ranks are not given

17. Rank are equal
R = 1 −
6[∑𝐷2+
1
12
(𝑚3−𝑚)+
1
12
(𝑚3−𝑚)
𝑛3−𝑛

18. REGRESSION
 1.Y on X
Y=a+ bX
ΣY=Na+bΣx
ΣXY=aΣX+bΣX²
 2.X on Y
X=a+ bY
ΣX=Na+bΣY
ΣXY=aΣY+bΣY²

19. Equation using coefficient (Using
Mean)
 1.Y on X
 Y-Y̅=byx(X-X̅) byx= 𝑁.𝛴𝑥𝑦−𝛴𝑥.𝛴𝑦
𝑁.𝛴𝑥²−(𝛴𝑥)²
 2.X on Y
 X-X̅=bxy(Y-Y̅) bxy= 𝑁.𝛴𝑥𝑦−𝛴𝑦.𝛴𝑥
𝑁.𝛴𝑦²−(𝛴𝑦)²

20. Assumed mean
 1.Y on X
Y-Y̅=byx(X-X̅)
byx= 𝑁.𝛴𝑑𝑥𝑑𝑦−𝛴𝑑𝑥.𝛴𝑑𝑦
𝑁.𝛴𝑑𝑥²−(𝛴𝑑𝑥)²
 2. X on Y
X-X̅=bxy(Y-Y̅)
bxy= 𝑁.𝛴𝑑𝑥𝑑𝑦−𝛴𝑑𝑦.𝛴𝑑𝑥
𝑁.𝛴𝑑𝑦²−(𝛴𝑑𝑦)²

21. Time series
Least square method
 YC = a +bx
 if x =0 then
 a =
∑y
𝑁
 b =
∑xy
∑x²