3. AIRTHMATIC MEAN
Formula Individual Discrete Continuous
DIRECT 𝜮𝑿
𝑵
𝜮𝒇𝑿
𝑵
𝜮𝒇𝒎
𝑵
SHORT CUT
A+
𝜮𝒅
𝑵
A+
𝜮𝒇𝒅
𝑵
A+
𝜮𝒇𝒅
𝑵
STEP
DEVIATION
A+
𝚺𝐟𝐝′
𝑵
∗ 𝐢 A+
𝜮𝒇𝒅
𝑵
∗ 𝐢
(d=X-X͞ )
4. WEIGHTED MEAN
• * WEIGHTED MEAN -
∑𝑾𝑿
∑𝑾
• HERE, ∑𝑾 IS SUM OF WEIGHT
• ∑𝑾𝑿 IS SUM OF WX = W *X
5. COMBINED MEAN
• X123 =
HERE, N1 IS NO. OF VALUE of 1ST SERIES , N2 IS NO. OF VALUE OF 2ND SERIES
6. MEDIAN ( M )
Individual & Discrete
M= Size of N+1 th item
2
(when in points add = L+U
2
N = NO. OF SERIES OR SUM OR
FREFUANCY
Continuous
M = Size of N th item
2
N/2 lies in particular C.I.
M= l1
𝑁
2
−𝑐𝑓
𝑓
∗ 𝑖
7. MODE ( Z )
• (1. INDIVIDUAL SERIES = MOST RECCURING NO.
• (2. DISCRETE SERIES = BIGGEST NO. IN F , IT STRAIGHT
VALUE IN ‘X’
(3. CONTINUE SERIES = f1 =biggest no. in ‘F’ , f0 = previous no. from
f1 and f2 = next no. from f1.
Z=𝐿1 +
𝑓1−𝑓0
2𝑓1−𝑓0−𝑓2
*I OR Z=3M-2X͞ ( AIRHTMATIC MEAN
)
16. CO-RELATION
• KARL PEARSON METHODS :-
2. SPEARMEN METHODS :-
(3. CON CURRENT DEVIATION :-
rc = + +
𝟐𝒄 −𝒏
𝒏
(Actual mean) Assumed mean) Actual data
r=
𝚺𝐱𝐲
𝚺𝐱 𝟐.𝚺𝐲 𝟐
r=
𝐍.𝚺𝐝𝐱𝐝𝐲−𝚺𝐝𝐱.𝚺𝐝𝐲
𝐍𝚺𝐝𝐱²− 𝚺𝐝𝐱 𝟐. 𝐍.𝚺𝐝𝐲²−(𝚺𝐝𝐲)²
r=
𝐍.𝚺𝐗𝐘−𝚺𝐗.𝚺𝐘
𝐍.𝚺𝐗²− 𝚺𝐗 𝟐. 𝚺𝐘²−(𝚺𝐘)²
WHEN RANK ARE GIEVAN WHEN RANK ARE NOT
GIVEN
WHENRANK ARE EQUAL
R= 1 -
𝟔𝜮𝐃𝟐
𝐍𝟑 −𝐍
R= 1 -
𝟔𝜮𝐃𝟐
𝐍𝟑 −𝐍 R= 1 -
𝟔(𝜮𝐃𝟐+
𝟏
𝟏𝟐
𝒎𝟑−𝒎+
𝟏
𝟏𝟐
𝒎𝟑−𝒎+
𝟏
𝟏𝟐
𝒎𝟑−𝟑)
𝐍𝟑 −𝐍
17. REGRESSION
• (1. ALGEBRIC METHOD :-
( 2. NON – ALGEBRIC METHOD –
( I. ACTUAL METHOD :- co- efficient = bxy x byx
(3. ASSUMED METHOD :- co- efficient = bxy x byx
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
1.Y on X
Y-Y̅=byx(X-X̅) byx=
𝚺𝐱𝐲
𝚺𝐱²
2.X on Y
X-X̅=bxy(Y-Y̅ ) bxy=
𝚺𝐱𝐲
𝚺𝐲²
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
18. TIME SERIES
• Least square method - Yс = a +bX
• if x =0 then
a =
∑𝒚
𝑵
b =
∑𝒙𝒚
∑𝐱²
