Economic class 11

1. CORRELATION
&
INDEX NUMBER

2. CORRELATION

3. Correlation
 Correlation coefficient(CC) measures the relation between two variables.
(how they are related)
 It measures strengths and direction of relationship.
 Strength of a relationship means values of correlation coefficient (CC) between +1
and -1 denoted by π and ρ.
 Direction of a relationship means sign of CC is either values of CC
R is +1 (Perfect positive)
R is -1 (Perfect negative)
R is 0 (No relation/weak)

4. Properties of correlation
1. CC has no unit
2. Negative value of R shows (inverse relation)
3. The CC will always remain between -1 and +1
4. If the CC is close to 1, the relationship is strong.
5. If xy values are far from eachother, it shows weak relationship.
6. If R is zero, it has a weak or no relation.
7. If R is +1 or -1, it shows perfect correlation.

5. Methods of Estimating
Correlation
Scatter
graph
Pearson’s
coefficient
Spearman’s
Rank

6. Q1. Calculate Spearman’s rank correlation coefficient
x 87 22 33 75 37
y 29 63 52 46 48
x R₁ y R₂ D=R₁-R₂ D2
87 5 29 1 4 16
22 1 63 5 -4 16
33 2 52 4 -2 4
75 4 46 2 2 4
37 3 48 3 0 0
40
Rst = 1- 6ΣD2
N3 -N

7. Rst = 1- 6ΣD2
N3 -N
= 1- 6(40)
53 -5
= 1- 240
= 1- 240
120
= 1 - 2
1
= 1- 2 =
125-5
Solution:

8. Q2. Calculate Karl Pearson’s rank correlation coefficient
X a = x-x a2 Y b = y-y b2 ab
6 6-18=-12 144 10 10-19=-9 81 108
8 8-18=-10 100 12 12-19=-7 49 70
12 -6 36 15 -4 16 24
15 -3 9 15 -4 16 12
18 0 0 18 -1 1 0
20 2 4 25 6 36 12
24 6 36 22 3 9 18
28 10 100 26 7 49 70
31 13 169 28 9 81 117
162 598 171 338 431
Cpr = Σab
√Σa2 × Σb2
Found,

9. Solution:
Finding mean: X = ΣX = 162 = 18
N 9
Y = ΣY = 171 = 19
N 9
√Σa2 × Σb2
Cpr = Σab
= 431
√ 598 × 338
= 431 =
449.53

10. Scatter graph
 A scatter graph is a statistical diagram which
gives a visual representation of bivariate data (x
and y).
 Scatter graph visually shows the correlation.

11. INDEX
NUMBER

12. What is index number?
 It is a statistical technique used to interpret, analyse and compare large
number of data easily.
 Index numbers compare current year data with base year data.
 Base year:- In a base year, original data is equated to a value of 100.
 Simple data = (R.1) CY × 100
R.D.BY
 Weighted index:- Its definition is as same as Index number, but it is an Index
made up of a combination of other Index.
 Calculating Index number without base year
= Current year’s raw value × previous year’s index number
Previous year’s raw value

13. Importance or Uses of index number
 Economic barometer
 Study of economic trends
 Policy formulation
 Forecasting
 Inflation
 Purchasing power
 Growth
Types of Index number
 Price index number
 Quantity index number
 Value of index number

14. Methods of finding Index Number
Unweighted/
Simple
Weighted
Simple
Aggregative
method (SAM)
Simple Price
Relative method
(SA-PRM)
Weighted
Aggregative
Method
(WAM)
Weighted Price
Relative Method
(W-PREM)
Lespeyers Paasches Fisher
Given (P1 data)
(P2 data)
Find R = P1 × 100
(W is also given)
P01 = ΣRW
ΣW

15. Laspeyre’s Method: P01= ΣP1Q0 × 100
ΣP0Q0
Paasche’s Method: P01= ΣP1Q1 × 100
ΣP0Q1
Formula to find Index Number

16. Commodity
Base year Current year
Price
P0
Quantity Q0 Price
P1
Quantity Q1
A 10 12 12 15
B 7 15 5 20
C 5 24 9 20
D 16 5 14 5
Q1. Complete in Laspeyre’s Method and Paasche’s Method

17. Commodity
Base year Current year
P0 Q0 P1 Q0 P0 Q1 P1 Q1
Price P0
Quantity
Q0
Price
P1
Quantity
Q1
A 10 12 12 15 120 144 150 180
B 7 15 5 20 105 75 140 100
C 5 24 9 20 120 216 100 180
D 16 5 14 5 80 70 80 70
425 505 470 530
Solution:
Laspeyre’s Method:
P01= ΣP1Q0 × 100 = 101 × 100
ΣP0Q0
= 1.1 × 100 =
85
Paasche’s Method:
P01= ΣP1Q1 × 100 = 530 × 100
ΣP0Q1
= 1.1 × 100 =
470

18. Commodity
Price in
2004
P0
Price in
2008
P1
Quantity in
Base Year Q0
Quantity in
Current Year
Q1
A 12 15 5 25
B 24 30 20 40
C 36 45 25 15
D 48 75 10 20
E 60 125 20 25
Q2. Complete in Laspeyre’s Method and Paasche’s Method

19. Commodity
Price in
2004
P0
Price in
2008
P1
Quantity in
Base Year
Q0
Quantity in
Current
Year Q1
P0 Q0 P1 Q0 P0 Q1 P1 Q1
A 12 15 5 25 60 75 300 375
B 24 30 20 40 480 600 960 1200
C 36 45 25 15 900 1125 540 675
D 48 75 10 20 480 750 960 1500
E 60 125 20 25 1200 2500 1500 3125
3120 5050 4260 6875
Solution:
Laspeyre’s Method:
P01= ΣP1Q0 × 100 = 5050 × 100
ΣP0Q0
= 1.61 × 100 =
3120
Paasche’s Method:
P01= ΣP1Q1 × 100 = 6875 × 100
ΣP0Q1
= 1.61 × 100 =
4260

20. SAPRM (U PREM)
P01 = Σ P1 × 100
P0
753.10=
6
Unweighted
(P0) 2010
price
(P1) 2011
price
P1 × 100
A 45 55 122.2
B 60 70 116.67
C 20 30 150.00
D 50 75 150.00
E 85 90 105.88
F 120 130 108.55
380 450 753.10
SAM
P01 = ΣP1 × 100
ΣP0
450 × 100 = 118.42
380
P0
N

21. Calculate price Index of current year w.r.t base year for following
data
Goods A B C D E
Price in
2010
10 20 5 2 4
Price in
2020
100 40 25 18 32
(P0) Price
in 2010
(P0) Price
in 2010 Wt (W)
R=P1 × 100 R W
A 10 100 1
B 20 40 2
C 5 25 3
D 2 18 2
E 4 32 1
Weighted price
relative method
(WE-PREM)
P01 = ΣRW
ΣW
P0