Kerala Plus Two Answer Key 2023 Statistics

SECOND YEAR

Kerala Board
Answer Key
2023

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SECOND YEAR HIGHER SECONDARY EXAMINATION MARCH 2023

PARTm

SUBJECT: STATISTICS

CODE NO: SY- 532 VERSION:
SCORES: 60 2 HOURS

Qn, Sub Total
Answer Key / Value Points Score
No. Qns Score
1 Explanation/graphical presentation of three types of correlation-
1+1+1 3
Positive, Negative, Zero (for writing names only give liz score each)
2 (a) (iii)perpendicular OR (iv) intersect 1
(b) (7 1
bxy =r_x
(7y 3
0.65 x 4 liz + liz
1.5= => (7y = 1.73
(7y

3 E(X) = LXP(x) liz
=OxO.1 + 1xO.3 + 2x0.4+3x0.2 = 1.7 liz
E(X2) = LX2 P(x) liz
3
= 02 X 0.1 + 12x 0.3 + 22 x 0.4 + 32 x 0.2 = 3.7 liz
VeX) = E(X2) _(E(X»)2 liz
=3.7-1.72 =3.7-2.89=0.81 liz
4 (a) Definition of cdf. 1
3
(b) Any two properties of cdf (l score each) 2
5 (a) (iv) 0.5 1
(b) Given mean J1 = 28 , standard deviation (J =5

P(25 < X < 30) =p(25-28 < X -28 < 30-28) liz
555 3
= P(-0.6 < Z < 0.4) liz
= P(O < Z < 0.6) + P(O < Z < 0.4) liz
= 0.2257 + 0.1554 = 0.3811 liz
6 (a) (ii) 2 I
(b) Any four properties of normal curve (liz score each) 4x~=2
3

7 V(7;) = V(2X1 + 2X2 - 3X3) = 4V(X1)+4V(X2)+9V(XJ = 4cr2 +4cr2 + 9cr2 = 17cr2 1
V(T2) = V(X1 +2X2 -2X3) = V(X1) +4V(X2)+4V(XJ = cr2 +4cr2 +4cr2 = 9cr1 3
1
Here V(T2) < V(l;). Hence T2 the efficient estimator.
1

Qn, Sub Total
Answer Key / Value Points Score
No. Qns Score
8 (a) (i) unbiased
1
(b) (ii) Moment estimate of f.1 = x
1
= ~>
n
= 201 = 16.75
12
Y2+Y2
3

9 (a) Definition or Explanation of assignable causes
1

(b) Normality, homogeneity, independence, additivity 3
4x~=2

10
Source df SS MSS F Fa
Between 8 361.6 45.2
12.91 2.95
3
Within 11 38.5 3.5 2

Total 19 400.1
r-:C><C>< (4x Y2 )

F > Fa so we reject null hypothesis Y2+Y2
11
(a) (iv) irregular variation 1
3
Explanation of cyclical variation with or without diagram OR 2
(b)
Definition of cyclical variation
12 (a) (iv) current year quantity 1
3
(b) Any four uses of index numbers. 4x)'i=2

13 (a)
Let 2x+3y-31 = 0----(1), 5x+4y-28 = 0---(2)
Let us assume that eqn (1) is the regression line ofY on X and eqn (2) is the
regression line of X on Y. Now eqn (1) becomes,
-2 31 -2
3y = -2x+3l => y=-x+- :.bvx =- 1
3 3 . 3
Similarly eqn (2) becomes,
-4 28 -4
5x = -4y+28 => x=-y+- :. bT}= - 1
5 5 5 4
-2 -4 8
Now b xb =-x-=-<l Y2
yx T}' 3 5 15
Our assumption is right. So the regression line of Y on X is 2x + 3y - 31 = 0 Y2
(b)
r=±~b yx xb xy Y2

= ±~ = ±.J0.53 = -0.73 Y2
15

Qn, Sub Total
Answer Key / Value Points Score
No. Qns Score
14 (a) 1
dy = 12x2 -4x+ 7
dx
d2y
-=24x-4 1
dx2
(b) 1
J:(X'-2)dx~[x:I -[2xl: 4

Yz
~(; -0)-(4-0)
8 -4
=--4=-=-1.33
Yz
3 3
15 (a) (ii) Poisson distribution 1
(b) np =4, npq =3 li
3
npq = 3 => 4 x q = 3 => q=- li
4
3 1
:.p=l-q=I--=- li
4 4
4
1
Now, np=4 =>nx-=4 =>n=4x4=16 li
4
The pdf is,
P(x) = nC,pXq"-X,x = 0,1,2, ....n li

=16Cx 4" (1 J (3r-
4" X ,x = 0,1,2,...,16 li

16 (a) (i) X(~) 1

(b)
SINo Sample Sample Mean
1 3,5 4
2 3,7 5
3 3,9 6
4 3,11 7
5 5,7 6 2
4
6 5,9 7
7 5,11 8
8 7,9 8
9 7,11 9
10 9,11 10
Total 70

(-) =-=-=7
EX LX 70 1
n 10

3

Qn, Sub Total
Answer Key / Value Points Score
No. Qns Score
17 (a) (iii) Chi - square test 1
(b) (i) Definition/Explanation of level of significance 1 4
(ii) Definition/Explanation of power of a test 1
(iii) Definition/Explanation of critical region
1
18
3 yearly 3 yearly
No. of
Year moving moving
deaths
total average
2011 175

2012 190 550 183.33

2013 185 570 190
2+2 4
2014 195 560 186.67

2015 180 578 192.67

2016 203 580 193.33

2017 197 652 217.33

2018 252

19
r= nLXY-LXLY
1
~nLX2 _(LX)2 x~nLy2 _(Ly)2
X Y X2 y2 XY
18 12 324 144 216
28 19 784 361 532
12 21 144 441 252
2
25 34 625 1156 850
22 25 484 625 550
15 20 225 400 300
7 15 49 225 105 5
16 14 256 196 224
LX= 143 LY= 160 :L,xz= 2891 LYz= 3548 ~>IT= 3029

8x3029-143x160
:.r= ~8x2891-(143)2 X~8X3548-(160)2 1

= 1352 = 0.495
..)2679 x ..)2784
1
Alternative method: [Covariance = 21.13 (1 score). s.d(x) = 6.47 (Yz score.
s.d(y) = 6.6 (Yz score), r = 0.495 (Yz + Yz Score)]

Qn, Sub Total
Answer Key / Value Points Score
No. Qns Score
20 (a) Lx=434, LR=59

x= LX = 434 =36.17 - LR 59
m 12
R=-=-=4.92
m 12
Yz+Yz
The control limits of x chart are,
CL= x=36.17 Yz 5
VCL = x + A2Ii = 36.17 +O.729x4.92 = 39.76 Yz
LCL = x -A2R = 36.17 -0.729x4.92 = 32.58 Yz
(b) Drawing x chart 2
The process is out of control. Yz
(Give 1score for rough diagram)
21
Po % P1 q1 Poqo P1qO Poq1 P1Q1
30 5 39 5 150 195 150 195

27 8 45 4 216 360 108 180

36 7 38 6 252 266 216 228 2

42 3 45 4 126 135 168 180

744 956 642 783 5
Total

. LP1QO 956
(1) Laspeyre'sIndexNo.= L xl00= -xl00=128.49 1
PoQo 744

(ii) Paasche's Index No.~ E p, q, x 100 ~ 783 x I 00 ~ 121.96
POQ1 642
1

(iii) Fisher's Index No.= ..}Lx P = ..}128.49x 121.96 = 125.18 1

SINo Name & School Signature

Dr. Manoj K
I
HSS Panangad, Mathilakam, Thissur

2
Dr. Biju G V J~'
Govt V&HSS Vatiyoorkavu, Thiruvananthapuram
Dr. Sajish Kumar M
3
MNKM HSS Chittilencherry, Palakkad
Vidya Ramachandran
4
TD HSS Thuravoor, Alappuzha
SmithaMS
5
SN HSS Sreekandeswaram, Poochackal, Alappuzha ~
Seby Jose P
6
MSM HSS Kallingalparamba, Malappuram
Jyothi B
7
Govt HSS Korom, Payyannoor, Kannur
Shanthi K
8
Govt HSS Chayoth, Hosdurg, Kasargod
Unnikrishnan E
9 Shree Durga Parameswary AHSS, Dharmathadka
Kasar od