Kerala Plus One Answer Key 2023 Statistics

FIRST YEAR

Kerala Board
Answer Key
2023

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FIRST YEAR mGHER SECONDARY EXAMINATION MARCH 2023

PARTll

SUBJECT: STATISTICS

CODE NO: FY - 432 VERSION:

SCORES: 60 2 HOURS

Qn, Sub Total
Answer Key / Value Points Score
No. Qns Score
Age 5 -10 10-15 15-20 20-25 25- 30 30- 35 Total
1 Freq 6 8 18 14 6 3 55 2 2
%freq 10.9 14.5 32.7 25.5 10.9 5.5 100

2 (a) (iii) ° 1
2
(b) (ii) 26 1
3 The data in ascending order: 54,55,57,58,60,61,67
n=7

QI = -4-
(r
n+ 1
value = 2 value = 55 (formula only X score)
nd
X

Q3 = 3 x ( n:

QD= Q3-QI
1
r value = 6th value = 61 (formula only X score)

= 61-55 = -6 = 3 (formula only X score)
X
2

2 2 2
X+X
4 [32 = 1142
1
112
= _!E_ = _!E_ = 1.44 X 2
(9.2)2 84.64
Since [32< 3 , the distribution is platy kurtic. X
5 P(AUB) = P(A)+P(B)-P(Aand B) I
2
-~+li-Ys-Ys
- 4 2 8- 8 I
6 • If the population is infinite or large.
• If the units under study are destroyed in the course of 2
inspection. 2xl
Or any two similar points /two examples)
7 (a) (ii) P C Mahalanobis I

Minimum two points on anyone of Biostatistics, Actuarial Science, 3
(b) 2 xl
Agricultural Statistics. (Writing the name only give 1score)

Qn, Sub Total
Answer Key / Value Points Score
No. Qns Score
8 (a) Pilot survey 1
Comparison between primary and secondary data with any 4 3
(b) relevant points. 4xYz=2

9 Appropriate questionnaire with any 4 relevant questions other than
3 3
personal questions.
10 Average speed is the HM of the given speeds.
1 1 1
---I-
HM n x I

1(1 1 1 1 1)
="5 12+15+ 16 +18+19 Yz
1 0.3207 3
=-( 0.0833 + 0.0667 + 0.0625 + 0.0556 + 0.0526) = Yz
5 5
5 1
:.HM= =15.6 km/hr
0.3207
(Give 3scoreif the HM is calculatedusing any other relevantformula or
procedure)(Give 1scorefor finding AM).
11 Mean = 50, Mode = 45
Mean - Mode = 3(Mean - Median) 1
50-45 =3(50-Median) 1
3Median = 150-5 = 145 Yz
Median = 14% = 48.33 Yz 3

OR
Give full score if solved using the formula
Mode = 3Median - 2Mean

12 (a) 1. Positive skewness - Explanation/Diagram 1

2. Negative Skewness - Explanation/Diagram 1
3

(b) (i) PI = 0 1

13 1. Convenience sampling 1
2. Judgment sampling 1 3
3. Quota sampling 1

Qn, Sub Total
Answer Key / Value Points Score
No. ns Score
14 (i) Proper sketch. 2

(ii)
Science Commerce Humanities
Sub Sub Sub Total
L B G T B G T B G T
~ Total Total Total
Malayalam
2 4
Hindi

Sanskrit

Total

(OR correct table give 4 score.)

15 Multiple Bar Diagram
140 ~-------------------------------
120 -+--------------
100
80 II Sales{OOO)

60 • Income (OOO)
40 • Profit (OOO) 4
4
20
o
2000 2001 2002

(Drawing sub divided or percentage bar diagram give 3score)

16 1, 3,4, 6, 7, 7, 8, 8, 9, 10, 11
n =11
n + 1)11l ( 11+ 1)Ih rd
Ql = ( -4- value = -4- value = 3 value =4 I

n + 1)lh ( 11 + 1)lh value = 6th value = 7
Q2 = ( -2- value = -2-
1

Q3 = (
3(
n4+
1))111 value = (3(114+ 1))lh value = 9th value= 9
1 4
Minimum value = 1 Maximum value = 11
The box plot is

o 1 2 3 4 5 6 7 8 9 10 11 12 1
(Rough diagram of box plot give 2 score)

Qn, Sub Total
Answer Key / Value Points Score
No. Qns Score
17
Mean = I x = 8 + 10 + 6 + 7 + 5 + 4 + 2 = 6 1
n 7
Ilx-Meanl = 2+4+0+1+1+2+4 =14
lYi 4

MD about mean = Ilx-Meanl
n =-
14
=2
1+ Yi
7
18 4 1
(i) --- 1
52 13
26 1
(ii) - = - 1
52 2
4
2 1
(iii) --- I
52 26
1 1
(iv) -
52
19 P(A) = 0.25, P(B) = 0.35, P(C) = 0.40 1

p(~) = 0.03, p( %) = 0.02, p( %) = 0.05 1
By total probability theorem 4
P(D) = P(A) x p(~) + P(B) x p( %) + P(C) x p( %) 1

= 0.25 x 0.03 + 0.35 x 0.02 + 0.40 x 0.05 = 0.0345 1
20 Less than CFT Greater then CFT
Upper limit LCF Lower limit GCF
10 5 0 70
20 16 10 65
30 43 20 54 2
40 62 30 27
50 67 40 8
60 70 50 3

so

C
70 I ...
u 60 Less then ogive 6
m
50
u1
ati 40
ve 4
fre 30
qu 20
en
cy 10 Greater than ogive
0
0 10 20 30
Class lirnits
40 50
-
60 70

Qn, Sub Total
Answer Key / Value Points Score
No. Qns Score
21 (a) Modal class = 20 - 30
Mode = 1+ (1; - fo)c I
21; - /0 - J;
Here, 1=20, fo = 10,1; = 20, /2 = 11,c = 10 1
Mode = 20+ (20-1O)xIO
2x20-10-11 1

= 20+100=25.26
19
1 6

(b) nl = 253, n2 = 312, X; = 11.8, x2 = 12.3
x = nIX; + n2x2 1
nl +n2
= 253 x 11.8 + 312 x 12.3 = 6823 = 12.08 1
565 565

22 For Kamataka
LX = 114, Lx2 = 2614
X= ~> n
= 114 =22.8
5

<T=~~X' _(x)' = 2~14 -(22.S)' =-./2.96 =1.72

SD
CV= --x100 1
Mean
= 1.72 x 100 = 7.54
22.8

For Kerala
6
LX = 126, Lx2 = 3214
x= L> = 126 =25.2
n 5

(Y = !Lx2 _(X)2 = 3214 -(25.2)2 = .J7.76 = 2.79
~ n 5
CV = 2.79 x 100 = 11.07
25.2
Here CV is less for Kamataka. So the price in Kamataka is stable
than the price in Kerala. 1

(Comparison using standard deviation only givefoil score)

5

~-r
SINo Name & School Signature tr-;
Dr. Manoj K
I
HSS Panangad, Mathilakam, Thissur -=--(
Dr. Biju G V ~.
2
Govt V&HSS Vatiyoorkavu, Thiruvananthapuram

3
Dr. Sajish Kumar M
MNKM HSS Chittilencherry, Palakkad 9/~ ~

4
Vidya Ramachandran
TD HSS Thuravoor, Alappuzha
Smitha MS
'2P
5 ~'
SN HSS Sreekandeswaram, Poochackal, Alappuzha
Seby Jose P
6
MSM HSS Kallingalparamba, Malappuram ~

7

8
Jyothi B
Govt HSS Korom, Payyannoor, Kannur
Shanthi K
Govt HSS Chayoth, Hosdurg, Kasargod
«:~-f) . /
»<,>,
'
",/ ./
...'
Unnikrishnan E
9 Shree Durga Parameswary AHSS, Dharmathadka
~~
Kasargod