Karnataka 2nd PUC Question Paper 2026 Statistics

£ÉÆÃAzÀt ¸ÀASÉå :
Registration No. :

V1 – 2026
«µÀAiÀÄ ¸ÀAPÉÃvÀ /
31 (NS)
Subject Code

¸ÀASÁå±Á¸ÀÛç / STATISTICS
(Kannada and English Versions)

[¸ÀªÀÄAiÀÄ: 3 UÀAmÉUÀ¼ÀÄ] [MlÄÖ ¥Àæ±ÉßUÀ¼À ¸ÀASÉå : 38] [UÀjµÀ× CAPÀUÀ¼ÀÄ : 80]
[Time : 3 Hours] [Total No. of questions : 38] [Max. Marks : 80]

(Kannada Version)
¸ÀÆZÀ£ÉUÀ¼ÀÄ : 1. ¸ÁATåPÀ PÉÆõÀ×PÀUÀ¼ÀÄ ªÀÄvÀÄÛ D¯ÉÃR PÁUÀzÀUÀ¼À£ÀÄß
«£ÀAwAiÀÄ ªÉÄÃgÉUÉ ¥ÀÆgÉʸÀ¯ÁUÀĪÀÅzÀÄ.
2. ªÉÊeÕÁ¤PÀ UÀtPÉÆÃ¥ÀPÀgÀtUÀ¼À£ÀÄß §¼À¸À§ºÀÄzÀÄ.
3. PÁAiÀÄðzÀ J¯Áè ºÀAvÀUÀ¼À£ÀÄß ¸ÀàµÀÖªÁV vÉÆÃj¸ÀvÀPÀÌzÀÄÝ.
4. Ë»ÝWÜ -J zÀ°è£À ¥Àæ±ÉßUÀ½UÉ ¥ÀæxÀªÀĪÁV §gÉzÀ
GvÀÛgÀUÀ¼À£ÀÄß ªÀiÁvÀæ ªÀiË®åªÀiÁ¥À£ÀzÀ°è ¥ÀjUÀt¸À¯ÁUÀĪÀÅzÀÄ.
5. D¯ÉÃR ºÉÆA¢gÀĪÀ ¥Àæ±ÉßUÉ ¥ÀAiÀiÁðAiÀĪÁV ¥Àæ±Éß ¥ÀwæPÉAiÀÄ
PÉÆ£ÉAiÀÄ°è ¥ÀævÉåÃPÀ «¨sÁUÀz° À è zÀ馅 «PÀ®ZÉÃvÀ£À
«zÁåyðUÀ½UÉ «ªÀgÀuÁvÀäPÀ ¥Àæ±ÉßAiÀÄ£ÀÄß ¤ÃqÀ¯ÁVzÉ.
Ë»ÝWÜ – J
I. ¤ÃrgÀĪÀ DAiÉÄÌUÀ½AzÀ CvÀåAvÀ ¸ÀÆPÀÛªÁzÀ GvÀÛgÀªÀ£ÀÄß DAiÉÄÌ ªÀiÁr
§gɬÄj : (5 × 1 = 5)
1) ªÀÄPÀ̼À£ÀÄß ºÉgÀĪÀ ªÀAiÀĹì£À ªÀÄ»¼ÉAiÀÄjUÉ d¤¸ÀĪÀ d£À£ÀªÉÃ
a) ¥sÀ®ªÀAwPÉ b) ªÀÄÈvÀÄå¹Üw
c) §zÀÄPÀĽAiÀÄĪÀ C£ÀÄ¥ÁvÀ d) ¥sÀ®¨sÀjvÀvÉ
P.T.O.

31 (NS) -2-

2) 2020 PÉÌ ºÉÆð¹zÁUÀ 2024 gÀ°è ªÀ¸ÀÄÛUÀ¼À ¨É¯É ±ÉÃPÀqÁ 10 gÀµÀÄÖ
PÀrªÉÄAiÀiÁVzÉ. 2024 gÀ ¸ÀÆZÁåAPÀªÀÅ
a) 10 b) 90
c) 100 d) 110

3) ¤AiÀÄvÁAPÀ n = 10 EgÀĪÀ t-«vÀgÀuÉAiÀÄ ¸ÀgÁ¸Àj
a) 0 b) 5
c) 10 d) 20

4) ¤zÀ±ÀðPÀ C£ÀÄ¥ÁvÀzÀ ¤AiÀÄvÀ zÉÆõÀªÀÅ
PQ P
a) b)
n n

PQ Q
c) d)
n n

5) MAzÀÄ DlªÀ£ÀÄß ¤µÀàPÀë¥ÁvÀzÀ DlªÉAzÀÄ ºÉüÀ¨ÉÃPÁzÀgÉ DlzÀ ªÀiË®åªÀÅ

a) V ≠0 b) V =1
c) V =2 d) V =0

II. DªÀgÀtzÀ°è ¤ÃrgÀĪÀ ¸ÀÆPÀÛªÁzÀ GvÀÛgÀUÀ¼À£ÀÄß Dj¸ÀĪÀ ªÀÄÆ®PÀ
©lÖ ¸ÀܼÀUÀ¼À£ÀÄß ¨sÀwð ªÀiÁrj : (5 × 1 = 5)

[¤AiÀÄvÁAPÀ, PÀ¤µÀ×, UÀjµÀ×, zÉÆõÀAiÀÄÄPÀÛ, 100, ¤AiÀÄvÀ ¥Àæ¸ÁªÀiÁ£Àå]

6) DzsÁgÀ ªÀµÀðzÀ ¸ÀÆZÁåAPÀzÀ ¨É¯É ____________.
7) ____________ «vÀgÀuÉAiÀÄ°è «ZÀ®£É ªÀÄvÀÄÛ ¤AiÀÄvÀ «ZÀ®£ÉUÀ¼ÀÄ
¸ÀªÀÄ£ÁVgÀÄvÀÛªÉ.

-3- 31 (NS)

8) ¸ÀªÀĶ×AiÀÄ ¸ÁATåPÀ ¹ÜgÁAPÀªÀ£ÀÄß ____________ J£ÀÄߪÀgÀÄ.
9) MAzÀÄ CxÀªÁ ºÉZÀÄÑ zÉÆõÀUÀ¼À£ÀÄß ºÉÆA¢gÀĪÀ ªÀ¸ÀÄÛ ____________
ªÀ¸ÀÄÛ.
10) MAzÀÄ G¥ÀPÀgÀtªÀ£ÀÄß ªÀµÀðzÀ PÉÆ£ÉAiÀÄ°è §zÀ¯Á¬Ä¸À®Ä ªÁ¶ðPÀ
¸ÀgÁ¸Àj ªÉZÀѪÀÅ ____________ DVgÀÄvÀÛzÉ.

III. ºÉÆA¢¹ §gɬÄj : (5 × 1 = 5)

11) J §

a) M§â ªÀÄ»¼ÉAiÀÄ NRR = 1.1 i) ©AzÀÄ CAzÁf¸ÀÄ«PÉ

b) DzsÁgÀ ªÀµÀðzÀ ¨sÁgÀ ii) CAvÀgÁ¼ÀzÀ CAzÁf¸ÀÄ«PÉ

c) t-«vÀgÀuÉAiÀÄ°è ¸ÀgÁ¸ÀjAiÀÄÄ iii) ¸ÀgÀPÀÄ zÁ¸ÁÛ£ÀÄ

d) CAzÁfUÁV ¥Àæ¸ÁÛ¦¹zÀ MAzÀÄ iv) d£À¸ÀASÉå KjPÉAiÀiÁUÀÄwÛÛzÉ
¸ÀA¨sÀªÀ¤ÃAiÀÄvÉAiÀÄ ¨É¯É

e) ªÀ¸ÀÄÛUÀ¼À ¨sËwPÀ ±ÉÃRgÀuÉ v) ¯Áå¸ÉàAiÀÄgÀ£À ¨É¯É ¸ÀÆZÁåAPÀ

vi) 0

IV. F PɼÀV£À ¥Àæ±ÉßUÀ½UÉ GvÀÛj¹ : (5 × 1 = 5)

12) ‘¥sÀ®¨sÀjvÀvÉ’AiÀÄ£ÀÄß ªÁåSÁ夹.

13) PÁ® ¸ÀgÀtÂAiÀÄ°è C¤AiÀÄ«ÄvÀ §zÀ¯ÁªÀuÉUÉ MAzÀÄ PÁgÀtªÀ£ÀÄß w½¹.

14) AiÀiÁªÀ ¨É¯ÉUÉ p ¢é¥ÀzÀ «vÀgÀuÉ ¸À«ÄävÀªÁVgÀÄvÀÛzÉ?

31 (NS) -4-

15) ®PÁëºÀð ªÀÄlÖªÀ£ÀÄß ªÁåSÁ夹.

16) MAzÀÄ gÉÃSÁvÀäPÀ PÀæªÀÄ«¢ü ¸ÀªÀĸÉåAiÀÄ D¯ÉÃR «zsÁ£ÀzÀ ±ÀPÀå ¥ÀjºÁgÀªÀÅ
KPÉ ªÉÆzÀ®£ÉAiÀÄ ZÀvÀÄxÁðA±ÀzÀ°è EgÀÄvÀÛzÉ?

Ë»ÝWÜ & ©

V. D PæÙÜX®Ü ¿ÞÊÜâ¨Ý¨ÜÃÜã LzÀÄ ±ÜÅÍæ°WÜÚWæ EñܤÄÔ : (5 × 2 = 10)

17) ªÁå¥ÁgÀ ZÀPÀæzÀ £Á®ÄÌ ºÀAvÀUÀ¼À£ÀÄß §gɬÄj.

18) CAvÀªÉÃð±À£À ªÀÄvÀÄÛ §»ªÉÃð±À£ÀzÀ°è ¢é¥ÀzÀ «¸ÀÛgÀuÁ «zsÁ£ÀzÀ
PÀgÁgÀÄUÀ¼À£ÀÄß §gɬÄj.

1
19) MAzÀÄ §£ÉÆÃð° «vÀgÀuÉAiÀÄ°è p= DzÀgÉ ¸ÀgÁ¸Àj ªÀÄvÀÄÛ
2
«ZÀ®£ÉAiÀÄ£ÀÄß PÀAqÀÄ»r¬Äj.

20) ¥ÉÆÃAiÀÄì£ï «vÀgÀuÉAiÀÄ JgÀqÀÄ UÀÄt®PÀëtUÀ¼À£ÀÄß §gɬÄj.

21) ªÉÆzÀ®£ÉAiÀÄ vÀgÀºÀzÀ ªÀÄvÀÄÛ JgÀqÀ£ÉAiÀÄ vÀgÀºÀzÀ zÉÆõÀUÀ¼À£ÀÄß
ªÁåSÁ夹.

22) eÉÆÃr t-¥ÀjÃPÉëAiÀÄ°è n = 5 , d = 3 .4 ªÀÄvÀÄÛ Sd = 2 DzÀgÉ ¥ÀjÃPÁë
¤zÀ±ÀðdzÀ ªÀiË®å JµÀÄÖ?

-5- 31 (NS)

23) GvÁàzÀ£Á ¥ÀæQæAiÉÄAiÀÄ°è£À Kj½vÀUÀ½UÉ JgÀqÀÄ jÃwAiÀÄ PÁgÀtUÀ¼À£ÀÄß
w½¹j.

24) R = 5000 ªÀ¸ÀÄÛUÀ¼ÀÄ ªÀµÀðPÉÌ C1 = gÀÆ. 2/ªÀ¸ÀÄÛ/ªÀµÀðPÉÌ ªÀÄvÀÄÛ
C3 = gÀÆ. 200/¸À®PÉÌ JAzÀÄ PÉÆmÁÖUÀ Q 0 £ÀÄß PÀAqÀÄ»r¬Äj.

Ë»ÝWÜ & ¹

VI. F PɼÀV£À AiÀiÁªÀÅzÁzÀgÀÆ £Á®ÄÌ ¥Àæ±ÉßUÀ½UÉ GvÀÛj¹ : (4 × 5 = 20)

25) F PɼÀV£À zÀvÁÛA±ÀPÉÌ ªÉÆvÀÛ ªÀåAiÀÄ «zsÁ£À¢AzÀ UÁæºÀPÀ ¨É¯É
¸ÀÆZÁåAPÀªÀ£ÀÄß PÀAqÀÄ»r¬Äj.

¨É¯É (gÀÆ.) ¥ÀjªÀiÁt
¥ÀzÁxÀðUÀ¼ÀÄ
2019 2024 2019
A 4 8 20
B 10 12 40
C 15 20 40
D 25 40 50

26) F zÀvÁÛA±ÀPÉÌ ¢é¥ÀzÀ «¸ÀÛgÀuÁ «zsÁ£À¢AzÀ 2019 ªÀÄvÀÄÛ 2025 gÀ
ªÀµÀðUÀ½UÉ ¯Á¨sÀªÀ£ÀÄß CAvÀªÉÃð±À£À ªÀÄvÀÄÛ §»ªÉÃð±À£À CAzÁf¹.

ªÀµÀð : 2015 2017 2019 2021 2023 2025

¯Á¨sÀ (gÀÆ.) 8 14 – 21 30 –

31 (NS) -6-

27) MAzÀÄ ¨ÁtªÀÅ VqÀPÉÌ §rAiÀÄĪÀ ¸ÀA¨sÀªÀ¤ÃAiÀÄvÉ 1 DVzÉ. MAzÀÄ ªÉüÉ
4
3 ¨ÁtUÀ¼À£ÀÄß VqÀzÀ PÀqÉUÉ UÀÄj Ej¹zÁUÀ

i) AiÀiÁªÀÅzÉà ¨ÁtUÀ¼ÀÄ VqÀPÉÌ §rAiÀÄ¢gÀĪÀ
ii) JgÀqÀÄ ¨ÁtUÀ¼ÀÄ VqÀPÉÌ §rAiÀÄĪÀ ¸ÀA¨sÀªÀ¤ÃAiÀÄvÉAiÀÄ£ÀÄß
PÀAqÀÄ»r¬Äj.

28) MAzÀÄ §ÄnÖAiÀÄ°è 10 ªÀiÁ«£À ºÀtÄÚUÀ½ªÉ. CªÀÅUÀ¼À°è 6 ªÀiÁVªÉ.
F §ÄnÖ¬ÄAzÀ 3 ªÀiÁ«£À ºÀtÄÚUÀ¼À£ÀÄß AiÀiÁzÀÈaÒPÀªÁV DAiÉÄÌ
ªÀiÁrzÁUÀ ªÀiÁVzÀ ºÀtÄÚUÀ¼À ¸ÀgÁ¸Àj ªÀÄvÀÄÛ «ZÀ®£ÉAiÀÄ£ÀÄß
PÀAqÀÄ»r¬Äj.

29) UÉÆâü GvÁàzÀ£ÉAiÀÄ ¤AiÀÄvÀ «ZÀ®£ÉAiÀÄÄ 10.2 JAzÀÄ H»¸À¯ÁVzÉ.
25 JPÀgÉ PÉëÃvÀæzÀ MAzÀÄ ¤zÀ±ÀðPÀªÀÅ ¤AiÀÄvÀ «ZÀ®£É 8.2 JAzÀÄ
vÉÆÃj¸ÀÄvÀÛzÉ. ±ÉÃ. 1 gÀ ®PÁëºÀðvÉ ªÀÄlÖzÀ°è UÉÆâü GvÁàzÀ£ÉAiÀÄ ¤AiÀÄvÀ
«ZÀ®£ÉAiÀÄÄ 10.2 VAvÀ PÀrªÉÄ EzÉAiÉÄà JA§ÄzÀ£ÀÄß ¥ÀjÃQë¹.

30) F PɼÀV£À ¸ÁUÁtÂPÁ ¸ÀªÀĸÉåUÉ ªÁAiÀÄĪÀå ªÀÄÆ¯É «zsÁ£À¢AzÀ ªÀÄÆ®
±ÀPÀå ¥ÀjºÁgÀªÀ£ÀÄß ¥ÀqÉzÀÄ ªÀÄvÀÄÛ MlÄÖ ¸ÁUÁtÂPÁ ªÉZÀѪÀ£ÀÄß ¯ÉQ̹.

UÉ
¥ÀÆgÉÊPÉ
D1 D2 D3 D4
O1 25 17 25 14 300
EAzÀ O2 15 10 18 24 500
O3 16 20 8 13 600

¨ÉÃrPÉ 75 325 500 500 1400

-7- 31 (NS)

31) MAzÀÄ AiÀÄAvÀæzÀ ¨É¯É gÀÆ. 8,000, EzÀgÀ ¤ªÀðºÀuÁ ªÉZÀÑ ªÀÄvÀÄÛ
ªÀÄgÀĪÀiÁgÁl ¨É¯ÉUÀ¼ÀÄ EAwªÉ.

ªÀµÀð : 1 2 3 4 5

¤ªÀðºÀuÁ ªÉZÀÑ (gÀÆ.) : 500 600 800 1,100 1,500

ªÀÄgÀĪÀiÁgÁl ¨É¯É (gÀÆ.) : 4,500 3,500 2,500 1,500 500

AiÀÄAvÀæzÀ §zÀ¯ÁªÀuÉAiÀÄ ¸ÀªÀÄÄavÀ CªÀ¢ü AiÀiÁªÀÅzÀÄ?

VII. F PɼÀV£À AiÀiÁªÀÅzÁzÀgÀÆ JgÀqÀÄ ¥Àæ±ÉßUÀ½UÉ GvÀÛj¹ : (2 × 5 = 10)

32) PÉ®¸ÀUÁgÀgÀ ªÁgÀzÀ PÀÆ°AiÀÄÄ ¥Àæ¸ÁªÀiÁ£Àå «vÀgÀuÉAiÀÄ°è ¸ÀgÁ¸Àj
gÀÆ. 3,000 ºÁUÀÆ ¤AiÀÄvÀ «ZÀ®£É gÀÆ. 500 UÀ¼ÉÆA¢UÉ ºÉÆA¢zÉ.
PÉ®¸ÀUÁgÀgÀ ªÁgÀzÀ PÀÆ°AiÀÄÄ
i) gÀÆ. 3,500 QÌAvÀ PÀrªÉÄ ªÀÄvÀÄÛ
ii) gÀÆ. 2,500 ªÀÄvÀÄÛ gÀÆ. 3,500 £ÀqÀÄªÉ EgÀĪÀ ¸ÀA¨sÀªÀ¤ÃAiÀÄvÉAiÀÄ£ÀÄß
¯ÉQ̹.

33) F zÀvÁÛA±À¢AzÀ ¸ÀgÁ¸ÀjUÀ¼À°è CxÀðUÀ©üðvÀ ªÀåvÁå¸À«zÉAiÉÄà JA§ÄzÀ£ÀÄß
¥ÀjÃQë¹. α = 0.01 G¥ÀAiÉÆÃV¹.

¤zÀ±ÀðPÀ UÁvÀæ ¸ÀgÁ¸Àj «ZÀ®£É

I 80 54 16

II 40 52 25

31 (NS) -8-

34) £É®PÉÌ ºÁ¸ÀĪÀ ºÉÆ¢PÉ vÀAiÀiÁj¸ÀĪÀ MAzÀÄ PÀA¥É¤AiÀÄ°è ¥Àæw
ZÀzÀgÀ «ÄÃlgï ºÉÆ¢PÉAiÀÄ°è£À ¸ÀgÁ¸Àj £ÀÆå£ÀvÉUÀ¼À ¸ÀASÉå λ1 = 4
DzÁUÀ £ÀÆå£ÀvÉUÀ¼À ¸ÀASÉåAiÀÄ ªÉÄð£À ªÀÄvÀÄÛ PɼÀV£À ¤AiÀÄAvÀæt
«ÄwUÀ¼À£ÀÄß ¤±ÀѬĹ.

35) F PɼÀV£À gÉÃSÁvÀäPÀ PÀæªÀÄ«¢ü ¸ÀªÀĸÉåAiÀÄ£ÀÄß D¯ÉÃR «zsÁ£À¢AzÀ ©r¹.
UÀjµÀÖUÉƽ¹ : Z = 2x + 3y
¤§AzsÀ£ÉUÀ½UÉ M¼À¥ÀlÄÖ : x + y ≥ 350
2 x + y ≤ 600
ªÀÄvÀÄÛ x ≥ 0, y ≥ 0

Ë»ÝWÜ & r

VIII. F PɼÀV£À AiÀiÁªÀÅzÁzÀgÀÆ JgÀqÀÄ ¥Àæ±ÉßUÀ½UÉ GvÀÛj¹ : (2 × 10 = 20)

36) F PɼÀV£À zÀvÁÛA±ÀPÉÌ A ªÀÄvÀÄÛ B ºÀ½îUÀ¼À ¤AiÀÄwÃPÀÈvÀ ªÀÄgÀt zÀgÀUÀ¼À£ÀÄß
PÀAqÀÄ»r¬Äj. AiÀiÁªÀ ºÀ½îAiÀÄÄ ºÉZÀÄÑ DgÉÆÃUÀåªÁVzÉ?

ªÀAiÉÆêÀUÀð ºÀ½î-A ºÀ½î-B DzÀ±Àð
(ªÀµÀðUÀ¼À°è) d£À¸ÀASÉå
d£À¸ÀASÉå ªÀÄgÀtUÀ¼ÀÄ d£À¸ÀASÉå ªÀÄgÀtUÀ¼ÀÄ
0-20 4000 68 8000 160 6000
20-40 9000 54 13000 65 12000
40-60 7000 91 10000 100 8000
60 ªÀÄvÀÄÛ ºÉZÀÄÑ 3000 129 4000 160 4000

-9- 31 (NS)

37) F PɼÀV£À zÀvÁÛA±ÀPÉÌ ¦ü±Àgï£À ¸ÀÆZÁåAPÀªÀÅ ¸ÀªÀÄAiÀÄ ªÀÄvÀÄÛ CA±À ªÀåwjPÀÛ
¥ÀjÃPÉëUÀ¼ÉgÀqÀ£ÀÄß vÀȦۥÀr¸ÀĪÀÅzÀÄ JAzÀÄ vÉÆÃj¹.

2019 2024
ªÀ¸ÀÄÛUÀ¼ÀÄ ¨É¯É (gÀÆ.) ¥ÀjªÀiÁt ¨É¯É (gÀÆ.) ¥ÀjªÀiÁt

A 10 15 14 25

B 14 20 20 30

C 17 30 15 45

D 20 25 30 32

38) a) F PɼÀV£À zÀvÁÛA±ÀPÉÌ 3 ªÀµÀðUÀ¼À ZÀ®£À ¸ÀgÁ¸ÀjUÀ¼À ªÀÄÆ®PÀ ¥ÀæªÀÈwÛ
¨É¯ÉUÀ¼À£ÀÄß PÀAqÀÄ»r¬Äj.

ªÀµÀð : 2000 2001 2002 2003 2004 2005 2006 2007 2008

ªÀiÁgÁl ('000) : 18 21 20 16 17 16 21 20 19

b) F zÀvÁÛA±ÀPÉÌ PÀ¤µÀ×vÀªÀÄ ªÀUÀðUÀ¼À «zsÁ£À¢AzÀ ¸ÀgÀ¼ÀgÉÃSÁ ¥ÀæªÀÈwÛ
¤AiÉÆÃf¹.

ªÀµÀð : 1980 1984 1988 1992 1996 2000

vÀAiÀiÁjPÉ ('000) : 16 20 19 14 18 21

31 (NS) -10-

«¨sÁUÀ – E

(zÀ馅 «PÀ®ZÉÃvÀ£À «zÁåyðUÀ½UÉ ªÀiÁvÀæ)

35) gÉÃSÁvÀäPÀ PÀæªÀÄ«¢ü ¸ÀªÀĸÉåAiÀÄ£ÀÄß D¯ÉÃR «zsÁ£À¢AzÀ ©r¸ÀĪÀ
ºÀAvÀUÀ¼À£ÀÄß §gɬÄj.

———————

-11- 31 (NS)

(English Version)

Instructions : 1. Statistical tables and Graph sheets will be supplied on
request.

2. Scientific calculators are allowed.

3. All working steps should be clearly shown.

4. For SECTION-A questions only the first written answers
will be considered for evaluation.

5. For the question having graph alternative question is given
at the end of the question paper in separate section for
visually challenged students.

SECTION – A

I. Choose the most appropriate answer from the choices given : (5 × 1 = 5)

1) The births occurring to women of child bearing age is called

a) Fertility b) Mortality
c) Survival ratio d) Fecundity

2) The prices of items decreased by 10% in 2024 as compared to 2020.
The index number for the year 2024 is

a) 10 b) 90
c) 100 d) 110

3) The parameter of a t- distribution n = 10 , then the mean is

a) 0 b) 5
c) 10 d) 20

31 (NS) -12-

4) The standard error of sample proportion is

PQ P
a) b)
n n

PQ Q
c) d)
n n

5) A game is said to be fair, if the value of the game is

a) V ≠0 b) V =1
c) V =2 d) V =0

II. Fill in the blanks by choosing the appropriate answers given in the brackets :
(5 × 1 = 5)

[Parameter, minimum, maximum, defective, 100, standard normal]

6) The value of the index number for the base year is ___________.

7) In ___________ distribution variance and standard deviation are equal.

8) A statistical constant of the population is called ___________.

9) An item having one or more defects is called ___________ item.

10) The equipment is replaced at the end of a year for which the annual
average cost is ___________.

-13- 31 (NS)

III. Match the following : (5 × 1 = 5)

11) A B

a) NRR per woman = 1.1 i) Point estimation

b) Base year weight ii) Interval estimation

c) The mean of a t-distribution iii) Inventory

d) Single value proposed as an iv) Population increased
estimate

e) Physical stock of goods v) Laspeyre’s price index number

vi) 0

IV. Answer the following questions : (5 × 1 = 5)

12) Define ‘Fecundity’.

13) Mention a cause of irregular variation in time series.

14) For what value of p binomial distribution is symmetrical?

15) Define level of significance.

16) In graphical method why feasible solution of linear programming problem
lies in the first quadrant?

SECTION – B

V. Answer any five of the following questions : (5 × 2 = 10)

17) Write four stages of business cycle.

18) Write the conditions for applying binomial expansion method of
interpolation and extrapolation.

31 (NS) -14-

1
19) If p = for a Bernoulli distribution find the mean and variance.
2

20) Mention the two features of Poisson distribution.

21) Define Type-I and Type-II errors.

22) In a paired t-test if n = 5 , d = 3.4 and Sd = 2 , then what would be the
value of the test statistic?

23) Mention two types of causes for variation in manufacturing process.

24) Given, R = 5000 units/year C1 = Rs. 2/unit/year and C3 = Rs. 200/cycle
find Q 0 .

SECTION – C

VI. Answer any four of the following questions : (4 × 5 = 20)

25) Calculate consumer price index number by aggregative expenditure
method.

Price (Rs.) Quantity
Commodities
2019 2024 2019
A 4 8 20
B 10 12 40
C 15 20 40
D 25 40 50

-15- 31 (NS)

26) Interpolate and extrapolate the profit for the years 2019 and 2025 by
using binomial expansion method for the following data :

Year : 2015 2017 2019 2021 2023 2025
Profit (Rs.) : 8 14 – 21 30 –

1
27) The probability of an arrow hitting a tree is . If 3 arrows are aimed at the
4
tree, find the probability that

i) no arrow hit the tree
ii) two arrows hit the tree.

28) A basket has 10 mangoes of which 6 are ripe. 3 mangoes are randomly
selected from the basket, find the mean and variance of the number of
ripe mangoes.

29) The standard deviation of production of wheat is assumed to be 10.2.
A sample of 25 acres showed that the standard deviation is 8.2. Test at
1% level of significance whether the standard deviation of production of
wheat is less than 10.2.

30) Find an initial basic feasible solution for the following transportation
problem by North-West Corner rule method and compute the total
transportation cost.

To
Supply
D1 D2 D3 D4
O1 25 17 25 14 300
From O2 15 10 18 24 500
O3 16 20 8 13 600
Demand 75 325 500 500 1400

31 (NS) -16-

31) The purchase price of a machine is Rs. 8,000. Its maintenance cost and
resale values are given below.
Year : 1 2 3 4 5
Maintenance cost (Rs.) : 500 600 800 1,100 1,500
Resale value (Rs.) : 4,500 3,500 2,500 1,500 500

What would be the optimum replacement period of machine?

VII. Answer any two of the following questions : (2 × 5 = 10)

32) The weekly wages of workers are normally distributed with mean
Rs. 3,000 and standard deviation Rs. 500. Calculate the probability of
workers whose weekly wages will be

i) less than Rs. 3,500

ii) between Rs. 2,500 and Rs. 3,500.

33) For the following data test whether means differ significantly.
Use α = 0.01.

Sample Size Mean Variance
I 80 54 16
II 40 52 25

34) In a floor mat manufacturing company the average number of defects per

square meter is known to be λ1 = 4 . Determine the control limits for the
number of defects per square meter.

-17- 31 (NS)

35) Solve the following linear programming problem graphically :

Maximize : Z = 2x + 3y

Subject to constraints : x + y ≥ 350
2 x + y ≤ 600
and x ≥ 0, y ≥ 0.

SECTION – D

VIII. Answer any two of the following questions : (2 × 10 = 20)

36) From the following data compute standardized death rates for Village A
and Village B. Which Village is more healthy?

Age Group Village-A Village-B Standard
(in years) Population
Population Deaths Population Deaths
0-20 4000 68 8000 160 6000
20-40 9000 54 13000 65 12000
40-60 7000 91 10000 100 8000
60 and above 3000 129 4000 160 4000

37) Show that Fisher’s index number satisfies time reversal test and factor
reversal test for the following data.

2019 2024
Items Price (Rs.) Quantity Price (Rs.) Quantity
A 10 15 14 25
B 14 20 20 30
C 17 30 15 45
D 20 25 30 32

31 (NS) -18-

38) a) Calculate the trend values for the following data by 3 yearly moving
averages.

Year : 2000 2001 2002 2003 2004 2005 2006 2007 2008
Sales ('000) : 18 21 20 16 17 16 21 20 19

b) For the following time series data fit a linear trend by the method of
least squares.
Year : 1980 1984 1988 1992 1996 2000
Production ('000) : 16 20 19 14 18 21

SECTION – E

(For Visually Challenged Students only)

35) Write the steps in the graphical method of solving linear programming
problem.

———————

-19- 31 (NS)

31 (NS) -20-

V1 – 2026
Subject Name : STATISTICS Subject Code : 31 (NS)
Registration No. of the candidate : ————————————
Invigilator’s Signature