12th Standard Business Maths English Medium - Applied Statistics 3 Mark Creative Question Paper and Answer Key 2022 - 2023 | QB365

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12th Standard Business Maths English Medium - Applied Statistics 3 Mark Creative Question Paper and Answer Key 2022 - 2023

Published on: 03/09/2022

QB365 provides a detailed and simple solution for every Possible Creative Questions in Class 12 Business Maths Subject - Applied Statistics, English Medium. It will help Students to get more practice questions, Students can Practice these question papers in addition to score best marks.

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Questions:

Generic 3

15 x 3 = 45

Calculate the cost of living index using family budget method for the following data talking the base year as 1995.

Commodity	Weight	Price(per unit)
Commodity	Weight	1995	1996
A	40	16	20
B	25	40	60
C	5	0.5	0.5
D	20	5.12	6.25
E	10	2	1.50

Construct the cost of living index for 2000 taking 1999 as the base year from the following data using Aggregate Expenditure method.

Commodity	Quantity (kg)	Price
Commodity	2000	2000	2003
A	6	5.75	6
B	1	5	8
C	6	6	9
D	4	8	10
E	2	2	1.80
F	1	20	15

Construct the cost of living index number for 2003 on the basis of 2000 from the following data using family budget method

Items	Price		Weight
Items	2000	2003	2000
Food	200	280	30
Rent	100	200	20
Clothing	150	120	20
Fuel and Lighting	50	100	10
Miscellaneous	100	200	20

Calculate the cost of living index by aggregate expenditure method

Year	Quantity	Price
Year	2000	2000	2003
A	100	8	12
B	25	6	7.50
C	10	5	5.25
D	20	48	52
E	65	15	16.50
F	30	19	27

Calculate the seasonal indices for the following data using average method

Year	Quarter
Year	I	II	III	IV
1982	72	68	80	70
1983	76	70	82	74
1984	74	66	84	80
1985	76	74	84	78
1986	78	74	86	82

Calculate the trend values by tour year moving average method

Year	1978	1979	1980	1981	1982	1983	1984	1985	1986	1987	1988
Production (in tonnes)	614	615	652	678	681	655	717	719	708	779	757

Using four yearly moving average calculate the trend values

Year	1981	1982	1983	1984	1985	1986	1987	1988	1989	1990
Production (in tonnes)	464	515	518	467	502	540	557	571	586	612

Using three year moving average determine the trend values for the following data.

Year	1983	1984	1985	1986	1987	1988	1989	1990	1991	1992
Production (in tonnes)	21	22	23	25	24	22	25	26	27	26

From the data given below calculate seasonal indices

Year
Quarter	1984	1985	1986	1987	1988
I	40	42	41	45	44
II	35	37	35	36	38
III	38	39	38	36	38
IV	40	39	40	41	42

10.

From the data given below, construct a cost of living index number by family budget method for 1986 with 1976 as the base year.

Commodity	P	Q	R	S	T	U
Quantity in 1976	50	25	10	20	30	40
Price in 1976 (Rs)	10	5	8	7	9	6
Price in 1986 (Rs)	6	4	3	8	10	12

11.

Compute Fisher's price index number for the following data.

Commodity	Base Year		Current Year
Commodity	Price	Quantity	Price	Quantity
A	10	12	12	15
B	7	15	5	20
C	5	24	9	20
D	16	5	14	5

12.

Calculate the seasonal indices for the following data by the method of simple average.

Year	Quarters
Year	I	II	III	IV
1994	78	66	84	80
1995	76	74	82	78
1996	72	68	80	70
1997	74	70	84	74
1998	76	74	86	82

13.

Find a trend line to the following data by the method of sami-averages.

Years	1980	1981	1982	1983	1984	1985	1986
Sales	102	105	114	110	108	116	112

14.

Fit a trend line to the following data by graphic method.

Year	1978	1979	1980	1981	1982	1983	1984	1985	1986
Production of steel	20	22	24	21	23	25	23	26	25

15.

Fit a straight line trend for the following data using the method of least squares.

x	0	1	2	3	4
y	1	1	3	4	6

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Answers Key:

Generic 3

15 x 3 = 45

Commodity	Price(per unit)		Quantity V	\(\mathrm{p}=\frac{p_{1}}{p_{i_{1}}} \times 100\)	PV
Commodity	1995	1996	Quantity V	\(\mathrm{p}=\frac{p_{1}}{p_{i_{1}}} \times 100\)	PV
A	16	20	40	125	5000
B	40	60	25	150	3750
C	0.5	0.5	5	100	500
D	5.12	6.25	20	122.07	2441
E	2	1.50	10	75	750
Total			100		12441

Cost of living index \(=\frac{\sum P V}{\sum V}=\frac{12441}{100}=124.41\)

Commodity	Quantity 1999 q_o	Price		p₁q_o	p_oq_o
Commodity	Quantity 1999 q_o	1999 p_o	1999 p₁	p₁q_o	p_oq_o
A	6	5.75	6	36	34.5
B	1	5	8	8	5
C	6	6	9	54	36
D	4	8	10	40	32
E	2	2	1.80	3.6	4
F	1	20	15	15	20

Cost of living index
\(=\frac{\sum p_{1} q_{0}}{\sum p_{0} q_{0}} \times 100=\frac{156.6}{131.5} \times 100=119.09\)

Items	Price		Weight V	\(\mathrm{P}=\frac{P_{1}}{P_{0}} \times 100\)	PV
Items	P_o	P₁	2000	140	PV
Food	200	280	30	200	4200
Rent	100	200	20	80	4000
Clothing	150	120	20	200	1600
Fuel and Lighting	50	100	10	200	2000
Miscellaneous	100	200	20		4000
		Total	100		15800

Cost of iving index \(=\frac{\sum P V}{\sum V}=\frac{15800}{100}=158\)
Hence there is a 58% increases in cost of living index in 2003 compared to 2000

Year	Quantity	Price		p₁q_o	p_oq_o
Year	2000 q_o	2000 p_o	2003 p₁	p₁q_o	p_oq_o
A	100	8	12	1200	800
B	25	6	7.50	187.50	150
C	10	5	5.25	52.50	50
D	20	48	52	1040	960
E	65	15	16.50	1072.50	975
F	30	19	27	810	570
Total				4362.50	3505

Cost of living index
\( =\frac{\sum p_{1} q_{0}}{\sum p_{0} q_{0}} \times 100 \)
\( =\frac{4362.50}{3505} \times 100 \)
= 124.46

Year	Quarter
Year	I	II	III	IV
1982	72	68	80	70
1983	76	70	82	74
1984	74	66	84	80
1985	76	74	84	78
1986	78	74	86	82
Total	376	352	416	384
Average	75.2	70.4	83.2	76.8

Grand average = 76.4
Seasonal Index (S.I) \( =\frac{\text { Quarterly Average }}{\text { Grand Average }} \times 100 \)
S.I for I Quarter \( =\frac{75.2}{76.4} \times 100=98.4 \)
S.I for II Quarter \( =\frac{70.4}{76.4} \times 100=92.14 \)
S.I for III Quarter \( =\frac{83.2}{76.4} \times 100=108.9 \)
S.I for IV Quarter \( =\frac{76.8}{76.4} \times 100=100.52 \)

Year	Production	4 year centered movingTotal	4 yearly moving average	4 yearly centered moving average
1978	614		-	-
1979	615		-	-
		2559	639.75
1980	652			648.145
		2626	656.50
1981	678			661.50
		2666	666.50
1982	681			674.75
		2731	682.75
1983	655			687.875
		2772	693
1984	717			696.375
		2799	699.75
1985	719			715.25
		2923	730.75
1986	708		-	735.75
		2963	740.75
1987	779		-	-
1988	757		-	-

Year	Production	4 year movingTotal	4 year moving total centred	4 year moving total(Trend values)
1981	464		-
1982	515		-
		1964
1983	518		3966	495.75
		2002
1984	467		4029	503.63
		2027
1985	502		4093	511.63
		2066
1986	540		4236	529.50
		2170
1987	557		4424	553.00
		2254
1988	571		4580	572.50
		2326
1989	586		-	-
1990	612		-	-

Year	Production	Three year movingTotal	Three year moving Average
1983	21	-	-
1984	22	66	22
1985	23	70	23.33
1986	25	72	24
1987	24	71	23.67
1988	22	71	23.67
1989	25	73	24.33
1990	26	78	26
1991	27	79	26.33
1992	26	-	-

Year	Quarter
Year	I	II	III	IV
1984	40	35	38	40
1985	42	37	39	39
1986	41	35	38	40
1987	45	36	36	41
1988	44	38	38	42
Total	212	181	189	201
Average	42.4	36.2	37.8	41.2

Grand average = 39.15
Seasonal Index (S.I) \( =\frac{\text { Quarterly Average }}{\text { Grand Average }} \times 100 \)
S.I for I Quarter \( =\frac{42.4}{39.15} \times 100=108.3 \)
S.I for II Quarter \( =\frac{36.2}{39.15} \times 100=92.54 \)
S.I for III Quarter \( =\frac{37.8}{39.15} \times 100=96.55 \)
S.I for IV Quarter \( =\frac{41.2}{39.15} \times 100=102.68 \)

10.

Commodity	Price		Quantity V	P = \(\frac {p_{1}}{p_{0}} \times 100\)	PV
Commodity	P₀	P₁	Quantity V	P = \(\frac {p_{1}}{p_{0}} \times 100\)	PV
P	10	6	50	60	3000
Q	5	4	25	80	2000
R	8	3	10	37.5	375
S	7	8	20	114.29	2285.8
T	9	10	30	111.11	3333.3
U	6	12	40	200	8000
			175		18994.1

Cost ofliving index = \(\frac{\sum PV}{\sum V}\) = \(\frac {18994.1}{175}\) = 108.54

11.

Commodity	Base Year		Current Year
Commodity	p₀	q₀	p₁	q₁
A	10	12	12	15
B	7	15	5	20
C	5	24	9	20
D	16	5	14	5

p₁q₀	p₀q₀	p₁q₁	p₀q₁
144	120	180	150
75	105	100	140
216	120	180	100
70	80	70	80
505	425	530	470

Fisher's ideal index = \(\sqrt \frac {\sum p_{1}q_{0}\times \sum p_{1}q_{1}}{\sum p_{0}q_{0}\times \sum p_{0}q_{1}} \times 100\)
= \(\sqrt{\frac{505}{425} \times \frac {430}{470}} \times 100\)
\(P^{F}_{01}\) = 115.75

12.

Year	Quarters
Year	I	II	III	IV
1994	78	66	84	80
1995	76	74	82	78
1996	72	68	80	70
1997	74	70	84	74
1998	76	74	86	82
Total	376	352	416	384
Average	75.2	70.4	83.2	76.8

Grand average = \(\frac {75.2+70.4+83.2+76.8}{4}\)
= \(\frac {305.6}{4}\) = 76.4
Seasonal index S.I = \(\frac {Quarterly average}{Grand average} \times 100\)
Hence, S.I for I quarter = \(\frac {75.2}{76.4} \times 100\) = 98.4
S.I for II quarter =  \(\frac {70.4}{76.4} \times 100\) = 92.14
S.I for III quarter =  \(\frac {83.2}{76.4} \times 100\) = 108.9
S.I for IV quarter =  \(\frac {76.8}{76.4} \times 100\) = 100.5

13.

No of years = 7 (odd), by omitting the middle year we have

14.

15.

x	y	x²	xy
0	1	0	0
1	1	1	1
2	3	4	6
3	4	9	12
4	6	16	24
10	15	30	43

Let y= ax + b be the best line of fit.
The normal equations are
a\(\sum\)x + nb = \(\sum\)y
a\(\sum\)x² + b\(\sum\)x = \(\sum\)xy
10a+ 5b = 15
⇒ 2a+b = 3 ...(1)
30a + 10b = 43
⇒ 3a+b = 4.3 ....(2)
(1)-(2) ⇒ - a = -1.3
⇒ a = 1.3
Substituting a = 1.3 in (1) we get,
2(1.3) + b = 3
⇒ 2.6 + b = 3
⇒ b = 3 - 2.6 = 0.4
∴ The line of best fit isy = 1.3x + 0.4