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12th Standard English Medium Business Maths Subject Applied Statistics Book Back 3 Mark Questions with Solution Part - I

Published on: 04/06/2021

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Std: 12th Standard - Business Maths and Statistics

chapter: - Book back Questions

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Questions:

Generic 3

5 x 3 = 15

An Enquiry was made into the budgets of the middle class families in a city gave the following information.

Expenditure	Food	Rent	Clothing	Fuel	Rice
Price(2010)	150	50	100	20	60
Price(2011)	174	60	125	25	90
Weights	35	15	20	10	20

What changes in the cost of living have taken place in the middle class families of a city?

From the following data, calculate the trend values using fourly moving averages.

Year	1990	1991	1992	199	1994	1995	1996	1997	1998
Sales	506	620	1036	673	588	696	1116	738	663

Calculate by a suitable method, the index number of price from the following data:

Commodity	2002		2012
Commodity	Price	Quantity	Price	Quantity
A	10	20	16	10
B	12	34	18	42
C	15	30	20	26

State the different methods of measuring trend.

Write a brief note on seasonal variations

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Answers Key:

Generic 3

5 x 3 = 15

Expenditure	Weights (V)	Rent 2010 (p0)	Price 2011 (p1)	P = \(\frac {p_{1}}{p_{0}} \times 100\)	PV
Food	35	150	174	116	4060
Rent	15	50	60	120	1800
Clothing	20	100	125	125	2500
Fuel	10	20	25	125	1250
Rice	20	60	90	150	3000
	100				12610

Cost of living index number = \(\frac {\sum PV}{\sum V}\) = \(\frac {12610}{100}\) = 126.10
∴ The cost ofliving has increased upto 26.10% in 2011 as compared to 2010.

The treand values is using fourly moving average given below

Year	Sales	4 Yearly moving total	4 Yearly moving average
1990	506	-	-

1991	620
		2835	708.75
1992	1036
		2917	729.25
1993	673
		2993	748.25
1994	588
		3073	768.25
1995	696
		3138	784.5
1996	1116
		3213	803.25
1997	738

1998	663

Commodity	2002		2012
Commodity	Price(p₀)	q(₀)	p₁	q₁
A	10	20	16	10
B	12	34	18	42
C	15	30	20	26

p₀q₀	p₀q₁	p₁q₀	p₁q₁
200	100	320	160
408	504	612	756
450	390	600	520
1058	994	1532	1436

Laspeyre's price index number
\(P^{L}_{01}\) = \({\frac {\sum p_{1}q_{0}}{\sum p_{0}q_{0}}} \times 100\)
= \(\frac {1532}{1058} \times 100\) = 144.8
Paasche's pirce index number
\(P^{L}_{01}\) = \({\frac {\sum p_{1}q_{1}}{\sum p_{0}q_{1}}} \times 100\)
= \(\frac {1436}{994} \times 100\) = 144.4

The different methods of measurements of trends are
(i) Free hand or graphic method
(ii) Method of semi averages
(iii) Method of moving averages
(iv) Method of least squares

Tendency movements are due to nature, which repeat themselves periodically in every seasons. These variations repeat themselves in less than one year time. It is measured in an interval of time.
Seasonal variations may be influenced by natural force, social customs and traditions.