STA304 ASSIGNMENT NO. 1 FALL 2022 || 100% RIGHT SOLUTION || APPLIED STATISTICS || BY VuTech

STA304 ASSIGNMENT NO. 1 FALL 2022

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STA304 ASSIGNMENT NO. 1 FALL 2022 || 100% RIGHT SOLUTION || APPLIED STATISTICS || BY VuTech

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STA304

APPLIED STATISTICS

ASSIGNMENT NO. 1

FALL 2022

LAST DATE: 22-11-2022

Question 1:

Given the prices of three commodities, Using 1990 as the base period, compute, simple average of relatives price indices using

i.        A.M

ii.       Median

Year	Prices
	A	B	C
1990	30.00	12.00	20.00
1991	35.50	13.50	23.50
1992	32.50	14.50	25.00
1993	32.50	14.00	25.00

 

Solutions:

Price Relatives

Year	Price Relatives
	A	B	C
1990	(30.00/30.00)*100= 100	(12.00/12.00)*100	(20.00/20.00)*100=100
1991	(35.50/30.00)*100=101.6	(13.50/12.00)*100 = 112.5	(23.50/20.00)*100=117.5
1992	(32.50/30.00)*100=108.3	(14.50/12.00)*100 = 120.8	(25.00/20.00)*100=125
1993	(32.50/30.00)*100=108.3	(14.00/12.00)*100=116.6	(25.00/20.00)*100=125

 

Now A.M and Median

 

                   A.M = `\frac{Sum of all observations}{Total number of Observations}`

 

Year	Price Relatives			Total	A.M	Median
	A	B	C
1990	100	100	100	300	300/3=100	100
1991	101.6	112.5	117.5	331.6	331/3=110.53	112.5
1992	108.3	120.8	125	354.1	354.1/3=118.03	120.8
1993	108.3	116.6	125	349.9	349.9/3=116.63	116.6

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Question 2

The following table gives the production of cotton cloth (in million yards) for Pakistan from 1954 to 1963.

 

Year	1954	1955	1956	1957	1958	1959	1960	1961	1962	1963
Production	282	389	438	470	511	555	564	630	662	681

 

Find out the index numbers by taking:

i.        1954 as base year

ii.       Average of 1958,59,60 as base period.

Solution

i.        1954 as base year

 

Year Production		Price Relatives
		1954 as base year
1954	282	(282/282)*100=100
1955	389	(389/282)*100=137.94
1956	438	(438/282)*100=155.32
1957	470	(470/282)*100=166.67
1958	511	(511/282)*100=181.21
1959	555	(555/282)*100=196.81
1960	564	(564/282)*100=200
1961	630	(630/282)*100=223.40
1962	662	(662/282)*100=234.75
1963	681	(681/282)*100=241.49

 

ii.       Average of 1958,59,60 as the base period.

Average of 1958,59,60 =  `\frac{511 + 555 + 564}{3}` = `\frac{1630}{3}` = 543.33

Year Production		Price Relatives
		1954 as base year
1954	282	(282/543.33)*100=51.90
1955	389	(389/543.33)*100=71.59
1956	438	(438/543.33)*100=80.61
1957	470	(470/543.33)*100=86.50
1958	511	(511/543.33)*100=94.04
1959	555	(555/543.33)*100=102.15
1960	564	(564/543.33)*100=103.80
1961	630	(630/543.33)*100=115.95
1962	662	(662/543.33)*100=121.84
1963	681	(681/543.33)*100=125.34

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