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Tamil Nadu Board of Secondary EducationHSC Commerce इयत्ता १२

HSC Commerce इयत्ता १२ - Tamil Nadu Board of Secondary Education Question Bank Solutions for Business Mathematics and Statistics

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Business Mathematics and Statistics
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Explain cyclic variations

[9] Applied Statistics
Chapter: [9] Applied Statistics
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Discuss about irregular variation

[9] Applied Statistics
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Define seasonal index

[9] Applied Statistics
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Explain the method of fitting a straight line

[9] Applied Statistics
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State the two normal equations used in fitting a straight line

[9] Applied Statistics
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State the different methods of measuring trend

[9] Applied Statistics
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Compute the average seasonal movement for the following series

Year Quarterly Production
I II III IV
2002 3.5 3.8 3.7 3.5
2203 3.6 4.2 3. 4.1
2004 3.4 3.9 37 4.2
2005 4.2 4.5 3 4.4
2006 3.9 4.4 4.2 4.6
[9] Applied Statistics
Chapter: [9] Applied Statistics
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The following figures relates to the profits of a commercial concern for 8 years

Year Profit (₹)
1986 15,420
1987 15,470
1988 15,520
1989 21,020
1990 26,500
1991 31,950
1992 35,600
1993 34,900

Find the trend of profits by the method of three yearly moving averages

[9] Applied Statistics
Chapter: [9] Applied Statistics
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Find the trend of production by the method of a five-yearly period of moving average for the following data:

Year Production ('000)
1979 126
1980 123
1981 117
1982 128
1983 125
1984 124
1985 130
1986 114
1987 122
1988 129
1989 118
1990 123
[9] Applied Statistics
Chapter: [9] Applied Statistics
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The following table gives the number of small-scale units registered with the Directorate of Industries between 1985 and 1991. Show the growth on a trend line by the free hand method.

Year No. of units (in '000)
195 10
986 22
1987 36
198 62
1989 55
1990 0
1991 34
1992 50
[9] Applied Statistics
Chapter: [9] Applied Statistics
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The annual production of a commodity is given as follows:

Year production (in tones)
1995 155
1996 162
1997 171
19988 182
1999 158
2000 880
2001 178

Fit a straight line trend by the method of least squares

[9] Applied Statistics
Chapter: [9] Applied Statistics
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Determine the equation of a straight line which best fits the following data 

Year 2000 2001 2002 2003 2004
Sales (₹ '000) 35 36 79 80 40

Compute the trend values for all years from 2000 to 2004

[9] Applied Statistics
Chapter: [9] Applied Statistics
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The sales of a commodity in tones varied from January 2010 to December 2010 as follows:

In Year 2010 Sales (in tones)
Jan 280
Feb 240
Mar 270
Apr 300
May 280
Jun 290
Jul 210
Aug 200
Sep 230
Oct 200
Nov 230
Dec 210

Fit a trend line by the method of semi-average

[9] Applied Statistics
Chapter: [9] Applied Statistics
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Use the method of monthly averages to find the monthly indices for the following data of production of a commodity for the years 2002, 2003 and 2004

2002 2003 2004
15 20 18
18 18 25
17 16 21
19 13 11
16 12 14
20 15 16
21 22 19
18 16 20
17 18 1
15 20 16
14 17 18
18 15 20
[9] Applied Statistics
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Calculate the seasonal indices from the following data using the average method:

Year I Quarter II Quarter III Quarter IV Quarter
2008 72 68 62 76
2009 78 74 78 72
2010 74 70 72 76
2011 76 74 74 72
2012 72 72 76 68
[9] Applied Statistics
Chapter: [9] Applied Statistics
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The following table shows the number of salesmen working for a certain concern:

Year 1992 1993 1994 1995 1996
No. of
salesman
46 48 42 56 52

Use the method of least squares to fit a straight line and estimate the number of salesmen in 1997

[9] Applied Statistics
Chapter: [9] Applied Statistics
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Choose the correct alternative:

A time series is a set of data recorded

[9] Applied Statistics
Chapter: [9] Applied Statistics
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Choose the correct alternative:

A time series consists of

[9] Applied Statistics
Chapter: [9] Applied Statistics
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Choose the correct alternative:

The components of a time series which is attached to short term fluctuation is

[9] Applied Statistics
Chapter: [9] Applied Statistics
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Choose the correct alternative:

Factors responsible for seasonal variations are

[9] Applied Statistics
Chapter: [9] Applied Statistics
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