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12th Business Maths Weekly Test - 3 ( Applied Statistics )

St. Britto Hr. Sec. School - Madurai

12th Business Maths Weekly Test - 3 ( Applied Statistics )-Aug 2020

Time : 1.30 Hours

Part - A

Multiple Choice Question - Answer All Question

Factors responsible for seasonal variations are

Weather
Festivals
Social customs
All the above

The additive model of the time series with the components T, S, C and I is

y=T+S+C×I
y=T+S×C×I
y=T+S+C+I
y=T+S×C+I

\(\overset {-}{X}\)chart is a

attribute control chart
variable control chart
neither Attribute nor variable control chart
both Attribute and variable control chart

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

Secular trend
Seasonal variations
Cyclic variation
Irregular variation

A time series consists of

Five components
Four components
Three components
Two components

Least square method of fitting a trend is

Most exact
Least exact
Full of subjectivity
Mathematically unsolved

Laspeyre’s index = 110, Paasche’s index = 108, then Fisher’s Ideal index is equal to:

110
108
100
109

Cost of living at two different cities can be compared with the help of

Consumer price index
Value index
Volume index
Un-weighted index

A typical control charts consists of

CL, UCL
CL, LCL
CL, LCL, UCL
UCL, LCL

R is calculated using

x_max-x_min
x_min-x_max
\(\overset{-}{x}\)_max-\(\overset{-}{x}\)_min
\(\overset{=}{x}\)_max-\(\overset{=}{x}\)_min

Part - B

Generic 2 - Answer All Question

The following table shows the number of salesmen working for a certain concern:

Year 1992 1993 1994 1995 1996

No. of salesmen 46 48 42 56 52

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

State the two normal equations used in fitting a straight line.

Discuss about Cost of Living Index Number.

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

Commodity 2002 2012

Price Quantity Price Quantity

A 10 20 16 10

B 12 34 18 42

C 15 30 20 26

The following figures relates to the profits of a commercial concern for 8 years

Year 1986 1987 1988 1989 1990 1991 1992 1993

Profit (Rs.) 15,420 15,470 15,520 21,020 26,500 31,950 35,600 34,900

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

Part - C

Generic 3 - Answer All Question

Calculate four-yearly moving averages of number of students studying in a higher secondary school in a particular city from the following data.

Year 2001 2002 2003 2004 2005 2006 2007 2008

Sales 124 120 135 140 145 158 162 170

Calculate the seasonal index for the monthly sales of a product using the method of simple averages.

Months Jan Feb Mar Apr May June July Aug Sep Oct Nov Dec

Year

2001 15 41 25 31 29 47 41 19 35 38 40 30

2002 20 21 27 19 17 25 29 31 35 39 30 44

2003 18 16 20 28 24 25 30 34 30 38 37 39

Fit a trend line by the method of semi-averages for the given data.

Year 2000 2001 2002 2003 2004 2005 2006

Production 105 115 120 100 110 125 135

Given below are the data relating to the production of sugarcane in a district.
Fit a straight line trend by the method of least squares and tabulate the trend values.

Year 2000 2001 2002 2003 2004 2005 2006

Prod. of Sugarcane 40 45 46 42 47 50 46

Calculate the seasonal index for the quarterly production of a product using the method of simple averages.

Year I Quarter II Quarter III Quarter IV Quarter

2005 255 351 425 400

2006 269 310 396 410

2007 291 332 358 395

2008 198 289 310 357

2009 200 290 331 359

2010 250 300 350 400

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