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12th Business Maths Monthly Test - 1 ( Applied Statistics )

St. Britto Hr. Sec. School - Madurai

12th Business Maths Monthly Test - 1 ( Applied Statistics )-Aug 2020

Time : 2.30 Hours

Part - A

Multiple Choice Question - Answer All Question

The component of a time series attached to long term variation is trended as

Cyclic variation
Secular variations
Irregular variation
Seasonal variations

The LCL for R chart is given by

\({ D }_{ 2 }\bar { R } \)
\({ D }_{ 2 }\overset { = }{ R } \)
\({ D }_{ 3 }\overset { = }{ R } \)
\({ D }_{ 3 }\bar { R } \)

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

Most commonly used index number is:

Volume index number
Value index number
Price index number
Simple index number

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

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

The seasonal variation means the variations occurring with in

A number of years
within a year
within a month
within a week

Another name of consumer’s price index number is:

Whole-sale price index number
Cost of living index
Sensitive
Composite

The upper control limit for \(\overset {-}{X}\) chart is given by

\(\bar { X } +{ A }_{ 2 }\bar { R } \)
\(\overset { = }{ X } +{ A }_{ 2 }R\)
\(\overset { = }{ X } +{ A }_{ 2 }\bar { R } \)
\(\overset { = }{ X } +{ A }_{ 2 }\overset { = }{ R } \)

The quantities that can be numerically measured can be plotted on a

p - chart
c – chart
x bar chart
np – chart

While computing a weighted index, the current period quantities are used in the:

Laspeyre’s method
Paasche’s method
Marshall Edgeworth method
Fisher’s ideal method

Consumer price index are obtained by:

Paasche’s formula
Fisher’s ideal formula
Marshall Edgeworth formula
Family budget method formula

The assignable causes can occur due to

poor raw materials
unskilled labour
faulty machines
all of them

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

110
108
100
109

A typical control charts consists of

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

Which of the following Index number satisfy the time reversal test?

Laspeyre’s Index number
Paasche’s Index number
Fisher Index number
All of them

Part - B

Generic 2 - Answer All Question

The following data show the values of sample means and the ranges for ten samples of size 4 each. Construct the control chart for mean and range chart and determine whether the process is in control

Sample number 1 2 3 4 5 6 7 8 9 10

\(\overset{-}{X}\) 29 26 37 34 14 45 39 20 34 23

R 39 10 39 17 12 20 05 21 23 15

Calculate the Laspeyre’s, Paasche’s and Fisher’s price index number for the following data. Interpret on the data.

Commodities Base Year Current Year

Price Quantity Price Quantity

A 170 562 72 632

B 192 535 70 756

C 195 639 95 926

D 187 128 92 255

E 185 542 92 632

F 150 217 180 314

7 12.6 12.7 12.5 12.8

8 12.4 12.3 12.6 12.5

9 12.6 12.5 12.3 12.6

10 12.1 12.7 12.5 12.8

Determine the equation of a straight line which best fits the following data

Year 2000 2001 2002 2003 2004

Sales(Rs.'000) 35 36 79 80 40

Compute the trend values for all years from 2000 to 2004

Define secular trend.
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.

Calculate Fisher’s index number to the following data. Also show that it satisfies Time Reversal Test.

Commodity Price in Rupees per unit Number of units

Price (Rs.) Quantity (Kg) Price (Rs.) Quantity (Kg)

Food 40 12 65 14

Fuel 72 14 78 20

Clothing 36 10 36 15

Wheat 20 6 42 4

Others 46 8 52 6

Calculate price index number for 2005 by (a) Laspeyre’s (b) Paasche’s method

Commodity 1995 2005

Price Quantity Price Quantity

A 5 60 15 70

B 4 20 8 35

C 3 15 6 20

Explain Paasche’s price index number.

What is the need for studying time series?

Write the control limits for the mean chart.

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

Explain the method of fitting a straight line.

From the following data, calculate the control limits for the mean and range chart.

Sample No. 1 2 3 4 5 6 7 8 9 10

Sample Observations 50 51 50 48 46 55 45 50 47 56

55 50 53 53 50 51 48 56 53 53

52 53 48 50 44 56 53 54 49 55

49 50 52 51 48 47 48 53 52 54

54 46 47 53 47 51 51 57 54 52

Define Time Reversal Test.

Construc \(\overset {-}{X}\) and R charts for the following data:

Sample Number Observations

1 32 36 42

2 28 32 40

3 39 52 28

4 50 42 31

5 42 45 34

6 50 29 21

7 44 52 35

8 22 35 44

( Given for n=3, A₂=0.58,D₃=0 and D₄=2.115)

State the uses of time series.

Part - C

Generic 3 - Answer All Question

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

The following data gives the readings for 8 samples of size 6 each in the production of a certain product. Find the control limits using mean chart.

Sample 1 2 3 4 5 6

Mean 300 342 351 319 326 333

Range 25 37 20 28 30 22

Given for n = 6, A₂ = 0.483,

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

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

The data shows the sample mean and range for 10 samples for size 5 each. Find the control limits for mean chart and range chart.

Sample 1 2 3 4 5 6 7 8 9 10

Mean 21 26 23 18 19 14 14 20 16 10

Range 5 6 9 7 4 6 8 9 4 7

A machine drills hole in a pipe with a mean diameter of 0.532 cm and a standard deviation of 0.002 cm. Calculate the control limits for mean of samples 5.

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

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

Year 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004

Number of students 332 317 357 392 402 405 410 427 435 438

You are given below the values of sample mean ( X ) and the range ( R ) for ten samples of size 5 each. Draw mean chart and comment on the state of control of the process.

Sample number 1 2 3 4 5 6 7 8 9 10

\(\overset{-}{X}\) 43 49 37 44 45 37 51 46 43 47

R 5 6 5 7 7 4 8 6 4 6

Given the following control chart constraint for :n=5, A₂=0.58, D₃=0 and D₄=2.115

Fit a trend line by the method of freehand method for the given data

Year 2000 2001 2002 2003 2004 2005 2006 2007

Sales 30 46 25 59 40 60 38 65

The following data gives readings of 10 samples of size 6 each in the production of a certain product. Draw control chart for mean and range with its control limits.

Sample 1 2 3 4 5 6 7 8 9 10

Mean 383 508 505 582 557 337 514 614 707 753

Range 95 128 100 91 68 65 148 28 37 80

Part - D

Generic 5 - Answer All Question

Construct the cost of living index number for 2011 on the basis of 2007 from the given data using family budget method.

Commodities Price Weights

2007 2011

A 350 400 40

B 175 250 35

C 100 115 15

D 75 105 20

E 60 80 25

Calculate Fisher’s price index number and show that it satisfies both Time Reversal Test and Factor Reversal Test for data given below.

Commodities Price Quandity

2003 2009 2003 2009

Rice 10 13 4 6

Wheat 125 18 7 8

Rent 25 29 5 9

Fuel 2511 14 8 10

Miscellaneous 14 17 6 7

the Laspeyre’s, Paasche’s and Fisher’s price index number for the following data. Interpret on the data.

Commodities Price Quandity

2000 2010 2000 2010

Rice 38 35 6 7

Wheat 12 18 7 10

Rent 10 15 10 15

Fuel 25 30 12 16

Miscellaneous 30 33 8 10

Calculate Fisher’s price index number and show that it satisfies both Time Reversal Test and Factor Reversal Test for data given below.

Commodities Base Year Current Year

Price Quantity Price Quantity

Rice 150 5 11 6

Wheat 12 6 13 4

Rent 14 8 15 7

Fuel 16 9 17 8

Transport 18 7 19 5

Miscellaneous 20 4 21 3

Construct Fisher’s price index number and prove that it satisfies both Time Reversal Test and Factor Reversal Test for data following data.

Commodities Base Year Current Year

Price Quantity Price Quantity

Rice 40 5 48 4

Wheat 45 2 42 3

Rent 90 4 95 6

Fuel 85 3 80 2

Transport 50 5 65 8

Miscellaneous 65 1 72 3

Calculate the cost of living index number by consumer price index number for the year 2016 with respect to base year 2011 of the following data.

Commodities Price Quantity

Base year Current year

Rice 32 48 25

Sugar 25 42 10

Oil 54 85 6

Coffe 250 460 1

Tea 175 275 2

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