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

St. Britto Hr. Sec. School - Madurai

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

Time : 1.30 Hours

Part - A

Multiple Choice Question - Answer All Question

Another name of consumer’s price index number is:

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

Least square method of fitting a trend is

Most exact
Least exact
Full of subjectivity
Mathematically unsolved

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

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

The seasonal variation means the variations occurring with in

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

A time series is a set of data recorded

Periodically
Weekly
successive points of time
all the above

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

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

Factors responsible for seasonal variations are

Weather
Festivals
Social customs
All the above

The assignable causes can occur due to

poor raw materials
unskilled labour
faulty machines
all of them

Most commonly used index number is:

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

Consumer price index are obtained by:

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

Part - B

Generic 2 - Answer All Question

Define Index Number

Write note on Fisher’s price index number
What do you mean by process control?

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

Ten samples each of size five are drawn at regular intervals from a manufacturing process. The sample means (\(\overset{-}{X}\)) and their ranges (R) are given below:

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

\(\overset {-}{X}\) 49 45 48 53 39 47 46 39 51 45

R 7 5 7 9 5 8 8 6 7 6

Calculate the control limits in respect of \(\overset {-}{X}\) chart. (Given A₂=0.58, D₃=and D4=2.115)

State the uses of Cost of Living Index Number.

Part - C

Generic 3 - Answer All Question

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

Year 1995 1996 1997 1998 1999 2000 2001 2002

Sales 6.7 5.3 4.3 6.1 5.6 7.9 5.8 6.1

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

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

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

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

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

Year 1990 1991 1992 1993 1994 1995 1996 1997

Sales 15 11 20 10 15 25 35 30

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

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

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

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