Measurements of Components

IMPORTANT

Measurements of Components: Overview

This Topic covers sub-topics such as Secular Trend, Cyclic Variation, Irregular Variation, Method of Least Squares for Measurement of Trend, Graphical Method for Measuring Trend, Seasonal Variation/Indices and, Semi-Average Method for Measuring Trend

Important Questions on Measurements of Components

MEDIUM

IMPORTANT

mathematics>Time Series and Forecasting>Measurements of Components> Q 1

The rainfall data in mm is given against each year or quarter. Obtain seasonal Indices.

Year/Quarter	$2009$	$2010$	$2011$	$2012$
$I$	$38.2$	$38.5$	$55.8$	$50.5$
$II$	$166.8$	$250.9$	$277.7$	$197$
$III$	$612.6$	$773.1$	$717.8$	$706.1$
$IV$	$72.2$	$153.1$	$65.8$	$101.1$

HARD

IMPORTANT

mathematics>Time Series and Forecasting>Measurements of Components> Q 2

Estimate the trend values using semi averages method for the give data which is consumption of cotton against year.

Year	$2003$	$2004$	$2005$	$2006$	$2007$	$2008$	$2009$	$2010$
Consumption of cotton(Thousands of bales)	$677$	$696$	$747$	$755$	$766$	$777$	$785$	$836$

MEDIUM

IMPORTANT

mathematics>Time Series and Forecasting>Measurements of Components> Q 3

The following table shows the area covered for cultivation of Ragi in Tamil Nadu (in ‘ $000$ hectares). Find the trend values using semi averages method.

Year	$2003$	$2004$	$2005$	$2006$	$2007$	$2008$	$2009$	$2010$
Area(in ' $000$ hectares)	$118$	$109$	$100$	$95$	$94$	$90$	$82$	$76$

HARD

IMPORTANT

mathematics>Time Series and Forecasting>Measurements of Components> Q 4

Calculate the number of telephones for the year $2000$ .

Year	$1990$	$1991$	$1992$	$1993$	$1994$	$1995$
No. of telephones (in $100$ 's)	$20$	$21$	$23$	$25$	$27$	$29$

Fit a straight line trend by the method of least squares.

HARD

IMPORTANT

mathematics>Time Series and Forecasting>Measurements of Components> Q 5

The following data states the number of ATM centers during $1995$ to $2001$ . Obtain the trend values using semi averages method

Year	$1995$	$1996$	$1997$	$1998$	$1999$	$2000$	$2001$
Number of ATM centres	$50$	$63$	$75$	$100$	$109$	$120$	$135$

HARD

IMPORTANT

mathematics>Time Series and Forecasting>Measurements of Components> Q 6

The following data describes the export quantity of a company in millions against year.

Fit a straight line trend and estimate the export for the year $2005$ .

Year	$1995$	$1996$	$1997$	$1998$	$1999$	$2000$	$2001$
Export (in millions)	$12$	$13$	$13$	$16$	$16$	$19$	$23$

HARD

IMPORTANT

mathematics>Time Series and Forecasting>Measurements of Components> Q 7

Obtain seasonal correction for the data given in the following table which gives quarterly expenditure over a number of years

Year/Quarter	$2000$	$2001$	$2002$	$2003$
$I$	$78$	$84$	$92$	$100$
$II$	$62$	$64$	$70$	$81$
$III$	$56$	$61$	$63$	$72$
$IV$	$71$	$82$	$83$	$96$

HARD

IMPORTANT

mathematics>Time Series and Forecasting>Measurements of Components> Q 8

Given that. the data of production of thousand tonnes against year. Find the value of production for the year $1995$ by using the method of least squares

Year	$1990$	$1991$	$1992$	$1993$	$1994$
Production $(1000' s tonnes)$	$70$	$72$	$88$	$90$	$92$

HARD

IMPORTANT

mathematics>Time Series and Forecasting>Measurements of Components> Q 9

Yield of ground nut in Kharif season in India for the years $2003 - 04$ to $2009 - 10$ are given below. Perform $3$ -year moving averages.

Year	$2003 - 04$	$2004 - 05$	$2005 - 06$	$2006 - 07$	$2007 - 08$	$2008 - 09$	$2009 - 10$
Yield(kg/hectare)	$1320$	$909$	$1097$	$689$	$1386$	$1063$	$835$

HARD

IMPORTANT

mathematics>Time Series and Forecasting>Measurements of Components> Q 10

The data of production of steel in million tons against year is given then, Draw a trend line by using the method of semi averages.

Year	$1992$	$1993$	$1994$	$1995$	$1996$	$1997$
Production of steel in million tons	$21$	$23$	$25$	$23$	$26$	$25$

MEDIUM

IMPORTANT

mathematics>Time Series and Forecasting>Measurements of Components> Q 11

Calculate the seasonal indices for the rain fall (in $mm$ ) data in Tamil Nadu given below by simple average method.

Year	Season $I$	Season $I I$	Season $I I I$	Season $I V$
$2001$	$118.4$	$260.0$	$379.4$	$70$
$2002$	$85.8$	$185.4$	$407.1$	$8.7$
$2003$	$129.8$	$336.5$	$403.1$	$12.0$
$2004$	$283.4$	$360.7$	$472.1$	$14.3$
$2005$	$231.7$	$308.5$	$828.8$	$15.9$