Name: Uses of Index Numbers
Uploaded: 2019-07-19
Duration: 7 min 36 s
Description: Index numbers are used to measure changes in the value of money. A study of the rise or fall in the value of money is essential for determining the direction...

Question

Coded monthly sales figures of a particular brand of T.V. for $18$ months commencing January $1, 2005$ are as follows:

Year	Jan.	Feb.	March	April	May	June
$2005$	$18$	$16$	$23$	$27$	$28$	$19$
	July	Aug.	Sep.	Oct.	Nov.	Dec.
	$31$	$29$	$35$	$27$	$28$	$24$
$2006$	Jan.	Feb.	March	April	May	June
$2006$	$24$	$28$	$29$	$30$	$29$	$22$

Calculate six monthly moving averages and display these and the original figures on the same graph, using the same axes for both.

Accepted Answer

The given time period is even which indicates that we have to determine centred moving averages.

The first six monthly moving average is $\frac{18 + 16 + 23 + 27 + 28 + 19}{6} = \frac{131}{6} = 21.83$ .

The second six monthly moving average is $\frac{16 + 23 + 27 + 28 + 19 + 31}{6} = \frac{144}{6} = 24$ .

Similarly, the third, fourth, fifth, sixth, seventh, eighth, ninth, tenth, eleventh, twelfth and thirteenth six monthly moving averages are $\frac{23 + 27 + 28 + 19 + 31 + 29}{6} = \frac{157}{6} = 26.17, \frac{27 + 28 + 19 + 31 + 29 + 35}{6} = \frac{169}{6} = 28.17, \frac{28 + 19 + 31 + 29 + 35 + 27}{6} = \frac{169}{6} = 28.17, \frac{19 + 31 + 29 + 35 + 27 + 28}{6} = \frac{169}{6} = 28.17, \frac{31 + 29 + 35 + 27 + 28 + 24}{6} = \frac{174}{6} = 29,$

$\frac{29 + 35 + 27 + 28 + 24 + 24}{6} = \frac{167}{6} = 27.83, \frac{35 + 27 + 28 + 24 + 24 + 28}{6} = \frac{166}{6} = 27.67, \frac{27 + 28 + 24 + 24 + 28 + 29}{6} = \frac{160}{6} = 26.67, \frac{28 + 24 + 24 + 28 + 29 + 30}{6} = \frac{163}{6} = 27.17, \frac{24 + 24 + 28 + 29 + 30 + 29}{6} = \frac{164}{6} = 27.33 and \frac{24 + 28 + 29 + 30 + 29 + 22}{6} = \frac{162}{6} = 27$ respectively.

Now, The first six monthly centre moving average is $\frac{21.83 + 24}{2} = 22.915$ .

The second six monthly centre moving average is $\frac{24 + 26.17}{2} = 25.085$

Similarly, the third, fourth, fifth, sixth, seventh, eighth, ninth, tenth, eleventh and twelfth six monthly centre moving averages are $\frac{26.17 + 28.17}{2} = 27.17, \frac{28.17 + 28.17}{2} = 28.17, \frac{28.17 + 28.17}{2} = 28.17, \frac{28.17 + 29}{2} = 28.585, \frac{29 + 27.83}{2} = 28.415,$

$\frac{27.83 + 27.67}{2} = 27.75, \frac{27.67 + 26.67}{2} = 27.17, \frac{26.67 + 27.17}{2} = 26.92, \frac{27.17 + 27.33}{2} = 27.25 and \frac{27.33 + 27}{2} = 27.165,$ respectively.

Thus, the $quarterly moving average$ are $22.915, 25.085, 27.17, 28.17, 28.17, 28.585, 28.415, 27.75, 27.17, 26.92, 27.25 and 27.165$ which are represented as the dotted line and the actual figures by regular line in the graph below:

	Cost in $2009$ $(per kg)$	Cost in $2010 (per kg)$	Weights
Sugar	$3$	$7$	$3$
Milk	$3$	$3.50$	$4$
Coffee	$90$	$120$	$2$

	Cost in $2009$ $(per kg)$	Cost in $2010 (per kg)$	Weights
Sugar	$3$	$7$	$3$
Milk	$3$	$3.50$	$4$
Coffee	$90$	$120$	$2$

Commodity	$p_{0} (₹)$	$q_{0}$	$p_{1} (₹)$
Sugar	$9.00$	$20 kg$	$15.00$
Flour	$5.00$	$40 kg$	$10.00$
Milk	$6.00$	$10 lt$	$15.00$

Types of worker	Rate of pay $(₹ / h o u r)$	Average number of hours worked per week		Number of workers employed
		June	November
Skilled	$6.50$	$37$	$38.5$	$26$
Semi-Skilled	$5.10$	$38.5$	$39.5$	$14$
Unskilled	$3.50$	$40.5$	$40$	$42$

Year	$1981$	$1982$	$1983$	$1984$	$1985$	$1986$	$1987$	$1988$	$1989$	$1990$
No. of students	$332$	$317$	$357$	$392$	$402$	$405$	$510$	$427$	$405$	$438$

Important Questions on Index Numbers and Moving Averages

Learn and Prepare for any exam you want !

	Jan-March	April-June	July-Sept.	Oct.-Dec
$2000$	$74$	$56$	$48$	$69$
$2001$	$83$	$52$	$49$	$81$
$2002$	$94$	$60$	$48$	$79$