Assuming a four yearly cycle, calculate the trend by the method of moving averages from the following data:

Year	$1984$	$1985$	$1986$	$1987$	$1988$	$1989$	$1990$	$1991$	$1992$	$1993$
Value	$12$	$25$	$39$	$54$	$70$	$87$	$105$	$100$	$82$	$65$

The profit of a soft drink firm (in thousands of rupees) during each month of the year is as given below:

Calculate the four monthly moving averages and plot these and the original data on a graph sheet.

The number of road accidents in the city due to rash driving, over a period of $3$ years, is given in the following table:

Calculate four quarterly moving averages and illustrate them and original figures on one graph using the same axes for both.

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

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

Calculate, correct to one decimal place, the index number for the cost of a cup of coffee in $2010$ using weighted price relatives.

Calculate, correct to one decimal place, the index number for the cost of a cup of coffee in $2010$ using weighted aggregates taking the index number for $2009 \text{to be} 100$ in each case.

Due to change in prices, the cost of living index for the working class in a city rose to $225 \text{in April from} 180 \text{in March} 2003$. The index of food became $252 \text{from} 198$, that of clothing from $185 \text{to} 205$, that of fuel and lighting from $175 \text{to} 195$ and that of miscellaneous from $138 \text{to} 212$. The index of rent, however remained unchanged at $150$. Find the weights of all the groups if the weights of clothing, fuel and lighting, and rent were the same.

The following data relate to the pay of workers employed at a factory.

Calculate a weighted aggregate index of average weekly pay for November $\text{(June}=100\text{)}$, using the number of workers employed as a weighting factor.