Moving Average Worksheet

Using the data table constructed in the Moving Average Illustration, carry out the following tasks:

1. Plot this data yourself on a graph.
2. Comment on the trend.
3. What does this moving average data tell you about the state of the UK economy over this six year period?

Worksheet on Summations

In a remote village, land is divided amongst the people in rectangular blocks. Six main families control the blocks of land and the size of each block is given in the table below.

Draw a table with columns headed: x, y, x - y, 2x, and 2y.

Length of plot (x)	Breadth of plot (y)	x + y	x - y	2x	2y
12	8	20	4	24	16
15	9	24	6	30	18
20	12	32	8	40	24
14	7	21	7	28	14
10	9	19	1	20	18
10	8	18	2	20	16
x =81	y =53	(x + y) =134	(x - y) =28	2x =162	2y =106

Prove that the following rules are correct: USE CALNET Qs TO TEST THIS

1. (x + y) = x + y
   134 = 81 + 53
   
   
2. (x - y) = x - y
   28 = 81 - 53
   
   
3. 2x = 2x
   162 = 2 x 81
   
   Law dictates that the length of each plot will be increased to 20 metres. As a result it can be seen that 20 = 6 x 20. This illustrates the rule that a = na, where a is a constant and n is the number of times it has to be added.
   
   Now tackle the following questions: CALNET Qs TO TEST THIS
   
   
4. What is the total length of fence if each x is able to build a fence around the perimeter of each plot? (calculate 2x + 2y)
   2 x 81 + 2 x 53 =
   162 + 106 = 268
   
   
5. What is the total area of land surrounded by fencing? (Calculate xy)
   
   12 x 8 = 96
   15 x 9 = 135
   20 x 12 = 240
   14 x 7 = 98
   10 x 9 = 90
   10 x 8 = 80
   739m²
   
   
6. The law now dictates that each plot of land should be reduced by 1.5 metres.
   From the summations carried out above, calculate:
   
   1. the new total length of fencing - use the relationship (x - a) = x - a = x - na
      
      
   2. x - a = (12 - 1.5 ) + (15 - 1.5) + (20 - 1.5) + (14 - 1.5) + (10 - 1.5) + (10 - 1.5)
      = 72 (as proved by the above relationship).
      New total length of fencing = 2x + 2 y
      = 2 x 72 + 2 x 53
      = 144 + 106 = 250m²
      
      
   3. the new total area of enclosed land.
      use the relationship (x - a)y = xy - ay = xy - ay
      
      = (12 - 1.5).8 + (15 - 1.5).9 + (20 - 1.5).12 + (14 - 1.5).7 + (10 - 1.5).9 + (10 - 1.5).8
      = 10.5 x 8 + 13.5 x 9 + 18.5 x 12 + 12.5 x 7 + 8.5 x 9 + 8.5 x 8
      = 84 + 121.5 + 222 + 87.5 + 76.5 + 68
      = 659.5m²
      

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