Different Types of Averages

April moving average sales       =  ( 3200 + 2900 + 3700 + 3400) 4  =  3300

May Moving Average sales       =  ( 2900 + 3700 + 3400 + 3900)/ 4 =  3475

June Moving average sales       =  ( 3700 + 3400 +3900 + 3800)/ 4  =  3700

July Moving average sales        =  ( 3400 + 3900 +3800 +  3750)/ 4 =  3713

August moving average           =   ( 3900 + 3800 3750 + 3850)/ 4   =   3825

September Moving average      =   ( 3800 + 3750 + 3850 + 3720) 4 =   3780

October Moving average         =   ( 3750 + 3850 + 3720 + 3950) /4 =   3818

From the quartely sales figures it seems there is no trend at all. However, the moving averages reveals that there is a slight upward movement of sales ona quarterly basis. That is moving averages are important in time series analysis than other averages if applied correctly and chosing the appropriate moving averages given the data.

Geometric averages

If one wants to calculate average growth rates for the future from the past data the geometric averages are accurate than the simple average of annual growth rates for given years. Say one wants to calcualte the long-term growth rate of sales from the past recent years as follows using simple averages from the past records and geometric averages from the past records. The following are the figures for the period 2006 to 2009 period of sales.

Year   Sales

2006   100

2007   130

2008   91

2009   118.3

The annual growth rates are 2006 – 200 7 = 130 -100/100 = 30 %

The annual rate for 2007 – 2008 period = 91- 130/130 = -30%

The annual growth rate for 2008 -2009 period = 118.3 – 91/ 91 = 30 %

The simple average for these 3 year growth rate for these three period is = 30 -30 + 30/3 = 10%. This is an indication of typical growth rate for any given year. However to predict the growth rate in long -run from the past records it is beast to calculate the growth rate as geometric average. On the basis of geometric average one must multiply ( 1+ the grorht rate for period 1)* ( 1+ growth rate for period 2) + ( 1+ growth rate for period 3) and get the cube root of these figures and take away 1. For example in this instance The geometric growth rate for the past 3 years is [(1.3)*(0.7) **1.3)] to the power of 1/3 – 1 = 5.76%. If one applys this rate to the 2006 figure one can get the eact figure of 118.3. That is 100*(1.0576) to the power of 3 = 118.3. That is if one wants to predict the long term growth rates from past figures then simple averages are misleading compared to geometric averages. That is for forecasting purposes geometric averages are good estimates of long-term growth rates than simple average growth rates as estimates.