Whether you are using the 50day, 100day or 200day moving average, the method of calculation and the manner in which the moving average is interpreted remain the same. A moving average is simply an arithmetic mean of a certain number of data points. The only difference between a 50day moving average and a 200day moving average is the number of time periods used in the calculation. The 50day moving average is calculated by summing up the past 50 data points and then dividing the result by 50, while the 200day moving average is calculated by summing the past 200 days and dividing the result by 200. (To learn more, see our Moving Averages tutorial.)
As the question implies, many technical traders use these averages as an aid in choosing where to enter or exit a certain position, which then causes these levels to act as strong support or resistance. Simple moving averages (SMA) are often viewed as a lowrisk area to place transactions, since they correspond to the average price that all traders have paid over a given time frame. For example, a 50day moving average is equal to the average price that all investors have paid to obtain the asset over the past 10 trading weeks (that is, over the past two and a half months), making it a commonly used support level. Similarly, the 200day moving average represents the average price over the past 40 weeks, which is used to suggest a relatively cheap price compared to the price range over most of the past year. Once the price falls below this average, it may act as resistance because individuals who have already taken a position may consider closing the position to ensure that they do not suffer a large loss.
Critics of technical analysis say that moving averages act as support and resistance because so many traders use these indicators to inform their trading decisions. For more on this debate, see Can technical analysis be called a selffulfilling prophecy?

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