A moving average of a share price is simply the average of the share prices of the last so many days.
To work out a five-day moving average, for example, you add up the prices for the last five days and divide by five. Then each day you update it by dropping the earliest price used for the previous day's calculation and adding the latest price.
You can then plot a line of the moving average, which you will see smoothes out share price movements, giving you (hopefully) a clearer view of the price trend thanks to the fact that it sorts the serious moves from the background noise.
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You can use 5, 10, 100, 20 or any other number of days to make your moving average, depending on your aims - the longer a time period you use, the smoother your line will be. Most chartists will look at a few different moving averages at a time (say 20 day and 100 day) when they're looking at charts.
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