Because, whatever the underlying distribution, as more and more samples are taken from ANY population, the average of those samples will have a standard normal distribution whose mean will be their average. The normal (or Gaussian) distribution is symmetric and so its mean lies at the centre of the probability distribution.
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It is called central tendency because it represents the averages. Central tendency has three measurements: # Mean # Mode # Median
I’ve talked in some recent posts about central tendency and how stock prices may be considered to cluster around a central value over time. I mentioned the mean, median, and mode as three common measures of central tendency. I also touched one of the main problems with using the mean – its outsized sensitivity to extreme values. Let’s look at another measure that investment analysts are much more likely to consider, the moving average. Since stock prices plotted on a graph create lines that can look like a random zigzag with no rhyme or reason, it’s often necessary to create a trend line to show the overall movement of the stock price without all the noise of major up-and-down jumps. This process of showing the overall trend and ignoring the smaller deviations from that trend is called “smoothing” the data. One method that is often used to smooth the data when it comes to stock price lines is the moving average. The way a moving average works is to take into account the most recent observations and create an average of them. So let’s say you have a stock for which you’re trying to smooth out the price line. If you want to create a moving average you have to first decide over which period you’re looking at. Many investment analysts will look at a 20 day moving average. That simply means that they will plot a line that shows, on each day, a point that is equal to the average price over the previous 20 days. So this line will shift along with the price line, but it will move more slowly and less erratically. This line is much more effective than the long-term historic average price line because it will filter out the extreme values that may have occurred in time periods longer than 20 days ago. Another problem with using a long term average price as a measure of central tendency is that prices do shift over time and the most recent price is more of a predictor of the next price than the price from three months ago or a few years ago. For this reason the moving average is a more apt predictor of the prices to expect next than the long-term historic average price.
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