Let's do a few more examples to hit this point home. If you look at the example above, the first digit in each number (24, 26) is 2, and the last digits in each (4, 6) equals 10. the last digit of both numbers must equal 10.the first digits of both numbers must be the same.There are a few restrictions, or caveats, that must be adhered to: If you thought this method was too good to be true, well, you're right. Hate Math? These Mental Tricks Will Have You Multiplying Faster Than Einstein Ever Could! That's some next level Harry Potter-style magic, right? A Few Restrictions
So for 24 multiplied by 26, it would be 4 (second digit in first number) x 6 (second digit in second number) = 24.Ģ and 4 are the the last digits of the answer. Now take the second digit of the first number (4 for 24) and multiple that by the second digit of the second number (6 for 26), which will give you the remaining digits of the answer. This means that 6 is our first digit in the answer. So for 24 multiplied by 26, it would be 2 (first digit in first number) multiplied by 3 (one digit higher) = 6. Start by taking the first digit of the first number (2 for 24) and multiplying that by the number directly higher than it, which will give you the first digit(s) of the answer. Mental math for the win! Now, this trick will only apply in a few multiplication settings, but more on that later.įor the first example, let's calculate the following: 24 x 26 = This is great when you need to speed through multiplication homework, and is also good for impressing your math teacher or peers, or as just a cool party trick (depending on your crowd). the average distance of observations from its mean), we move to MAD.When you need to crunch numbers quickly - and I mean really quickly - there's a cool method you can use to multiply two numbers together in just a few seconds. But a set can have its observations quite far from the mean, on an average, as compared to another set having the same mean. M => around which number the observations are centered. Hence, σ is conveniently used everywhere. σ loosely includes the information provided by MAD, but it isn't vice versa. TL DR if you have data that are due to many underlying random processes or which you simply know to be distributed normally, use standard deviation function.Įach of the three parameters - Mean (M), Mean Absolute Deviation (MAD) and Standard Deviation (σ), calculated for a set, provide some unique information about the set which the other two parameters don't. In this case, the mean deviation might be more appropriate. On the other hand, if you have a single random variable, the distribution might look like a rectangle, with an equal probability of values appearing anywhere within a range. So if your data is normally distributed, the standard deviation tells you that if you sample more values, ~68% of them will be found within one standard deviation around the mean.
Intuitively, you can think of the mean deviation as measuring the actual average deviation from the mean, whereas the standard deviation accounts for a bell shaped aka "normal" distribution around the mean. If you look at the equation, you can see the standard deviation more heavily weights larger deviations from the mean. Standard deviation is the right way to model dispersion for normally distributed phenomena. So, I disagree with some of the answers given here - standard deviation isn't just an alternative to mean deviation which "happens to be more convenient for later calculations". In other words, the standard deviation is a term that arises out of independent random variables being summed together. Where $Y$ is the probability of getting a value $x$ given a mean $\mu$ and $\sigma$…the standard deviation! They both measure the same concept, but are not equal.
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