In one sentence, describe what the following article is about: Take all of your calculated returns and add them together. Then, divide by the number of returns you are using, n, to find the mean return. This represents the average return over the time period you are measuring. Specifically, the mean, m, is calculated as follows: m =(R1+R2+...Rn)/(n). For example, imagine that you had 5 periods that had calculated returns of 0.2, -0.1, -0.3, 0.4, and 0.1. You would add these together to get 0.3 then divide by the number of periods, n, which is 5. Therefore, your mean, m, would be 0.3/5, or 0.06. For every return, Rn, a deviation, Dn, from the mean return, m, can be found. The equation for finding Dn can be expressed simply as Dn=Rn-m. Complete this calculation for all returns within the range you are measuring.  Using the previous example, you would subtract your mean, 0.06, from each of the returns to get a deviation for each. These would be: D1=0.2-0.06, or 0.14 D2=-0.1-0.06, or -0.16 D3=-0.3-0.06, or -0.36 D4=0.4-0.06, or 0.34 D5=0.1-0.06, or 0.04 Your next step is to find the mean variance of the returns by summing the squared individual deviations from the mean of the returns. The equation for finding the variance, S, can be expressed as: S=(D1^2+D2^2+...Dn^2)/(n-1). Again, sum the squares of the deviations, Dn, and divide by the total number of variances minus 1, n-1, to get your mean variance.  First, square your deviations from the last step. These would be, in order: 0.0196, 0.0256, 0.1296, 0.1156, 0.0016. Sum these numbers to get 0.292. Then, divide by n-1, which is 4, to get 0.073. So, S=0.073 in the example. The volatility is calculated as the square root of the variance, S. This can be calculated as V=sqrt(S). This "square root" measures the deviation of a set of returns (perhaps daily, weekly or monthly returns) from their mean. It is also called the Root Mean Square, or RMS, of the deviations from the mean return. It is also called the standard deviation of the returns.  In the example, this would just be the square root of S, which is 0.073. So, V=0.270. This number has been rounded to three decimal places. You may choose to keep more decimals to be more accurate.  A stock whose price varies wildly (meaning a wide variation in returns) will have a large volatility compared to a stock whose returns have a small variation. By way of comparison, for money in a bank account with a fixed interest rate, every return equals the mean (i.e., there's no deviation) and the volatility is 0.
Summary: Find the mean return. Calculate the deviations from the mean. Find the variance. Calculate the volatility.

In one sentence, describe what the following article is about: Stomach discomfort, including ulcers, may contribute to some horses' desire to crib. By switching to a diet that helps reduce ulcers, such as alfalfa hay, you may help eliminate stomach problems, which in turn,  may reduce the horse's cribbing. If your horse is already on alfalfa, you may want to try other options for reducing cribbing.  Change your horse's diet over slowly. Begin mixing some of the new diet in with the old a little at a time, gradually adding more each day. That will help reduce digestive issues. If you suspect that ulcers are causing your horse's cribbing, it's best to get your veterinarian to do a scope of its stomach to get a proper diagnosis. If ulcers are present, your vet can provide you with treatment options and ways to manage the ulcers, which will help heal your horse and reduce the cribbing. Sugary feeds may encourage your horse to crib more, so opt for a low-sugar version, like plain oats, when you're feeding grains in addition to hay. It may be that sugar lights up the same reward center in the brain that cribbing does, so when your horse gets sugar, it may want to keep the feeling going. Look for feeds that have a higher percentage of fat and fiber rather than starch and sugar. You can also try giving the horse hay before you feed it grain, which may cut down on cribbing, as well. If a horse has something to keep its mouth occupied, namely hay or a large pasture for grazing, it's less likely to crib. By having hay around, you encourage the horse to nibble on the hay throughout the day instead of inappropriate things like your barn or your fences. If your horse has trouble with overeating, try a slow feeder. These feeders give your horse a little bit of hay at a time, slowing down how much it can take, but your horse will still be nibbling most of the time. Because stomach discomfort may contribute to cribbing, have your horse seen by the vet if you haven't already. That way, the vet can rule out any stomach problems, such as ulcers or other intestinal issues, that you'll want to get taken care of.  Your vet may suggest an antacid for certain conditions. If your horse doesn't have a stomach problem and cribbing has been a chronic problem, your vet may suggest having surgery to help prevent cribbing.
Summary: Feed the horse alfalfa hay to prevent ulcers. Avoid grain feeds that are high in sugar. Provide hay at all times to keep your horse occupied. Ask your veterinarian to see if there's an underlying reason your horse cribs.

In one sentence, describe what the following article is about: Use a tie that you won’t be wearing anymore. The tie should be 100% silk. A tie made of any other material won’t work. Choose a tie that has an interesting pattern. Dark purple, blue, and red ties work the best.  It doesn't necessarily have to be a beautiful tie. “Uglier” ties sometimes make the most beautiful eggs. If you don't have any ties laying around, silk ties can be found cheap at most thrift shops. Be creative and give free rein to your imagination as you make more eggs.
Summary:
Find a silk tie. That's it!