INPUT ARTICLE: Article: Monitoring moon phases is not as accurate of a way to keep time as making a sundial or measuring by the North Star. Based on the current lunar phase, the moon will only be visible in the night sky for a certain amount of time and it will be easiest to see when it is full or almost full. For example, during a full moon, the moon will be visible in the sky all night (for approximately 12 hours). The moon will be harder to spot throughout the night when it is not full. Knowing when the sun set will give you a baseline time to start tracking the time with the moon since the moon rises about 1 hour after the sun sets. If you can, look up the time that the sun set before you observe the moon’s position and add 1 hour to this time to create a baseline time. For example, if the sun set at 6:30 pm, and the moon is just now visible on the horizon, then it is approximately 7:30 pm. You can use the moon to tell time by dividing the sky into quarters and noting the moon’s position in the sky. Find the middle of the sky, and then divide these 2 halves in half to divide the sky into quarters going from east to west. This won’t give you an accurate time, but you can get a good estimate. Look at the moon's position in the sky in relation to where it rose.  For example, if the moon is ¼ of the way across the sky from where it rose, then it is about 3 hours past sundown. If the moon is halfway across the sky, then it is approximately 6 hours past sundown. If the moon is ¾ of the way across the sky, then it is 9 hours past sundown. The location of the moon in the sky along with the time the sun set, will allow you to calculate an approximate time. Once you have noted these details, add the number of hours for the position of the moon to the time of sunset.  For example, if the sun set at 7:00 pm, and the moon in halfway across the sky, then the approximate time is 1:00 am. If the sun set at 6:15 pm, and the moon is ¾ of the way across the sky, then the approximate time is 3:15 am.

SUMMARY: Use the moon to tell time only when it is at its brightest. Find out what time the sun set. Track the position of the moon to determine the approximate time. Use the moon’s position to calculate the approximate time.


INPUT ARTICLE: Article: The variance is a figure that represents how far the data in your sample is clustered around the mean.  This figure will give you an idea of how far your data is spread out. Samples with low variance have data that is clustered closely about the mean. Samples with high variance have data that is clustered far from the mean. Variance is often used to compare the distribution of two data sets. This will give you a figure of how much each data point differs from the mean.  For example, in our sample of test scores (10, 8, 10, 8, 8, and 4) the mean or mathematical average was 8. 10 - 8 = 2; 8 - 8 = 0, 10 - 8 = 2, 8 - 8 = 0, 8 - 8 = 0, and 4 - 8 = -4. Do this procedure again to check each answer. It is very important you have each of these figures correct as you will need them for the next step. You will need each of these figures to find out the variance in your sample.  Remember, in our sample we subtracted the mean (8) from each of the numbers in the sample (10, 8, 10, 8, 8, and 4) and came up with the following: 2, 0, 2, 0, 0 and -4. To do the next calculation in figuring out variance you would perform the following: 22, 02, 22, 02, 02, and (-4)2 = 4, 0, 4, 0, 0, and 16. Check your answers before proceeding to the next step. This figure is called the sum of squares.  In our example of test scores, the squares were as follows: 4, 0, 4, 0, 0, and 16. Remember, in the example of test scores we started by subtracting the mean from each of the scores and squaring these figures: (10-8)^2 + (8-8)^2 + (10-8)^2 + (8-8)^2 + (8-8)^2 + (4-8)^2 4 + 0 + 4 + 0 + 0 + 16 = 24. The sum of squares is 24. Remember, n is how many numbers are in your sample. Doing this step will provide the variance. The reason to use n-1 is to have sample variance and population variance unbiased.    In our sample of test scores (10, 8, 10, 8, 8, and 4) there are 6 numbers. Therefore, n = 6. n-1 = 5. Remember the sum of squares for this sample was 24. 24 / 5 = 4.8 The variance in this sample is thus 4.8.

SUMMARY: Find the variance. Subtract the mean from each of your numbers in your sample. Square all of the numbers from each of the subtractions you just did. Add the squared numbers together. Divide the sum of squares by (n-1).


INPUT ARTICLE: Article: Not having friends may be from a variety of different causes. Take some time to consider your reasons. Also, keep in mind that you can choose to change your situation and seek out friends if you want. Some questions you might ask yourself to determine the reason why you don’t have friends at the moment include:  Have you undergone a significant change recently? Going away to college or moving to a new city can be part of the reason why you may not yet have friends. Likewise, having a falling out with friends can lead to isolation. Did you recently lose a friend or group of friends for some reason? Are you naturally introverted? If you tend to prefer your alone time to spending time with other people, then you might be an introvert. If this is the case, then not having friends may be due to a preference for solitude. However, you can still have friends and maintain your solitude. Have you been struggling with emotional turmoil lately? If you have been feeling down for a while and unable to motivate yourself to go out and seek friendship, then this could also be part of the reason why you don’t have friends. If so, it is important to seek help. Talk to your school counselor, someone in the counseling center at your college, or a trusted adult, such as a parent, teacher, or religious leader. It is important to accept yourself for who you are right now. Realize that there’s nothing wrong with you for being shy, different, or just not very social. Your worth as a person isn’t determined by how many friends you have, so don’t let anyone make you feel bad about yourself.  If your peers try to make fun of you, stand up for yourself. Don’t get into a physical fight, but do let people know you aren’t a pushover. If you want to make more friends in the future, accepting yourself as you are now is an important first step. Despite what society and other people might tell you, it’s perfectly okay to prefer spending time by yourself. There is nothing wrong with being quiet, introverted, and reserved. If you decide you don’t mind not having close friends, don’t let anyone tell you your preference is wrong. However, keep in mind that being alone all of the time is not healthy either. You may not want to be as social as other people, but having some degree of socialization is healthy. If being around people makes you nervous, ask yourself whether social anxiety could be holding you back from making friends. Other conditions like schizophrenia, bipolar disorder, ADHD, and autism can also make it difficult to befriend others. If you think you have a mental health disorder, ask your parents to take you to a doctor or therapist. If you feel persistently sad or hopeless, talk to your school counselor or a therapist. They can help you get to the bottom of your feelings and develop some strategies for coping socially.

SUMMARY:
Consider the reasons why you do not have friendships. Accept yourself the way you are. Decide if you even want to be more social or not. Consider whether you might have social anxiety or another condition. See a counselor or therapist.