What Are the First and Third Quartiles

The first and third quartiles are descriptive statistics that are measurements of position in a data set.  Similar to how the median denotes the midway point of a data set, the first quartile marks the quarter or 25% point.  Approximately 25% of the data values are less than or equal to the first quartile.  The third quartile is similar, but for the upper 25% of data values.  We will look into these ideas in more detail in what follows. The Median There are several ways to measure the center of a set of data. The mean, median, mode and midrange all have their advantages and limitations in expressing the middle of the data. Of all of these ways to find the average, the median is the most resistant to outliers. It marks the middle of the data in the sense that half of the data is less than the median. The First Quartile There’s no reason we have to stop at finding just the middle. What if we decided to continue this process? We could calculate the median of the bottom half of our data. One half of 50% is 25%. Thus half of half, or one quarter, of the data would be below this. Since we are dealing with a quarter of the original set, this median of the bottom half of the data is called the first quartile, and is denoted by Q1. The Third Quartile There is no reason why we looked at the bottom half of the data. Instead, we could have looked at the top half and performed the same steps as above. The median of this half, which we will denote by Q3 also splits the data set into quarters. However, this number denotes the top one quarter of the data. Thus three quarters of the data is below our number Q3. This is why we call Q3 the third quartile. An Example To make this all clear, let’s look at an example. It may be helpful to first review how to calculate the median of some data. Start with the following data set: 1, 2, 2, 3, 4, 6, 6, 7, 7, 7, 8, 11, 12, 15, 15, 15, 17, 17, 18, 20 There are a total of twenty data points in the set. We begin by finding the median. Since there is an even number of data values, the median is the mean of the tenth and eleventh values. In other words, the median is: (7 8)/2 7.5. Now look at the bottom half of the data. The median of this half is found between the fifth and sixth values of: 1, 2, 2, 3, 4, 6, 6, 7, 7, 7 Thus the first quartile is found to equal Q1 (4 6)/2 5 To find the third quartile, look at the top half of the original data set. We need to find the median of: 8, 11, 12, 15, 15, 15, 17, 17, 18, 20 Here the median is (15 15)/2 15. Thus the third quartile Q3 15. Interquartile Range and Five Number Summary Quartiles help to give us a fuller picture of our data set as a whole. The first and third quartiles give us information about the internal structure of our data. The middle half of the data falls between the first and third quartiles, and is centered about the median. The difference between the first and third quartiles, called the interquartile range, shows how the data is arranged about the median. A small interquartile range indicates data that is clumped about the median. A larger interquartile range shows that the data is more spread out. A more detailed picture of the data can be obtained by knowing the highest value, called the maximum value, and the lowest value, called the minimum value. The minimum, first quartile, median, third quartile and maximum are a set of five values called the five number summary. An effective way to display these five numbers is called a boxplot or box and whisker graph.

Teenage Drug Abuse A Wide Variety Of Social Influences,...

Makayla Logan Mrs.Loving English III 12 November 2014 Teenage drug abuse is an issue that can result from a wide variety of social influences, stressful events, and mental disorders. Drug abuse among adolescents is a troubling issue because it decreases focus, increases the chance of consistency in behavior during adulthood, increases the chances of developing emotional issues, permanently damages the brain, and damages tissues in every system that can lead to death. Previous scientific research has identified that social factors, including the media and peers, play an important role in psychological development and impact the adolescent s decision to start experimenting with substances (Edwards). Appropriate solutions for the teenage†¦show more content†¦Teens usually abuse certain drugs that people usually wouldn t think they used . The most popular drug that teen abuse is tobacco products, cannabinoids also known as marijuana, cold medications, inhalants such as gasoline or ammonia, depressants, stimulant, N arcotics like morphine, oxycodone,codeine, hallucinogens, Dissociative, or Club drugs like ecstasy know as X (Edwards). At least 3,900 children under the age of eighteen have either tried or have been offered one of these drugs (â€Å"Facts†). More teens die from prescription drugs and about fifty precent of those teens that are seniors in high school think that crack or cocaine is harmless to their body (â€Å"11†).Using drugs can put people in danger of HIV/AIDS when a person is high off drugs it can make or break their judgment (â€Å"Facts†).This will make them either use more drugs also known as a gateway drug like marijuana. Illicit drugs among teens remains really high due to a very popular drug marijuana. About 65% of seniors use marijuana every day (â€Å"DrugFacts†). Marijuana is a very common drug for teens to use. Teens do not consider marijuana to be harmful or addicting (Volkox).Marijuana may not be addicting to certain people, it depends o n your genes, family, peer and their success in school (Volkox).The use of marijuana can cause memory and concentration problems. It also impacts on your muscle coordination to react slower than people that don’t use marijuana (â€Å"Drugs†). Just

High Expectations. Free Essays

High expectations; harmful or helpful? Many parents want their child to be top of their class, make straight A’s, and be something to brag about at the parent teacher conferences. Having high expectations for your children helps their mind set, education, and end results. Some people think it overworks the kid or lowers their self-esteem, although it has been proven that children who were expected to reach their parents expectations, do. We will write a custom essay sample on High Expectations. or any similar topic only for you Order Now First of all, having high expectations for your kid at early age will help the child over time. They will grow up learning that they need to excel so they will not just one day, give up. Parents who set expectations usually see their children rise to their level of expectation. So setting the standards at high but achievable levels will cause children to step up even further making it easier in the long run. Some people do believe having these â€Å"goals†, for your child can lower their self-esteem, but how could someone’s self-esteem be low when they are successful and making profitable living just from the expectations that were set for them as a child? Parents who expect their child to make amazing grades, talk about school, and check up on their child’s progress in school regularly helps the child but if a parent neglects this week’s quiz in, let’s say math, they send the wrong message to their children. Helping them study for the math quiz is an important part of setting the expectation for college. For instance, many families in Asian countries have set the expectation for their child early on so they grow up thinking that if they don’t excel in school they are a disappointment. Therefore, these children overachieve in all that they do. They do great in school, go to college, and make a fairly nice living. This race has been known to be very smart and prosperous. So, wouldn’t it be great if everyone became successful from high expectations and a little push from the parent? Finally, the end results. Being a child with parents having high expectations is a gift. If the parent pushes them to reach their expectation that’s just helping the child be successful in life. Those parents just want them to live a happy-fat-wallet-life. People say it may over work the child but really that child is working towards success. A little hard work isn’t hurting anybody if they know the outcome. Say a child made outstanding grades all through school due to the parents pushing them to. Then, they went to college, let’s say Harvard; why? Because the kid grew up thinking he needed to excel. Well, that kid goes to Harvard, learns valuable skills, works hard for a high paying job, then ends up living an affluent life, successful and happy all because you had the right motivation. All in all, look where their parents pushed the kid to. They could of said, â€Å"Just try your best. † but no, they said, â€Å" You’re going to DO your best and your going to get there. † High expectations help you have the motivation to reach what is expected of you. Why are you expected to be your best? Because you will definitely not get there by just being â€Å"alright. † How to cite High Expectations., Essay examples