Determining Outliers in Statistics

Determining Outliers in Statistics Outliers are data values that differ greatly from the majority of a set of data. These values fall outside of an overall trend that is present in the data.  A careful examination of a set of data to look for outliers causes some difficulty. Although it is easy to see, possibly by use of a stemplot, that some values differ from the rest of the data, how much different does the value have to be to be considered an outlier?  We will look at a specific measurement that will give us an objective standard of what constitutes an outlier. Interquartile Range The interquartile range is what we can use to determine if an extreme value is indeed an outlier. The interquartile range is based upon part of the five-number summary of a data set, namely the first quartile and the third quartile. The calculation of the interquartile range involves a single arithmetic operation. All that we have to do to find the interquartile range is to subtract the first quartile from the third quartile. The resulting difference tells us how spread out the middle half of our data is. Determining Outliers Multiplying the interquartile range (IQR) by 1.5 will give us a way to determine whether a certain value is an outlier. If we subtract 1.5 x IQR from the first quartile, any data values that are less than this number are considered outliers. Similarly, if we add 1.5 x IQR to the third quartile, any data values that are greater than this number are considered outliers. Strong Outliers Some outliers show extreme deviation from the rest of a data set. In these cases we can take the steps from above, changing only the number that we multiply the IQR by, and define a certain type of outlier. If we subtract 3.0 x IQR from the first quartile, any point that is below this number is called a strong outlier. In the same way, the addition of 3.0 x IQR to the third quartile allows us to define strong outliers by looking at points which are greater than this number. Weak Outliers Besides strong outliers, there is another category for outliers. If a data value is an outlier, but not a strong outlier, then we say that the value is a weak outlier. We will look at these concepts by exploring a few examples. Example 1 First, suppose that we have the data set {1, 2, 2, 3, 3, 4, 5, 5, 9}. The number 9 certainly looks like it could be an outlier. It is much greater than any other value from the rest of the set. To objectively determine if 9 is an outlier, we use the above methods. The first quartile is 2 and the third quartile is 5, which means that the interquartile range is 3. We multiply the interquartile range by 1.5, obtaining 4.5, and then add this number to the third quartile. The result, 9.5, is greater than any of our data values. Therefore there are no outliers. Example 2 Now we look at the same data set as before, with the exception that the largest value is 10 rather than 9: {1, 2, 2, 3, 3, 4, 5, 5, 10}. The first quartile, third quartile, and interquartile range are identical to example 1. When we add 1.5 x IQR 4.5 to the third quartile, the sum is 9.5. Since 10 is greater than 9.5 it is considered an outlier. Is 10 a strong or weak outlier? For this, we need to look at 3 x IQR 9. When we add 9 to the third quartile, we end up with a sum of 14. Since 10 is not greater than 14, it is not a strong outlier. Thus we conclude that 10 is a weak outlier. Reasons for Identifying Outliers We always need to be on the lookout for outliers. Sometimes they are caused by an error. Other times outliers indicate the presence of a previously unknown phenomenon. Another reason that we need to be diligent about checking for outliers is because of all the descriptive statistics that are sensitive to outliers. The mean, standard deviation and correlation coefficient for paired data are just a few of these types of statistics.

A Detailed Break Down of a Teachers Job Description

A Detailed Break Down of a Teachers Job Description Teachers do much more than just teach. Their job descriptions are lengthy, much more than people realize. Most teachers work well after the final bell has ended. They take their work home with them. They spend several hours over the weekend working. Teaching is a difficult and misunderstood profession and requires a dedicated, patient, and willing person to keep up with all of the jobs demands. This article provides an in-depth look at a teacher’s job description.   A Teacher Must... A teacher must†¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦. have a comprehensive understanding of the content that they teach. They must continuously study and review new research within their content area. They must be able to break apart the foundations of new information and put into terms that their students can understand.A teacher must†¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦. develop weekly lesson plans that link their objectives with their required state standards. These plans must be engaging, dynamic, and interactive. These weekly plans must align strategically with their year-long lesson plans.A teacher must†¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦. always prepare a backup plan.  Even the most well-thought-out plans can fall apart. A teacher must be able to adapt and change on the fly according to their students’ needs.A teacher must†¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦. organize their classroom in such a way that it is student friendly and conducive to maximizing learning opportunities.A teacher must†¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦. decide whether or not a seating chart is appropriate. They must also decide when a change to that seating chart is necessary. A teacher must†¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦. decide on a behavior management plan for their classroom. They must adopt classroom rules, procedures, and expectation. They must practice their rules, procedures, and expectations on a daily basis. They must hold students accountable for their actions by determining an appropriate consequence when students fail to meet or follow those classroom rules, procedures, or expectations.A teacher must†¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦. attend and participate in all required district professional development.  They must learn the content being presented and figure out how to apply it to their classroom situation.A teacher must†¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦. attend and participate in optional professional development for areas that they recognize an individual weakness or an opportunity to learn something new. They do this because they want to grow and improve.A teacher must†¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦. spend time observing other teachers. They must have in-depth conversations with other educators. They must exchange ideas, ask for guidance, and be willing to listen to constructive criticism and advice. A teacher must†¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦. use the feedback from their evaluations as a driving force towards growth and improvement concentrating on areas that are scored lower.  They should ask the principal or evaluator for strategies or suggestions on how to improve those specific areas.A teacher must†¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦. grade and record every student’s papers in a timely manner. They must give their students timely feedback with suggestions for improvement. They must determine whether or not students have mastered a topic or are in need of re-teaching or remediation.A teacher must†¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦. develop and construct assessments and quizzes that align with classroom content and help determine if the lesson objectives are being met.A teacher must†¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦. break down data from assessments to self-assess whether or not how they are introducing the new content is successful or if changes need to be made.A teacher must†¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦. plan with other gr ade level and/or content level teachers determining common themes, objectives, and activities.A teacher must†¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦. keep the parents of their students informed of their progress on a regular basis. They must often communicate by routinely making phone calls, sending emails, having face-to-face conversations, and sending written notifications. A teacher must†¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦. find a way to engage parents in the learning process. They must keep parents actively involved with their child’s education by developing strategic cooperative learning opportunities.A teacher must†¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦. oversee classroom fundraising opportunities. They must follow all district procedures while tallying orders, submitting orders, counting money, turning in money, and sorting and distributing orders.A teacher must†¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦. serve as a sponsor for a class or club activity. As a sponsor, they must organize and oversee all of the activities. They must also attend all of the related activities and meetings.A teacher must†¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦. keep up with and study new instructional pedagogy. They must determine what is appropriate to utilize within their classroom and find a way to implement what they have learned in their daily lessons.A teacher must†¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦. keep up with the newest technological trends . They must become tech savvy to stay up with the digital generation. They must assess what technology would be advantageous to use in their classroom. A teacher must†¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦. organize and schedule all field trips in advance. They must follow all district protocol and get information out to parents in a timely manner.  They must create student activities that enhance the field trip and cement learning.A teacher must†¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦. develop emergency lesson plans and substitute plans for days that they have to miss work.A teacher must†¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦. attend extra-curricular activities. This demonstrates school pride and support for the students who participate in these events.A teacher must†¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦. sit on various committees to review and oversee critical aspects of the school such as budget, hiring new teachers, school safety, student health, and curriculum.A teacher must†¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦. monitor students while they are working independently. They must walk around the room, checking student progress, and assisting students who may not completely understand the assignment.A teacher mustâ⠂¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦. develop whole group lessons that keep every student engaged. These lessons must consist of entertaining and content-based activities that help students learn key concepts, making connections to prior learning, and building towards topics that will be introduced in the future. A teacher must†¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦. gather, prepare, and distribute all the materials needed to complete a lesson prior to when class begins. It is often beneficial for the teacher to go through a practice run of the activity before doing it with the students.A teacher must†¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦. model newly introduced content or concepts to their students walking students through the proper steps to solve the problem prior to giving the students the opportunity to do it themselves.A teacher must†¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦. develop ways to differentiate instruction to challenge all students without frustrating them while still ensuring that every student meets their learning objective.A teacher must†¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦. develop guided practice activities for each lesson where the entire class is able to work out or solve problems together. This allows the teacher to check for understanding, clear up misconceptions, and determine if further instruction is needed before turning them loose o n independent practice.A teacher must†¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦. formulate sets of questions that require both higher level and lower level responses. Furthermore, they must ensure that they give every student the opportunity to participate in the discussion. Finally, they must give those students an appropriate wait time and rephrase questions when necessary. A teacher must†¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦. cover and monitor a wide variety of duties including breakfast, lunch, and recesses.A teacher must†¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦. return parent phone calls and hold parent conferences whenever a parent requests a meeting. These phone calls and meetings must be held during their planning period or before/after school.A teacher must†¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦. monitor the health and safety of all their students. They must look for signs of abuse or neglect. They must report it anytime that they believe a student is in any potential danger.A teacher must†¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦. develop and cultivate relationships with their students. They must build a trusting rapport with each student and one built on a foundation of mutual respect.A teacher must†¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦. must pause from lessons to take advantage of teachable moments. They must use these moments to teach their students valuable life lessons that can carry on with them throughout their life.A teacher mus t†¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦. must have empathy for every student. They must be willing to put themselves in their students’ shoes and realize that life is a struggle for many of them. They must care enough to show their students that getting an education can be a game changer for them. A teacher must†¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦. evaluate students and complete referrals for many individual needs and services including special education, speech-language, occupational therapy, or counseling.A teacher must†¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦. create a system for organization within their classroom. They must file, clean, straighten, and rearrange when necessary.A teacher must†¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦. utilize the Internet and social media to search for activities, lessons, and teaching resources that they can utilize within or supplement a lesson.A teacher must†¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦. make enough copies for their students. They must fix the copy machine when there is a paper jam, add new copy paper when it is empty, and change toner when necessary.A teacher must†¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦. must counsel students when they bring a personal issue to them. They must be a willing listener capable of giving students great life advice that can help lead them to the right decisions.A teacher must†¦Ã¢â‚¬ ¦ †¦. establish healthy working relationships with their co-workers. They must be willing to help them out, answer questions, and work together in a team environment. A teacher must†¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦. take on a leadership role once they establish themselves. They must be willing to serve as a mentor teacher to beginning teachers and serve in leadership areas as necessary.A teacher must†¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦. change the decoration on their bulletin boards, doors, and classroom at various points in the year.A teacher must†¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦. help students identify their individual strengths and weaknesses. They then must help them set goals and lead them on the path towards reaching those goals.A teacher must†¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦. develop and lead small group activities focused on helping students acquire missing skills in areas such as reading or math.A teacher must†¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦. be a role model who is always aware of their environment and does not allow themselves to be in a compromising situation.A teacher must†¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦. be willing to go the extra mile for their students offering tutoring or extended help for students who may be struggling.A teacher must†¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦. arrive at school early, stay late, and spend part of their weekend to ensure that they are prepared to teach their students.