How To Calculate the Variance and Standard Deviation

Variance and standard deviation are two closely related measures of variation that you will hear about a lot in studies, journals, or statistics class. They are two basic and fundamental concepts in statistics that must be understood in order to understand most other statistical concepts or procedures. Below, we’ll review what they are and how to find the variance and standard deviation. Key Takeaways: Variance and Standard Deviation The variance and standard deviation show us how much the scores in a distribution vary from the average.The standard deviation is the square root of the variance.For small data sets, the variance can be calculated by hand, but statistical programs can be used for larger data sets. Definition By definition, variance and standard deviation are both measures of variation for interval-ratio variables. They describe how much variation or diversity there is in a distribution. Both the variance and standard deviation increase or decrease based on how closely the scores cluster around the mean. Variance is defined as the average of the squared deviations from the mean. To calculate the variance, you first subtract the mean from each number and then square the results to find the squared differences. You then find the average of those squared differences. The result is the variance. The standard deviation is a measure of how spread out the numbers in a distribution are. It indicates how much, on average, each of the values in the distribution deviates from the mean, or center, of the distribution. It is calculated by taking the square root of the variance. A Conceptual Example The variance and standard deviation are important because they tell us things about the data set that we can’t learn just by looking at the mean, or average. As an example, imagine that you have three younger siblings: one sibling who is 13, and twins who are 10. In this case, the average age of your siblings would be 11. Now imagine that you have three siblings, ages 17, 12, and 4. In this case, the average age of your siblings would still be 11, but the variance and standard deviation would be larger. A Quantitative Example Let’s say we want to find the variance and standard deviation of the age among your group of 5 close friends. The ages of you and your friends are 25, 26, 27, 30, and 32. First, we must find the mean age: (25 26 27 30 32) / 5 28. Then, we need to calculate the differences from the mean for each of the 5 friends. 25 – 28 -326 – 28 -227 – 28 -130 – 28 232 – 28 4 Next, to calculate the variance, we take each difference from the mean, square it, then average the result. Variance ( (-3)2 (-2)2 (-1)2 22 42)/ 5 (9 4 1 4 16 ) / 5 6.8 So, the variance is 6.8. And the standard deviation is the square root of the variance, which is 2.61. What this means is that, on average, you and your friends are 2.61 years apart in age. Although it’s possible to calculate the variance by hand for smaller data sets such as this one, statistical software programs can also be used to calculate the variance and standard deviation. Sample Versus Population When conducting statistical tests, it’s important to be aware of the difference between a population and a sample. To calculate the standard deviation (or variance) of a population, you would need to collect measurements for everyone in the group you’re studying; for a sample, you would only collect measurements from a subset of the population. In the example above, we assumed that the group of five friends was a population; if we had treated it as a sample instead, calculating the sample standard deviation and sample variance would be slightly different (instead of dividing by the sample size to find the variance, we would have first subtracted one from the sample size and then divided by this smaller number). Importance of the Variance and Standard Deviation The variance and standard deviation are important in statistics, because they serve as the basis for other types of statistical calculations. For example, the standard deviation is necessary for converting test scores into Z-scores. The variance and standard deviation also play an important role when conducting statistical tests such as t-tests. References Frankfort-Nachmias, C. Leon-Guerrero, A. (2006). Social Statistics for a Diverse Society. Thousand Oaks, CA: Pine Forge Press.

Essay Exploring Autism in Children - 2819 Words

Exploring Autism in Children Susan was a normal, happy, active infant. Her parents were so relieved that all her checkups at the pediatricians office indicated that her growth and development were above average. At 6 months she could sit up and crawl and at 10 months she was walking. She seemed to babble more than her older brother did at the same age and was talking at 16 months. All the milestones in her early development were ahead of schedule. One day when she was 18 months old, her mother found her sitting alone in the yard spinning the wheels of her wagon with such persistence that her mom joked with her friends that maybe Susan would be an engineer when she grew up. Susans mother began to notice many unusual behaviors†¦show more content†¦Susans parents decided to take her to the doctor. She went through many tests and she was eventually diagnosed with Autism. By the time she was three, there was no language or interaction. After years of physical therapy, behavioral therapy and speech/ language therapy, Susan is now 15 and enrolled in residential boarding school, where she receives 24-hour supervision and care. This program is more expensive then a regular school based setting, but has benefited Susan. She has aides to help her with her daily living skills. Susan is able to hold a job at a sheltered workshop under the supervision of her aide (Neuwirth Segal). Autism affects one out of every 500 births and over one million people have Autism in the United States. Autism is four times more common in boys than girls. If a girl is Autistic, the symptoms are usually much more severe. Girls tend to have more of the symptoms and lower intelligence. The following paper will describe the Autism Spectrum Disorder, specifically as it relates to young children with Autism. It will also identify different types of Autism and accompanying disorders. It will describe the history, known causes, characteristics and the hope for the future. The Individuals with Disabilities Education Act (IDEA) defines Autism as A developmental disability significantly affecting verbal and non-verbal communication and social interaction, generally evident before age three that adversely affectsShow MoreRelatedAutism Is A Psychological Disorder Essay817 Words   |  4 Pageslong ,2008 p.284) â€Å"autism is a neurological disorder that effect a person ability to communicate, to understand language, to play and to relate to others. A diagnose of autism is given when a person exhibits 6 or more of 12 symptoms listed across three major areas social interaction, communication, and behavior.† These symptoms can start as early as childhood. The Prevalence is 2% of the population and is it is more common in boys than girls. Also, there is no known cause for autism but has to haveRead MoreAutism : What Causes Autism? Essay1112 Words   |  5 Pages What is Autism? 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Adlerian Psychology a Dolls House free essay sample

Alfred Adler is a psychologist who developed a theory that can explain the characters’ actions in A Doll’s House. After many years of study, Adler realized the importance of motivation and how it affected people’s actions. This was later developed into a theory, known as the Adlerian Theory, which states that there must be a motivational force behind all behaviors (Fisher). Evidence of the Adlerian Theory is found in A Doll’s House by Henrik Ibsen through the actions of Krogstad, Torvald, and Nora. Family and friends are usually the most significant motivation to one’s actions because the concern for his or her family and friends will cause them to do whatever necessary to please them. The influence of family and friends may also affect one’s view of life and this would affect one to act differently in order to carry out his or her new attitude towards life (Boeree). We will write a custom essay sample on Adlerian Psychology a Dolls House or any similar topic specifically for you Do Not WasteYour Time HIRE WRITER Only 13.90 / page An individual is part of a larger whole, the society, which means that one must to live up to society’s expectations to gain respect and acceptance (The Theory and Application of Adlerian Psychology). This demonstrates how a social setting can influence one’s behaviors. One’s primary goal in life is to gain acceptance and feel significant. The inferiority complex is when one feels a 2 lack of worth (Fisher). To overcome the inferiority complex, one must strive to reach a goal, known as the superiority complex (Fisher). In the process of the superiority complex, one will strive for perfection (Fisher). The determination to be a perfect individual forces one to act certain ways. Due to Krogstad’s desire to perfect his social status, he realizes the first step is to persuade Torvald into giving him his position back at the bank. In order to do so, he must blackmail Nora into convincing Torvald that he is more capable of the job than anyone else. Without a job, he is seen as lazy and worthless by his society, therefore, fighting for a position he believes he deserves would make others perceive him as someone who will fight for what he believes in. This delivers an image of a respectable man to society and this is what he wants. The feeling of worth and significance can cause confidence and security (The Theory and Application of Adlerian Psychology). Also, he wishes to grab every possible opportunity for his children, and without a job, the availability of these opportunities are limited. The pressure from Krogstad’s society to be respected and the love he has for his children caused him to do whatever he can to win back his job. Torvald however, is a very successful man when it comes to his job, but having his whole life revolve around it causes him to drift away from his family. He has become so attached to his new position at the bank and is so caught up with pleasing those around him that he reserves no time to spend 3 with his family. Torvald’s priority is to impress the society with his abilities and he puts his family second. Torvald’s motivation to keep him putting his everything in the bank is the respect he gets from the community. Even though the family is financially stable, he will not let Nora take money without his consent. Torvald treats Nora like a child and does not think of her as an equal to himself (Hardwick). He does this because he wants control over Nora and he craves the feeling of superiority. Because of the power and control Torvald wants over Nora, he refused Nora to borrow money when he was ill. However, Nora borrowed a large sum from Krogstad under her father’s name without Torvald’s knowledge. Nora did not consider the consequences when she forged her father’s signature because she was more concerned with Torvald’s health. Nora borrowed the money regardless of Torvald’s disapproval because she loved Torvald and could not risk him dying (Hardwick). Nora being treated the way she did by Torvald caused her to feel worthless. Torvald calls Nora by pet names which shows Torvald’s impression of her as a child. Nora and Torvald has never had an important conversation in all those years they have been married, meaning Torvald did not think Nora was intelligent or mature enough to understand important matters (Downs). This motivated her to leave Torvald and find her true self. Leaving Torvald was Nora’s way of overcoming the inferiority complex and the process of her finding herself is 4 her step into the superiority complex. In conclusion, one’s actions are caused by his or her societal surroundings or his or her personal desires. In A Doll’s House by Henrik Ibsen, Krogstad blackmailing Nora in order to get his position back in the bank is caused by his need to be accepted in society. Torvald’s control of all money coming in the household is caused by his desire to be superior to Nora. Nora’s decision to leave Torvald is caused by her need to find herself. The Adlerian Theory applies to these characters because they all have a motivational force behind their actions.